Page from The Compendious Book on Calculation by Completion and Balancing by Muhammad ibn Mūsā al-Khwārizmī (c. AD 820)

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. A page from the book (Arabic for The Compendious Book on Calculation by Completion and Balancing), also known under a shorter name spelled as Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala and other transliterations) is a mathematical book written approximately 820 AD by the Persian... al-Khwārizmī redirects here. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ...

Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC), the Moscow Mathematical Papyrus (Egyptian mathematics c. 1850 BC), and the Rhind Mathematical Papyrus (Egyptian mathematics c. 1650 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. Of the approximately half million clay tablets excavated at the beginning of the 19th century, about 400 are of a mathematical nature. ... Babylonian clay tablet YBC 7289 with annotations. ... The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts discovered. ... This article or section is in need of attention from an expert on the subject. ... The Rhind Mathematical Papyrus ( papyrus British Museum 10057 and pBM 10058), is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ...

The Greek and Hellenistic contribution, influenced as it was by Egyptian and Babylonian mathematics, is generally considered the most important for greatly refining the methods (especially the introduction of mathematical rigor in proofs) and expanding the subject matter of mathematics.^[1] Islamic mathematics, in turn, developed and expanded the mathematics known to these ancient civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe. Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... ... In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... The 12th century saw a major search by European scholars for new learning, which led them to the Arabic fringes of Europe, especially to Spain and Sicily. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...

From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an ever increasing pace, and this continues to the present day. The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... This article is about the European Renaissance of the 14th-17th centuries. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ...

Prehistoric societies

The Ishango bone, dating to perhaps 18000 to 20000 B.C.

Long before the earliest written records, there are drawings that indicate some knowledge of elementary mathematics and of time measurement based on the stars. For example, paleontologists have discovered ochre rocks in a South African cave that were about 70,000 years old, adorned with scratched geometric patterns.^[2] Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old,^[3] suggest early attempts to quantify time.^[4] The Ishango bone is a tally stick, made of bone, which contains sequences of prime numbers, and some series of multiples. ... AD redirects here. ... Paleontology, palaeontology or palæontology (from Greek: paleo, ancient; ontos, being; and logos, knowledge) is the study of prehistoric life forms on Earth through the examination of plant and animal fossils. ... This article is about the color. ... For other uses, see Geometry (disambiguation). ... Stonehenge, England, erected by Neolithic peoples ca. ... In archaeology, an artifact or artefact is any object made or modified by a human culture, and often one later recovered by some archaeological endeavor. ... The Paleolithic or Palaeolithic – lit. ... The Upper Paleolithic (or Upper Palaeolithic) is the third and last subdivision of the Paleolithic or Old Stone Age as it is understood in Europe, Africa and Asia. ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ...

There is evidence that women devised counting to keep track of their menstrual cycles; 28 to 30 scratches on bone or stone, followed by a distinctive marker. Moreover, hunters and herders employed the concepts of one, two, and many, as well as the idea of none or zero, when considering herds of animals.^[5][6] Menstrual cycle In the female reproductive system, the menstrual cycle is a recurring cycle of physiologic changes that occurs in reproductive-age females. ...

The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old. One common interpretation is that the bone is the earliest known demonstration^[6] of sequences of prime numbers and of Ancient Egyptian multiplication. Predynastic Egyptians of the 5th millennium BC pictorially represented geometric spatial designs. It has been claimed that megalithic monuments in England and Scotland, dating from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.^[7] The Ishango bone is a tally stick, made of bone, which contains sequences of prime numbers, and some series of multiples. ... For other uses, see Nile (disambiguation). ... The Upper Paleolithic (or Upper Palaeolithic) is the third and last subdivision of the Paleolithic or Old Stone Age as it is understood in Europe, Africa and Asia. ... For other senses of this word, see sequence (disambiguation). ... In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... It has been suggested that this article or section be merged into Egyptian mathematics. ... The Predynastic Period of Egypt (prior to 3100 BC) is traditionally the period between the Early Neolithic and the beginning of the Pharaonic monarchy beginning with King Narmer. ... For other uses, see Geometry (disambiguation). ... This article is about the idea of space. ... Megalithic tomb, Mane Braz, Brittany Bronze age wedge tomb in the Burren area of Ireland For the record label, see Megalith Records. ... For other uses, see England (disambiguation). ... This article is about the country. ... This article is about the shape and mathematical concept of circle. ... Elliptical redirects here. ... The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ...

Ancient Near East (3rd millenium BC–500 BC)

Mesopotamia

Babylonian mathematics refers to any mathematics of the people of Mesopotamia (modern Iraq) from the days of the early Sumerians until the beginning of the Hellenistic period. It is named Babylonian mathematics due to the central role of Babylon as a place of study, which ceased to exist during the Hellenistic period. From this point, Babylonian mathematics merged with Greek and Egyptian mathematics to give rise to Hellenistic mathematics. Later under the Arab Empire, Mesopotamia, especially Baghdad, once again became an important center of study for Islamic mathematics. Babylonian clay tablet YBC 7289 with annotations. ... Babylonia was a state in southern Mesopotamia, in modern Iraq, combining the territories of Sumer and Akkad. ... Mesopotamia was a cradle of civilization geographically located between the Tigris and Euphrates rivers, largely corresponding to modern-day Iraq. ... Sumer ( Sumerian: KI-EN-GIR, Land of the Lords of Brightness[1], or land of the Sumerian tongue[2][3], Akkadian: Šumeru; possibly Biblical Shinar ), located in southern Mesopotamia, is the earliest known civilization in the world. ... For other uses, see Babylon (disambiguation). ... Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... The Arab Empire at its greatest extent The Arab Empire usually refers to the following Caliphates: Rashidun Caliphate (632 - 661) Umayyad Caliphate (661 - 750) - Successor of the Rashidun Caliphate Umayyad Emirate in Islamic Spain (750 - 929) Umayyad Caliphate of Córdoba in Islamic Spain (929 - 1031) Abbasid Caliphate (750-1258... Baghdad (Arabic: ) is the capital of Iraq and of Baghdad Governorate. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ...

In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework. This article or section is in need of attention from an expert on the subject. ... Cuneiform redirects here. ...

The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.^[8] Sumer ( Sumerian: KI-EN-GIR, Land of the Lords of Brightness[1], or land of the Sumerian tongue[2][3], Akkadian: Å umeru; possibly Biblical Shinar ), located in southern Mesopotamia, is the earliest known civilization in the world. ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... Times table redirects here. ... For other uses, see Geometry (disambiguation). ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...

The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs (see Plimpton 322).^[9] The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation to √2 accurate to five decimal places. This article is being considered for deletion in accordance with Wikipedias deletion policy. ... The reciprocal function: y = 1/x. ... A twin prime is a prime number that differs from another prime number by two. ... Of the approximately half million clay tablets excavated at the beginning of the 19th century, about 400 are of a mathematical nature. ... A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. ... In mathematics, a quadratic equation is a polynomial equation of the second degree. ...

Babylonian mathematics were written using a sexagesimal (base-60) numeral system. From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... This article is about different methods of expressing numbers with symbols. ... For other uses, see Decimal (disambiguation). ...

Egypt

Egyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars, and from this point Egyptian mathematics merged with Greek and Babylonian mathematics to give rise to Hellenistic mathematics. Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematics, when Arabic became the written language of Egyptian scholars. This article or section is in need of attention from an expert on the subject. ... Spoken in: Ancient Egypt Language extinction: evolved into Demotic by 600 BC, into Coptic by AD 200, and was extinct (not spoken as a day-to-day language) by the 17th century. ... Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... The Arab Empire at its greatest extent The Arab Empire usually refers to the following Caliphates: Rashidun Caliphate (632 - 661) Umayyad Caliphate (661 - 750) - Successor of the Rashidun Caliphate Umayyad Emirate in Islamic Spain (750 - 929) Umayyad Caliphate of Córdoba in Islamic Spain (929 - 1031) Abbasid Caliphate (750-1258... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... Arabic can mean: From or related to Arabia From or related to the Arabs The Arabic language; see also Arabic grammar The Arabic alphabet, used for expressing the languages of Arabic, Persian, Malay ( Jawi), Kurdish, Panjabi, Pashto, Sindhi and Urdu, among others. ...

The oldest mathematical text discovered so far is the Moscow papyrus, which is an Egyptian Middle Kingdom papyrus dated c. 2000–1800 BC.^{[citations needed]} Like many ancient mathematical texts, it consists of what are today called word problems or story problems, which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square this 4, result 16. You are to double 4, result 8. You are to square 2, result 4. You are to add the 16, the 8, and the 4, result 28. You are to take one third of 6, result 2. You are to take 28 twice, result 56. See, it is 56. You will find it right." The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts and perhaps our best indication of what ancient Egyptian mathematics might have been like near 2000 BC. They are both written on papyrus. ... The Middle Kingdom is: a old name for China a period in the History of Ancient Egypt, the Middle Kingdom of Egypt Categories: Disambiguation ... A frustum is the portion of a solid â€“ normally a cone or pyramid â€“ which lies between two parallel planes cutting the solid. ...

The Rhind papyrus (c. 1650 BC [1]) is another major Egyptian mathematical text, an instruction manual in arithmetic and geometry. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge^[10], including composite and prime numbers; arithmetic, geometric and harmonic means; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6)[2]. It also shows how to solve first order linear equations [3] as well as arithmetic and geometric series [4]. The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts and perhaps our best indication of what ancient Egyptian mathematics might have been like near 2000 BC. They are both written on papyrus. ... A composite number is a positive integer which has a positive divisor other than one or itself. ... In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ... The geometric mean of a collection of positive data is defined as the nth root of the product of all the members of the data set, where n is the number of members. ... In mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. ... In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. ... In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number. ... A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. ... // Definition In mathematics, an arithmetic series is the sum of the components of an arithmetic progression. ... In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. ...

Also, three geometric elements contained in the Rhind papyrus suggest the simplest of underpinnings to analytical geometry: (1) first and foremost, how to obtain an approximation of π accurate to within less than one percent; (2) second, an ancient attempt at squaring the circle; and (3) third, the earliest known use of a kind of cotangent. Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ... Squaring the circle: the areas of this square and this circle are equal. ... Trigonometry In trigonometry, the cotangent is a function (see trigonometric function) defined as: or An interpretation of the cotangent of an angle x is as follows. ...

Finally, the Berlin papyrus (c. 1300 BC [5] [6]) shows that ancient Egyptians could solve a second-order algebraic equation [7]. The Berlin papyrus is an ancient Egyptian papyrus document that was created circa 1800 BCE. This papyrus was found at the Saqqara ancient Egyptian burial ground in the early 19th Century. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...

Ancient Indian mathematics (3rd. millenium BC–200 AD)

Brahmi numerals in the first century CE

The earliest known mathematics in ancient India dates from 3000–2600 BC in the Indus Valley Civilization (Harappan civilization) of North India and Pakistan. This civilization developed a system of uniform weights and measures that used the decimal system, a surprisingly advanced brick technology which utilized ratios, streets laid out in perfect right angles, and a number of geometrical shapes and designs, including cuboids, barrels, cones, cylinders, and drawings of concentric and intersecting circles and triangles. Mathematical instruments included an accurate decimal ruler with small and precise subdivisions, a shell instrument that served as a compass to measure angles on plane surfaces or in horizon in multiples of 40–360 degrees, a shell instrument used to measure 8–12 whole sections of the horizon and sky, and an instrument for measuring the positions of stars for navigational purposes. The Indus script has not yet been deciphered; hence very little is known about the written forms of Harappan mathematics. Archeological evidence has led some to suspect that this civilization used a base 8 numeral system and had a value of π, the ratio of the length of the circumference of the circle to its diameter.^[11] This article is under construction. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... This article is about the history of the Indian Subcontinent prior to the Partition of British India in 1947. ... Excavated ruins of Mohenjo-daro, Pakistan. ... Dark green region marks the approximate extent of northern India while the regions marked as light green lies within the sphere of north Indian influence. ... For other uses, see Decimal (disambiguation). ... For other uses, see Brick (disambiguation). ... This article is about the mathematical concept. ... An angle (from the Lat. ... In geometry, a cuboid (also called a rectangular prism) is a solid figure bounded by six rectangular faces: a rectangular box. ... For other uses, see Barrel (disambiguation). ... This article is about the geometric object, for other uses see Cone. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... This article is about the shape and mathematical concept of circle. ... For other uses, see Triangle (disambiguation). ... This article is about the navigational instrument. ...   An Indus Valley seal with the seated figure termed pashupati. ... This article is under construction. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... This article is about different methods of expressing numbers with symbols. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... The circumference is the distance around a closed curve. ... DIAMETER is a computer networking protocol for AAA (Authentication, Authorization and Accounting). ...

Vedic mathematics began in the early Iron Age, with the Shatapatha Brahmana (c. 9th century BC), which approximates the value of π to 2 decimal places.^[8], and the Sulba Sutras (c. 800–500 BC) were geometry texts that used irrational numbers, prime numbers, the rule of three and cube roots; computed the square root of 2 to five decimal places; gave the method for squaring the circle; solved linear equations and quadratic equations; developed Pythagorean triples algebraically and gave a statement and numerical proof of the Pythagorean theorem. Shatapatha Brahmana (Brahmana of one-hundred paths) is one of the prose texts describing the Vedic ritual. ... Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ... The Sulba Sutras or Sulva Sutras are a text of Vedic mathematics. ... For other uses, see Geometry (disambiguation). ... In mathematics, an irrational number is any real number that is not a rational number — that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n non-zero. ... In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... The Rule of three is the method of finding the fourth term of a mathematical proportion when three terms are given, given that the products of the first and fourth terms are equal to the product of the second and third. ... Plot of y = In mathematics, the cube root of a number, denoted or x1/3, is the number a such that a3 = x. ... In mathematics, a square root (√) of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x. ... Squaring the circle: the areas of this square and this circle are equal. ... A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. ... In mathematics, a quadratic equation is a polynomial equation of the second degree. ... The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ...

Pāṇini (c. 5th century BC) formulated the grammar rules for Sanskrit. His notation was similar to modern mathematical notation, and used metarules, transformations, and recursions with such sophistication that his grammar had the computing power equivalent to a Turing machine. Pingala (roughly 3rd-1st centuries BC) in his treatise of prosody uses a device corresponding to a binary numeral system. His discussion of the combinatorics of meters, corresponds to the binomial theorem. Pingala's work also contains the basic ideas of Fibonacci numbers (called mātrāmeru). The Brāhmī script was developed at least from the Maurya dynasty in the 4th century BC, with recent archeological evidence appearing to push back that date to around 600 BC. The Brahmi numerals date to the 3rd century BC. Indian postage stamp depicting (2004), with the implication that he used (पाणिनि; IPA ) was an ancient Indian grammarian from Gandhara (traditionally 520–460 BC, but estimates range from the 7th to 4th centuries BC). ... Sanskrit grammatical tradition (, one of the six Vedanga disciplines) begins in late Vedic India, and culminates in the AṣṭādhyāyÄ« of Pāṇini (ca. ... Sanskrit ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... Look up transformation in Wiktionary, the free dictionary. ... This article is about the concept of recursion. ... For the formal concept of computation, see computation. ... For the test of artificial intelligence, see Turing test. ... Pingala (पिङ्गल ) is the supposed author of the Chandas shastra (, also Chandas sutra ), a Sanskrit treatise on prosody considered one of the Vedanga. ... Prosody may mean several things: Prosody consists of distinctive variations of stress, tone, and timing in spoken language. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Metre or meter (US) is the measurement of a musical line into measures of stressed and unstressed beats, indicated in Western music notation by a symbol called a time signature. ... In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... A tiling with squares whose sides are successive Fibonacci numbers in length In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. ... BrāhmÄ« refers to the pre-modern members of the Brahmic family of scripts. ... The Mauryan dynasty ruled the Mauryan empire, the first unified empire of India, from 322 BCE to 183 BCE. The rulers of the Mauryan dynasty were: Chandragupta Maurya (322 - 298 BCE) - founder of the Mauryan empire. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ...

Between 400 BC and AD 200, Jaina mathematicians began studying mathematics for the sole purpose of mathematics. They were the first to develop transfinite numbers, set theory, logarithms, fundamental laws of indices, cubic equations, quartic equations, sequences and progressions, permutations and combinations, squaring and extracting square roots, and finite and infinite powers. The Bakhshali Manuscript written between 200 BC and AD 200 included solutions of linear equations with up to five unknowns, the solution of the quadratic equation, arithmetic and geometric progressions, compound series, quadratic indeterminate equations, simultaneous equations, and the use of zero and negative numbers. Accurate computations for irrational numbers could be found, which includes computing square roots of numbers as large as a million to at least 11 decimal places. This article is under construction. ... Transfinite numbers, also known as infinite numbers, are numbers that are not finite. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, if two variables of bn = x are known, the third can be found. ... In mathematics, an index is a superscript or subscript to a symbol. ... Graph of a cubic polynomial: y = x3/4 + 3x2/4 âˆ’ 3x/2 âˆ’ 2 = (1/4)(x + 4)(x + 1)(x âˆ’ 2) In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power. ... In mathematics, a quartic equation is the result of setting a quartic function equal to zero. ... This is a page about mathematics. ... It has been suggested that this article or section be merged into Combination. ... In mathematics, a square root (√) of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... “Exponent” redirects here. ... The Bakhshali Manuscript is a mathematical manuscript written on birch bark which was found near the village of Bakhshali in what is now Pakistan in 1881. ... In mathematics, simultaneous equations are a set of equations where variables are shared. ... Zero redirects here. ... A negative number is a number that is less than zero, such as −3. ...

Greek and Hellenistic mathematics (c. 600 BC–300 AD)

Pythagoras of Samos

Greek mathematics refers to mathematics written in the Greek language between about 600 BC and AD 300.^[12] Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... Greek ( IPA: or simply IPA: — Hellenic) has a documented history of 3,500 years, the longest of any single natural language in the Indo-European language family. ... For the film of the same name, see Alexander the Great (1956 film). ...

Thales of Miletus

Greek mathematics was more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms.^[13]

Greek mathematics is thought to have begun with Thales (c. 624–c.546 BC) and Pythagoras (c. 582–c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by the mathematics of Egypt, Mesopotamia and India. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests. For the Defense and Security Company, see Thales Group. ... Pythagoras of Samos (Greek: ; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician[1] and founder of the religious movement called Pythagoreanism. ... Babylonian clay tablet YBC 7289 with annotations. ...

Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. Pythagoras is credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history.^[14] In his commentary on Euclid, Proclus states that Pythagoras expressed the theorem that bears his name and constructed Pythagorean triples algebraically rather than geometrically. The Academy of Plato had the motto, "Let none unversed in geometry enter here". For other uses, see Geometry (disambiguation). ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ... For other uses, see Euclid (disambiguation). ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ...

The Pythagoreans proved the existence of irrational numbers. Eudoxus (408–c.355 BC) developed the method of exhaustion, a precursor of modern integration. Aristotle (384—c.322 BC) first wrote down the laws of logic. Euclid (c. 300 BC) is the earliest example of the format still used in mathematics today, definition, axiom, theorem, proof. He also studied conics. His book, Elements, was known to all educated people in the West until the middle of the 20th century.^[15] In addition to the familiar theorems of geometry, such as the Pythagorean theorem, Elements includes a proof that the square root of two is irrational and that there are infinitely many prime numbers. The Sieve of Eratosthenes (c. 230 BC) was used to discover prime numbers. The Pythagoreans were a Hellenic organization of astronomers, musicians, mathematicians, and philosophers who believed that all things are, essentially, numeric. ... Eudoxus was the name of two ancient Greeks: Eudoxus of Cnidus (c. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... This article is about the concept of integrals in calculus. ... For other uses, see Aristotle (disambiguation). ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other uses, see Euclid (disambiguation). ... In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ... In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. ...

Archimedes (c.287–212 BC) of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of Pi.^[16] He also studied the spiral bearing his name, formulas for the volumes of surfaces of revolution, and an ingenious system for expressing very large numbers. For other uses, see Archimedes (disambiguation). ... Syracuse (Italian, Siracusa, ancient Syracusa - see also List of traditional Greek place names) is a city on the eastern coast of Sicily and the capital of the province of Syracuse, Italy. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... This article is about the physical quantity. ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... In mathematics, a series is often represented as the sum of a sequence of terms. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... Three 360° turnings of one arm of an Archimedean spiral An Archimedean spiral (also arithmetic spiral), is a spiral named after the 3rd-century-BC Greek mathematician Archimedes; it is the locus of points corresponding to the locations over time of a point moving away from a fixed point with... For other uses, see Volume (disambiguation). ... The parabola y=x2 rotated about the z-axis A surface of revolution is a surface created by rotating a curve lying on some plane (the generatrix) around a straight line (the axis of rotation) that lies on the same plane. ...

Chinese mathematics (c. 2nd millenium BC–1300 AD)

The Nine Chapters on the Mathematical Art.

The earliest extant Chinese mathematics dates from the Shang Dynasty (1600–1046 BC), and consists of numbers scratched on a tortoise shell [9] [10]. These numbers were represented by means of a decimal notation. For example, the number 123 is written (from top to bottom) as the symbol for 1 followed by the symbol for 100, then the symbol for 2 followed by the symbol for 10, then the symbol for 3. This was the most advanced number system in the world at the time, and allowed calculations to be carried out on the suan pan or (Chinese abacus). The date of the invention of the suan pan is not certain, but the earliest written mention dates from AD 190, in Xu Yue's Supplementary Notes on the Art of Figures. Knowledge of Chinese mathematics before 100 BC is somewhat fragmentary, and even after this date the manuscript traditions are obscure. ... Remnants of advanced, stratified societies dating back to the Shang period have been found in the Yellow River Valley. ... Suanpan (the number represented in the picture is 6,302,715,408) An extended version of a suanpan The suanpan (Simplified Chinese: ; Traditional Chinese: ; Pinyin: ) is an abacus of Chinese origin first described in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of...

In China, the Emperor Qin Shi Huang (Shi Huang-ti) commanded in 212 BC that all books in Qin Empire other than officially sanctioned ones should be burned. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics. The monarch known now as Qin Shi Huang (Chinese: ; pinyin: ; Wade-Giles: Chin Shih-huang) (259 BCE – September 10, 210 BCE),[1] personal name Yíng Zhèng, was king of the Chinese State of Qin from 247 BCE to 221 BCE (officially still under the Zhou Dynasty), and...

From the Western Zhou Dynasty (from 1046 BC), the oldest mathematical work to survive the book burning is the I Ching, which uses the 8 binary 3-tuples (trigrams) and 64 binary 6-tuples (hexagrams) for philosophical, mathematical, and mystical purposes. The binary tuples are composed of broken and solid lines, called yin (female) and yang (male), respectively (see King Wen sequence). Alternative meaning: Zhou Dynasty (690 CE - 705 CE) The Zhou Dynasty (周朝; Wade-Giles: Chou Dynasty) (late 10th century BC to late 9th century BC - 256 BC) followed the Shang (Yin) Dynasty and preceded the Qin Dynasty in China. ... Book burning is the practice of ceremoniously destroying by fire one or more copies of a book or other written material. ... Alternative meaning: I Ching (monk) The I Ching (Traditional Chinese: 易經, pinyin y jīng; Cantonese IPA: jɪk6gɪŋ1; Cantonese Jyutping: jik6ging1; alternative romanizations include I Jing, Yi Ching, Yi King) is the oldest of the Chinese classic texts. ... In mathematics, a tuple is a finite sequence (also known as an ordered list) of objects, each of a specified type. ... In mathematics, a tuple is a finite sequence (also known as an ordered list) of objects, each of a specified type. ... The King Wen sequence of the I Ching is a series of sixty four broken and unbroken lines, representing yin and yang respectively. ...

The oldest existent work on geometry in China comes from the philosophical Mohist canon c. 330 BC, compiled by the followers of Mozi (470–390 BC). The Mo Jing described various aspects of many fields associated with physical science, and provided a small wealth of information on mathematics as well. For other uses, see Geometry (disambiguation). ... Mohism (Chinese: ; pinyin: ; literally School of Mo) or Moism is a Chinese philosophy founded by Mozi. ... Mozi (Chinese: ; pinyin: ; Wade-Giles: Mo Tzu, Lat. ...

After the book burning, the Han dynasty (202 BC–220 AD) produced works of mathematics which presumably expand on works that are now lost. The most important of these is The Nine Chapters on the Mathematical Art, the full title of which appeared by AD 179, but existed in part under other titles beforehand. It consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans and dimension ratios for Chinese pagoda towers, engineering, surveying, and includes material on right triangles and π. It also made use of Cavalieri's principle on volume more than a thousand years before Cavalieri would propose it in the West. It created mathematical proof for the Pythagorean theorem, and a mathematical formula for Gaussian elimination. Liu Hui commented on the work by the 3rd century AD. Han Dynasty in 87 BC Capital Changan (206 BC–9 AD) Luoyang (25 AD–220 AD) Language(s) Chinese Religion Buddhism, Taoism, Confucianism, Chinese folk religion Government Monarchy History  - Establishment 206 BC  - Battle of Gaixia; Han rule of China begins 202 BC  - Interruption of Han rule 9 - 24  - Abdication... The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, probably composed in the 1st century AD, but perhaps as early as 200 BC. This book is the earliest surviving mathematical text from China that has come down to us by being copied by scribes and (centuries later... The Chinese Pagoda is a landmark in Birmingham. ... Surveyor at work with a leveling instrument. ... A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. ... Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ... Bonaventura Cavalieri (1598–1647) was an Italian mathematician whose legacy includes early work on logarithms and geometry, including the rule known today as Cavalieris principle. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ... In linear algebra, Gaussian elimination is an algorithm that can be used to determine the solutions of a system of linear equations, to find the rank of a matrix, and to calculate the inverse of an invertible square matrix. ... A possible likeness of Liu Hui on japanpostage stamp This is a Chinese name; the family name is 劉 (Liu) Liu Hui 劉徽 was a Chinese mathematician who lived in the 200s in the Wei Kingdom. ...

In addition, the mathematical works of the Han astronomer and inventor Zhang Heng (AD 78–139) had a formulation for pi as well, which differed from Liu Hui's calculation. Zhang Heng used his formula of pi to find spherical volume. There was also the written work of the mathematician and music theorist Jing Fang (78–37 BC); by using the Pythagorean comma, Jing observed that 53 just fifths approximates 31 octaves. This would later lead to the discovery of 53 equal temperament, and was not calculated precisely elsewhere until the German Nicholas Mercator did so in the 17th century. For other uses, see Zhang Heng (disambiguation). ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... Music theory is a field of study that investigates the nature or mechanics of music. ... Jing Fang (Chinese: ; pinyin: ; Wade-Giles: Ching Fang, 78-37 BC), born Li Fang (李房), courtesy name Junming (君明), was a Chinese music theorist, mathematician and astrologer born in present-day Puyang, Henan during the Han Dynasty. ... In music, when ascending from an initial (low) pitch by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging twelve times, one eventually reaches a pitch approximately seven whole octaves above the starting pitch. ... The perfect fifth or diapente is the interval between the first note (the root or tonic) and the fifth note in a major scale. ... For other uses, see Octave (disambiguation). ... In music, 53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into fifty-three equally large steps. ... Nicholas (Nikolaus) Mercator (c. ...

The Chinese also made use of the complex combinatorial diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (AD 1238–1398). In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. ... Yang Hui (楊輝, c. ...

Zhang Heng (78–139)

Zu Chongzhi (5th century) of the Southern and Northern Dynasties computed the value of π to seven decimal places, which remained the most accurate value of π for almost 1000 years. For other uses, see Zhang Heng (disambiguation). ... Zu Chongzhi (Traditional Chinese: ; Simplified Chinese: ; Hanyu Pinyin: ZÇ” ChōngzhÄ«; Wade-Giles: Tsu Chung-chih, 429–500), courtesy name Wenyuan (文遠), was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties. ... This article is about China. ...

Even after European mathematics began to flourish during the Renaissance, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline, until the Jesuit missionaries such as Matteo Ricci carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries. This article is about the European Renaissance of the 14th-17th centuries. ... The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ... Matteo Ricci. ...

Classical Indian mathematics (c. 400–1600)

Aryabhata

The Surya Siddhanta (c. 400) introduced the trigonometric functions of sine, cosine, and inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky. The cosmological time cycles explained in the text, which was copied from an earlier work, corresponds to an average sidereal year of 365.2563627 days, which is only 1.4 seconds longer than the modern value of 365.25636305 days. This work was translated into to Arabic and Latin during the Middle Ages. This article is under construction. ... The Hindu-Arabic numeral system originaju from the Hindu numeral system, which is a pure place value system, that requires a zero. ... For other uses, see Aryabhata (disambiguation). ... This article aims at providing a thorough (but not verse by verse) exposition of most important topics of and problems related to Surya Siddhanta and its comparison with ancient and modern astronomy, together with its use in astrology. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ...

Aryabhata, in 499, introduced the versine function, produced the first trigonometric tables of sine, developed techniques and algorithms of algebra, infinitesimals, differential equations, and obtained whole number solutions to linear equations by a method equivalent to the modern method, along with accurate astronomical calculations based on a heliocentric system of gravitation. An Arabic translation of his Aryabhatiya was available from the 8th century, followed by a Latin translation in the 13th century. He also computed the value of π to the fourth decimal place as 3.1416. In the 14th century, Madhava of Sangamagrama computed the value of π to the eleventh decimal place as 3.14159265359. For other uses, see Aryabhata (disambiguation). ... The versed sine, also called the versine and, in Latin, the sinus versus (flipped sine) or the sagitta (arrow), is a trigonometric function versin(θ) (sometimes further abbreviated vers) defined by the equation: versin(θ) = 1 − cos(θ) = 2 sin2(θ / 2) There are also three corresponding functions: the coversed... Wikibooks has a book on the topic of Trigonometry The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. ... Flowcharts are often used to graphically represent algorithms. ... This article is about the branch of mathematics. ... Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ... Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations. ... For other uses, see Astronomy (disambiguation). ... Gravity is a force of attraction that acts between bodies that have mass. ... Arabic can mean: From or related to Arabia From or related to the Arabs The Arabic language; see also Arabic grammar The Arabic alphabet, used for expressing the languages of Arabic, Persian, Malay ( Jawi), Kurdish, Panjabi, Pashto, Sindhi and Urdu, among others. ... Madhavan (മാധവന്) of Sangamagramam (1350–1425) was a prominent mathematician-astronomer from Kerala, India. ...

In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu-Arabic numeral system. It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. In the 10th century, Halayudha's commentary on Pingala's work contains a study of the Fibonacci sequence and Pascal's triangle, and describes the formation of a matrix. Brahmagupta ( ) (598–668) was an Indian mathematician and astronomer. ... Brahmaguptas theorem is a result in geometry. ... In mathematics, Brahmaguptas identity says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares. ... In geometry, Brahmaguptas formula formula finds the area of any quadrilateral. ... The main work of Brahmagupta, Brahmasphutasiddhanta (The Opening of the Universe), written in 628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both positive and negative numbers, a method for computing square roots, methods of solving linear and some quadratic... Zero redirects here. ... For the World of Warcraft ex-NPC, see Captain Placeholder. ... In mathematics and computer science, a numerical digit is a symbol, e. ... I like cream cheese, it tastes good on toast. ... For other uses, see Arabic numerals (disambiguation). ... Halayudha (हलायुध) was a 10th century Indian mathematician, wrote a commentary on Pingalas Chandah-shastra where Pingalas knowledge of the meru-prastaara (Pascals triangle) is explicitly mentioned. ... Pingala (पिङ्गल ) is the supposed author of the Chandas shastra (, also Chandas sutra ), a Sanskrit treatise on prosody considered one of the Vedanga. ... In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ... The first five rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ... In mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. ...

In the 12th century, Bhaskara first conceived differential calculus, along with the concepts of the derivative, differential coefficient and differentiation. He also stated Rolle's theorem (a special case of the mean value theorem), studied Pell's equation, and investigated the derivative of the sine function. From the 14th century, Madhava and other Kerala School mathematicians further developed his ideas. They developed the concepts of mathematical analysis and floating point numbers, and concepts fundamental to the overall development of calculus, including the mean value theorem, term by term integration, the relationship of an area under a curve and its antiderivative or integral, the integral test for convergence, iterative methods for solutions to non-linear equations, and a number of infinite series, power series, Taylor series, and trigonometric series. In the 16th century, Jyeshtadeva consolidated many of the Kerala School's developments and theorems in the Yuktibhasa, the world's first differential calculus text, which also introduced concepts of integral calculus. Bhaskara (1114-1185), also known as Bhaskara II and Bhaskara Achārya (Bhaskara the teacher), was an Indian mathematician-astronomer. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ... For other uses, see Derivative (disambiguation). ... A differential can mean one of several things: Differential (mathematics) Differential (mechanics) Differential signaling is used to carry high speed digital signals. ... Differentiation can mean the following: In biology: cellular differentiation; evolutionary differentiation; In mathematics: see: derivative In cosmogony: planetary differentiation Differentiation (geology); Differentiation (logic); Differentiation (marketing). ... In calculus, Rolles theorem states that if a function f is continuous on a closed interval and differentiable on the open interval , and then there is some number c in the open interval such that . Intuitively, this means that if a smooth curve is equal at two points then... In calculus, the mean value theorem states, roughly, that given a section of a smooth curve, there is a point on that section at which the derivative (slope) of the curve is equal (parallel) to the average derivative of the section. ... Pells equation is any Diophantine equation of the form where n is a nonsquare integer. ... The Kerala School was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which included as its prominent members Parameshvara, Nilakantha Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. ... Analysis has its beginnings in the rigorous formulation of calculus. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... For other uses, see Calculus (disambiguation). ... This article is about the concept of integrals in calculus. ... In mathematics, the integral test for convergence is a method used to test infinite series of non-negative terms for convergence. ... It has been suggested that this article or section be merged with Guess value. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... In mathematics, a series is a sum of a sequence of terms. ... In mathematics, a power series (in one variable) is an infinite series of the form where the coefficients an, the center c, and the argument x are usually real or complex numbers. ... Series expansion redirects here. ... Jyestadeva (1500-1610), was an astronomer of the Kerala school founded by Madhava of Sangamagrama and a student of Damodara. ... This article deals with the concept of an integral in calculus. ...

Mathematical progress in India stagnated from the late 16th century onwards due to political turmoil.

Islamic mathematics (c. 800–1500)

Muḥammad ibn Mūsā al-Ḵwārizmī

The Islamic Empire established across the Persia, Middle East, Central Asia, North Africa, Iberia, and in parts of India in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in Arabic, most of them were not written by Arabs, since much like the status of Greek in the Hellenistic world, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time. Persians contributed to the world of Mathematics alongside Arabs. The Hindu-Arabic numeral system originaju from the Hindu numeral system, which is a pure place value system, that requires a zero. ... al-KhwārizmÄ« redirects here. ... Template:Islamic Empire infobox The Ottoman Empire (1299 - 29 October 1923) (Ottoman Turkish: Devlet-i Aliye-yi Osmaniyye; literally, The Sublime Ottoman State, modern Turkish: Osmanlı Ä°mparatorluÄŸu), is also known in the West as the Turkish Empire. ... For other uses of this term see: Persia (disambiguation) The Persian Empire is the name used to refer to a number of historic dynasties that have ruled the country of Persia (Iran). ... A map showing countries commonly considered to be part of the Middle East The Middle East is a region comprising the lands around the southern and eastern parts of the Mediterranean Sea, a territory that extends from the eastern Mediterranean Sea to the Persian Gulf. ... Map of Central Asia showing three sets of possible boundaries for the region Central Asia located as a region of the world Central Asia is a region of Asia from the Caspian Sea in the west to central China in the east, and from southern Russia in the north to...  Northern Africa (UN subregion)  geographic, including above North Africa or Northern Africa is the northernmost region of the African continent, separated by the Sahara from Sub-Saharan Africa. ... The Iberian Peninsula, or Iberia, is located in the extreme southwest of Europe, and includes modern day Spain, Portugal, Andorra and Gibraltar. ... Arabic redirects here. ... For other uses, see Arab (disambiguation). ... The Persians of Iran (officially named Persia by West until 1935 while still referred to as Persia by some) are an Iranian people who speak Persian (locally named Fârsi by native speakers) and often refer to themselves as ethnic Iranians as well. ...

In the 9th century, Muḥammad ibn Mūsā al-Ḵwārizmī wrote several important books on the Hindu-Arabic numerals and on methods for solving equations. His book On the Calculation with Hindu Numerals, written about 825, along with the work of Al-Kindi, were instrumental in spreading Indian mathematics and Indian numerals to the West. The word algorithm is derived from the Latinization of his name, Algoritmi, and the word algebra from the title of one of his works, Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing). Al-Khwarizmi is often called the "father of algebra", for his fundamental contributions to the field.^[17] He gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots,^[18] and he was the first to teach algebra in an elementary form and for its own sake.^[19] He also introduced the fundamental method of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which Al-Khwarizmi originally described as al-jabr.^[20] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."^[21] al-KhwārizmÄ« redirects here. ... For the Christian theologian, see Abd al-Masih ibn Ishaq al-Kindi. ... This article is under construction. ... I like cream cheese, it tastes good on toast. ... Flowcharts are often used to graphically represent algorithms. ... This article is about the branch of mathematics. ... A page from the book (Arabic for The Compendious Book on Calculation by Completion and Balancing), also known under a shorter name spelled as Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala and other transliterations) is a mathematical book written approximately 820 AD by the Persian... Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. ... Reduction Formula We use the technique of integration by parts to evaluate a whole class of integrals by reducing them to simpler forms. ... Look up Problem in Wiktionary, the free dictionary. ... Expository writing is a mode of writing in which the purpose of the author is to inform, explain, describe, or define his or her subject to the reader. ...

Further developments in algebra were made by Al-Karaji in his treatise al-Fakhri, where he extends the methodology to incorporate integer powers and integer roots of unknown quantities. The first known proof by mathematical induction appears in a book written by Al-Karaji around 1000 AD, who used it to prove the binomial theorem, Pascal's triangle, and the sum of integral cubes.^[22] The historian of mathematics, F. Woepcke,^[23] praised Al-Karaji for being "the first who introduced the theory of algebraic calculus." Also in the 10th century, Abul Wafa translated the works of Diophantus into Arabic and developed the tangent function. Ibn al-Haytham was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable for determining the general formula for the sum of any integral powers. He performed an integration in order to find the volume of a paraboloid, and was able to generalize his result for the integrals of polynomials up to the fourth degree. He thus came close to finding a general formula for the integrals of polynomials, but he was not concerned with any polynomials higher than the fourth degree.^[24] Abu Bakr ibn Muhammad ibn al-Husayn Al-Karaji (953 - 1029), also known as Al-karkhi was a Persian mathematician and engineer. ... In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. ... Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. ... In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. ... The first five rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ... This article is about the concept of integrals in calculus. ... y=x³, for integer values of 1≤x≤25. ... For other uses, see Historian (disambiguation). ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... This article is about the branch of mathematics. ... For other uses, see Calculus (disambiguation). ... Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani (940 – 997 or 998) was a mathematician and astronomer in Baghdad. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... In mathematics, the word tangent has two distinct, but etymologically related meanings: one in geometry, and one in trigonometry. ... This article is about the scientist. ... In mathematics and elsewhere, the adjective quartic means fourth order, such as the function . ... Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ... In mathematics, a polynomial is an expression that is constructed from one variable or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents. ... This article is about the concept of integrals in calculus. ...

In the late 11th century, Omar Khayyam wrote Discussions of the Difficulties in Euclid, a book about flaws in Euclid's Elements, especially the parallel postulate, and laid the foundations for analytic geometry and non-Euclidean geometry.^{[citation needed]} He was also the first to find the general geometric solution to cubic equations. He was also very influential in calendar reform.^{[citation needed]} Tomb of Omar Khayam, Neishapur, Iran. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... a and b are parallel, the transversal t produces congruent angles. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. ... Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Graph of a cubic polynomial: y = x3/4 + 3x2/4 âˆ’ 3x/2 âˆ’ 2 = (1/4)(x + 4)(x + 1)(x âˆ’ 2) In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power. ... Calendar reform is any proposed reform of a calendar. ...

In the late 12th century, Sharaf al-Dīn al-Tūsī introduced the concept of a function,^[25] and he was the first to discover the derivative of cubic polynomials.^[26] His Treatise on Equations developed concepts related to differential calculus, such as the derivative function and the maxima and minima of curves, in order to solve cubic equations which may not have positive solutions.^[27] (1135 - 1213) was a Persian mathematician of the Islamic Golden Age (during the Middle Ages). ... This article is about functions in mathematics. ... For other uses, see Derivative (disambiguation). ... Graph of a cubic function; the roots are where the curve crosses the x-axis (y = 0). ... Local and global maxima and minima for cos(3Ï€x)/x, 0. ...

In the 13th century, Nasir al-Din Tusi (Nasireddin) made advances in spherical trigonometry. He also wrote influential work on Euclid's parallel postulate. In the 15th century, Ghiyath al-Kashi computed the value of π to the 16th decimal place. Kashi also had an algorithm for calculating nth roots, which was a special case of the methods given many centuries later by Ruffini and Horner. Nasir Tusi Abu Jafar Muhammad Ibn Muhammad Ibn al-Hasan Nasir al-Din al-Tusi (1201–1274) was a Persian scientist, of Shia Islamic belief, born in Tus, Khorasan, Iran. ... Spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... For other uses, see Euclid (disambiguation). ... a and b are parallel, the transversal t produces congruent angles. ... Kashani, dubbed, the Second Ptolemy, was an outstanding Persian mathematician of the middle ages. ... Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ... Paolo Ruffini (Valentano, 1765 ‑ Modena, 1822) was an Italian mathematician and philosopher. ... Horner is an English surname that derives from the occupation horner who is a person who cuts the horns off of cattle, or deals in horns, or plays a horn. ...

Other notable Muslim mathematicians included al-Samawal, Abu'l-Hasan al-Uqlidisi, Jamshid al-Kashi, Thabit ibn Qurra, Abu Kamil and Abu Sahl al-Kuhi. Ibn Yahya al-Maghribi Al-Samawal was a Moroccan born muslim mathematician and astronomer of the 12th century. ... Abul Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab mathematician, possibly from Damascus He wrote the earliest surviving book on the Hindu place-value system, known in the west as Arabic numerals, around 952. ... Kashani, dubbed, the Second Ptolemy, was an outstanding Persian mathematician of the middle ages. ... Abul Hasan Thabit ibn Qurra ibn Marwan al-Sabi al-Harrani, (826 – February 18, 901) was an Arab astronomer and mathematician. ... Abu Kamil Shuja ibn Aslam ibn Muhammad ibn Shuja (c. ... Abu Sahl Wijan (or Waijan) ibn Rustam al-Kuhi (also al-Quhi), was a Persian mathematician and astronomer. ...

Other achievements of Muslim mathematicians during this period include the development of algebra and algorithms (see Muhammad ibn Mūsā al-Khwārizmī), the development of spherical trigonometry,^[28] the addition of the decimal point notation to the Arabic numerals, the discovery of all the modern trigonometric functions besides the sine, al-Kindi's introduction of cryptanalysis and frequency analysis, the development of analytic geometry by Ibn al-Haytham, the beginning of algebraic geometry by Omar Khayyam, the first refutations of Euclidean geometry and the parallel postulate by Nasīr al-Dīn al-Tūsī, the first attempt at a non-Euclidean geometry by Sadr al-Din, the development of an algebraic notation by al-Qalasādī,^[29] and many other advances in algebra, arithmetic, calculus, cryptography, geometry, number theory and trigonometry. This article is about the branch of mathematics. ... Flowcharts are often used to graphically represent algorithms. ... al-KhwārizmÄ« redirects here. ... Spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... The decimal separator is used to mark the boundary between the integer and the fractional parts of a decimal numeral. ... For other uses, see Arabic numerals (disambiguation). ... Sine redirects here. ... For the Christian theologian, see Abd al-Masih ibn Ishaq al-Kindi. ... Close-up of the rotors in a Fialka cipher machine Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. ... In mathematics, physics and signal processing, frequency analysis is a method to decompose a function, wave, or signal into its frequency components so that it is possible to have the frequency spectrum. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. ... This article is about the scientist. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problematics of geometry. ... Tomb of Omar Khayam, Neishapur, Iran. ... A representation of Euclid from The School of Athens by Raphael. ... a and b are parallel, the transversal t produces congruent angles. ... Tusi couple from Vat. ... Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Mathematical notation is used in mathematics, and throughout the physical sciences, engineering, and economics. ... (1412 in Baza, Spain – 1486 in Béja, Tunisia) was an Arab Muslim mathematician and an Islamic scholar specializing in Islamic inheritance jurisprudence. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Cryptography (or cryptology; derived from Greek κρυπτός kryptós hidden, and the verb γράφω gráfo write or λεγειν legein to speak) is the study of message secrecy. ... For other uses, see Geometry (disambiguation). ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Wikibooks has a book on the topic of Trigonometry The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. ...

During the time of the Ottoman Empire from the 15th century, the development of Islamic mathematics became stagnant. Motto دولت ابد مدت Devlet-i Ebed-müddet (The Eternal State) Anthem Ottoman imperial anthem Borders in 1683, see: list of territories Capital Söğüt (1299–1326) Bursa (1326–1365) Edirne (1365–1453) Ä°stanbul (1453–1922) Government Monarchy Sultans  - 1281–1326 (first) Osman I  - 1918–22 (last) Mehmed VI Grand Viziers  - 1320...

Medieval European mathematics (c. 500–1400)

Medieval European interest in mathematics was driven by concerns quite different from those of modern mathematicians. One driving element was the belief that mathematics provided the key to understanding the created order of nature, frequently justified by Plato's Timaeus and the apocryphal biblical passage (in the Book of Wisdom) that God had ordered all things in measure, and number, and weight^[30]; however, many church authorities were opposed to attempts to understand the universe, the famed church father Augustine of Hippo himself declaring: For other uses, see Plato (disambiguation). ... Timaeus (Honour) (or Timæus) is a name that appears in several ancient (Greek) sources: Timaeus (dialogue), a Socratic dialogue by Plato Timaeus of Locri, the 5th-century Pythagorean philosopher, appearing in Platos s Timaeus. ... The biblical apocrypha includes texts written in the Jewish and Christian religious traditions that either were accepted into the biblical canon by some, but not all, Christian faiths, or are frequently printed in Bibles despite their non-canonical status. ... Wisdom or the Wisdom of Solomon is one of the deuterocanonical books of the Bible. ... The Church Fathers or Fathers of the Church are the early and influential theologians and writers in the Christian church, particularly those of the first five centuries of Christian history. ... Augustinus redirects here. ...

The good Christian should beware of mathematicians, .... The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.^[31].

For other uses, see Christian (disambiguation). ... This is an overview of the Devil. ...

Early Middle Ages (c. 500–1100)

Boethius provided a place for mathematics in the curriculum when he coined the term quadrivium to describe the study of arithmetic, geometry, astronomy, and music. He wrote De institutione arithmetica, a free translation from the Greek of Nicomachus's Introduction to Arithmetic; De institutione musica, also derived from Greek sources; and a series of excerpts from Euclid's Elements. His works were theoretical, rather than practical, and were the basis of mathematical study until the recovery of Greek and Arabic mathematical works.^[32][33] There are several persons called Bo thius: Philosophers: Anicius Manlius Severinus thius - to many scholars this is the Bo thius, a late-Roman writer best known for his works in philosophy and theology. ... The quadrivium comprised the four subjects taught in medieval universities after the trivium. ... Nicomachus (Gr. ... For other uses, see Euclid (disambiguation). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems...

Rebirth of mathematics in Europe (1100–1400)

In the 12th century, European scholars traveled to Spain and Sicily seeking scientific Arabic texts, including al-Khwarizmi's The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester, and the complete text of Euclid's Elements, translated in various versions by Adelard of Bath, Herman of Carinthia, and Gerard of Cremona.^[34][35] The 12th century saw a major search by European scholars for new learning, which led them to the Arabic fringes of Europe, especially to Spain and Sicily. ... Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983. ... A page from the book (Arabic for The Compendious Book on Calculation by Completion and Balancing), also known under a shorter name spelled as Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala and other transliterations) is a mathematical book written approximately 820 AD by the Persian... Robert of Chester (Robertus Castrensis) was an English arabist who flourished around 1150. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Adelard of Bath (Latin: Adelardus Bathensis) (c. ... Gerard of Cremona (Italian: Gerardo da Cremona; Latin: Gerardus Cremonensis; c. ...

These new sources sparked a renewal of mathematics. Fibonacci, writing in the Liber Abaci, in 1202 and updated in 1254, produced the first significant mathematics in Europe since the time of Eratosthenes, a gap of more than a thousand years. The work introduced Hindu-Arabic numerals to Europe, and discussed many other mathematical problems. For the number sequence, see Fibonacci number. ... Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ...

The fourteenth century saw the development of new mathematical concepts to investigate a wide range of problems.^[36] One important contribution was development of mathematics of local motion.

Thomas Bradwardine proposed that speed (V) increases in arithmetic proportion as the ratio of force (F) to resistance (R) increases in geometric proportion. Bradwardine expressed this by a series of specific examples, but although the logarithm had not yet been conceived, we can express his conclusion anachronistically by writing: V = log (F/R).^[37] Bradwardine's analysis is an example of transferring a mathematical technique used by al-Kindi and Arnald of Villanova to quantify the nature of compound medicines to a different physical problem.^[38] Thomas Bradwardine (c. ... For the Christian theologian, see Abd al-Masih ibn Ishaq al-Kindi. ... Arnaldus de Villa Nova or Arnaldus de Villanueva, Arnaldus Villanovanus, Arnaud de Ville-Neuve or Arnau de Vilanova, (ca. ...

One of the 14th-century Oxford Calculators, William Heytesbury, lacking differential calculus and the concept of limits, proposed to measure instantaneous speed "by the path that would be described by [a body] if ... it were moved uniformly at the same degree of speed with which it is moved in that given instant".^[39] The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford, who took a strikingly logico-mathematical approach to philosophical problems. ... William Heytesbury (a. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ... Wikibooks Calculus has a page on the topic of Limits In mathematics, the concept of a limit is used to describe the behavior of a function as its argument either gets close to some point, or as it becomes arbitrarily large; or the behavior of a sequences elements as...

Heytesbury and others mathematically determined the distance covered by a body undergoing uniformly accelerated motion (today solved by integration), stating that "a moving body uniformly acquiring or losing that increment [of speed] will traverse in some given time a [distance] completely equal to that which it would traverse if it were moving continuously through the same time with the mean degree [of speed]".^[40] This article is about the concept of integrals in calculus. ...

Nicole Oresme at the University of Paris and the Italian Giovanni di Casali independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled.^[41] In a later mathematical commentary on Euclid's Elements, Oresme made a more detailed general analysis in which he demonstrated that a body will acquire in each successive increment of time an increment of any quality that increases as the odd numbers. Since Euclid had demonstrated the sum of the odd numbers are the square numbers, the total quality acquired by the body increases as the square of the time.^[42] Portrait of Nicole Oresme: Miniature of Nicole Oresmes Traité de l’espere, Bibliothèque Nationale, Paris, France, fonds français 565, fol. ... The Sorbonne, Paris, in a 17th century engraving The historic University of Paris (French: ) first appeared in the second half of the 12th century, but was in 1970 reorganised as 13 autonomous universities (University of Paris I–XIII). ... Giovanni (or Johannes) di Casali (or Casale) was a friar in the Franciscan Order, a natural philosopher and a theologian. ...

Early modern European mathematics (c. 1400–1600)

In Europe at the dawn of the Renaissance, mathematics was still limited by the cumbersome notation using Roman numerals and expressing relationships using words, rather than symbols: there was no plus sign, no equal sign, and no use of x as an unknown.^{[citation needed]} This article is about the European Renaissance of the 14th-17th centuries. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ...

In 16th century European mathematicians began to make advances without precedent anywhere in the world, so far as is known today. The first of these was the general solution of cubic equations, generally credited to Scipione del Ferro c. 1510, but first published by Johannes Petreius in Nuremberg in Gerolamo Cardano's Ars magna, which also included the solution of the general quartic equation from Cardano's student Lodovico Ferrari . Graph of a cubic polynomial: y = x3/4 + 3x2/4 âˆ’ 3x/2 âˆ’ 2 = (1/4)(x + 4)(x + 1)(x âˆ’ 2) In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power. ... Scipione del Ferro (Bologna 1465–1526) was an Italian mathemtatician who first discovered a means to solve cubic equations. ... Johann(es) Petreius (died 1550) was a German printer in Nuremberg. ... Nürnberg redirects here. ... Gerolamo Cardano. ... In mathematics, a quartic equation is the result of setting a quartic function equal to zero. ... Lodovico Ferrari (February 2, 1522 - October 5, 1565) was an Italian mathematician. ...

From this point on, mathematical developments came swiftly, contributing to and benefiting from contemporary advances in the physical sciences. This progress was greatly aided by advances in printing. The earliest mathematical books printed were Peurbach's Theoricae nova planetarum (1472), followed by a book on commercial arithmetic, the Treviso Arithmetic (1478), and then the first extant book on mathematics, Euclid's Elements, printed and published by Ratdolt in 1482. Physical science is the branch of science including chemistry and physics, usually contrasted with the social sciences and sometimes including and sometimes contrasted with natural or biological science. ... For other uses, see Print. ... Georg Purbach (also Peuerbach, Peurbach, Purbach, Purbachius) (May 30, 1423 – April 8, 1461) was an Austrian astronomer and mathematician. ... The Treviso Arithmetic, or Arte dellAbbaco, is an Italian mathematics textbook written by an anonymous teacher in Treviso, Italy in 1478. ...

Driven by the demands of navigation and the growing need for accurate maps of large areas, trigonometry grew to be a major branch of mathematics. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Regiomontanus's table of sines and cosines was published in 1533.^[43] Wikibooks has a book on the topic of Trigonometry The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. ... For the crater, see Pitiscus (crater). ...

By century's end, thanks to Regiomontanus (1436–76) and Simon Stevin (1548–1620), among others, mathematics was written using Hindu-Arabic numerals and in a form not too different from the notation used today. Johannes Müller von Königsberg (June 6, 1436 – July 6, 1476), known by his Latin pseudonym Regiomontanus, was an important German mathematician, astronomer and astrologer. ... Simon Stevin Simon Stevin (1548/49 – 1620) was a Flemish mathematician and engineer. ...

17th century

The 17th century saw an unprecedented explosion of mathematical and scientific ideas across Europe. Galileo, an Italian, observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe, a Dane, had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. His student, Johannes Kepler, a German, began to work with this data. In part because he wanted to help Kepler in his calculations, John Napier, in Scotland, was the first to investigate natural logarithms. Kepler succeeded in formulating mathematical laws of planetary motion. The analytic geometry developed by René Descartes (1596–1650), a French mathematician and philosopher, allowed those orbits to be plotted on a graph, in Cartesian coordinates. Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... This article is about the astronomer. ... Kepler redirects here. ... For other people with the same name, see John Napier (disambiguation). ... The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is an irrational constant approximately equal to 2. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. ... René Descartes (French IPA:  Latin:Renatus Cartesius) (March 31, 1596 – February 11, 1650), also known as Renatus Cartesius (latinized form), was a highly influential French philosopher, mathematician, scientist, and writer. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

Building on earlier work by many predecessors, Isaac Newton, an Englishman, discovered the laws of physics explaining Kepler's Laws, and brought together the concepts now known as calculus. Independently, Gottfried Wilhelm Leibniz, in Germany, developed calculus and much of the calculus notation still in use today. Science and mathematics had become an international endeavor, which would soon spread over the entire world.^[44] Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Johannes Keplers primary contributions to astronomy/ astrophysics were the three laws of planetary motion. ... For other uses, see Calculus (disambiguation). ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...

In addition to the application of mathematics to the studies of the heavens, applied mathematics began to expand into new areas, with the correspondence of Pierre de Fermat and Blaise Pascal. Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling. Pascal, with his wager, attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite. In some sense, this foreshadowed the development of utility theory in the 18th–19th century. Pierre de Fermat Pierre de Fermat IPA: (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. ... Blaise Pascal (pronounced ), (June 20 [[1624 // ]] – August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Gamble redirects here. ... Pascals Wager (or Pascals Gambit) is the application by the French philosopher Blaise Pascal of decision theory to the belief in God. ... This article is about utility in economics and in game theory. ...

18th century

Leonhard Euler by Emanuel Handmann.

The most influential mathematician of the 1700s was arguably Leonhard Euler. His contributions range from founding the study of graph theory with the Seven Bridges of Königsberg problem to standardizing many modern mathematical terms and notations. For example, he named the square root of minus 1 with the symbol i, and he popularized the use of the Greek letter π to stand for the ratio of a circle's circumference to its diameter. He made numerous contributions to the study of topology, graph theory, calculus, combinatorics, and complex analysis, as evidenced by the multitude of theorems and notations named for him. Euler redirects here. ... Jakob Emanuel Handmann, born 1718 in Basel, died 1781 in Bern. ... Euler redirects here. ... A drawing of a graph. ... Map of Königsberg in Eulers time showing the actual layout of the seven bridges, highlighting the river Pregolya and the bridges. ... In mathematics, the imaginary unit (or sometimes the Latin or the Greek iota, see below) allows the real number system to be extended to the complex number system . ...

Other important European mathematicians of the 18th century included Joseph Louis Lagrange, who did pioneering work in number theory, algebra, differential calculus, and the calculus of variations, and Laplace who, in the age of Napoleon did important work on the foundations of celestial mechanics and on statistics. Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... Pierre-Simon Laplace Pierre-Simon Laplace (March 23, 1749 – March 5, 1827) was a French mathematician and astronomer, the discoverer of the Laplace transform and Laplaces equation. ... For other uses, see Napoleon (disambiguation). ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... This article is about the field of statistics. ...

19th century

Behavior of lines with a common perpendicular in each of the three types of geometry

Throughout the 19th century mathematics became increasingly abstract. In the 19th century lived Carl Friedrich Gauss (1777–1855). Leaving aside his many contributions to science, in pure mathematics he did revolutionary work on functions of complex variables, in geometry, and on the convergence of series. He gave the first satisfactory proofs of the fundamental theorem of algebra and of the quadratic reciprocity law. Johann Carl Friedrich Gauss (pronounced ,  ; in German usually Gauß, Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ... This article is about functions in mathematics. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... For other uses, see Geometry (disambiguation). ... In mathematics, a series is often represented as the sum of a sequence of terms. ... In mathematics, the fundamental theorem of algebra states that every complex polynomial in one variable and of degree  â‰¥  has some complex root. ... In mathematics, in number theory, the law of quadratic reciprocity connects the solvability of two related quadratic equations in modular arithmetic. ...

This century saw the development of the two forms of non-Euclidean geometry, where the parallel postulate of Euclidean geometry no longer holds. The Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the Hungarian mathematician Janos Bolyai, independently defined and studied hyperbolic geometry, where uniqueness of parallels no longer holds. In this geometry the sum of angles in a triangle add up to less than 180°. Elliptic geometry was developed later in the 19th century by the German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian geometry, which unifies and vastly generalizes the three types of geometry, and he defined the concept of a manifold, which generalize the ideas of curves and surfaces. Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... a and b are parallel, the transversal t produces congruent angles. ... A representation of Euclid from The School of Athens by Raphael. ... Nikolay Ivanovich Lobachevsky Nikolai Ivanovich Lobachevsky (Никола́й Ива́нович Лобаче́вский) (December 1, 1792–February 24, 1856 (N.S.); November 20, 1792–February 12, 1856 (O.S.)) was a Russian mathematician. ... János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician. ... Lines through a given point P and asymptotic to line l. ... Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. ... Bernhard Riemann. ... In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... An open surface with X-, Y-, and Z-contours shown. ...

The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton in Ireland developed noncommutative algebra. The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1 and in which, famously, 1 + 1 = 1. Boolean algebra is the starting point of mathematical logic and has important applications in computer science. Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. ... For other persons named William Hamilton, see William Hamilton (disambiguation). ... In mathematics, there is a close relationship between spaces, which are geometric in nature, and the numerical functions on them. ... Not to be confused with George Boolos. ... Boolean logic is a complete system for logical operations. ... Mathematical logic is a major area of mathematics, which grew out of symbolic logic. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

Augustin-Louis Cauchy, Bernhard Riemann, and Karl Weierstrass reformulated the calculus in a more rigorous fashion. Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Bernhard Riemann. ... Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. // Karl Weierstrass was born in Ostenfelde, Westphalia (today Germany). ...

Also, for the first time, the limits of mathematics were explored. Niels Henrik Abel, a Norwegian, and Évariste Galois, a Frenchman, proved that there is no general algebraic method for solving polynomial equations of degree greater than four. Other 19th century mathematicians utilized this in their proofs that straightedge and compass alone are not sufficient to trisect an arbitrary angle, to construct the side of a cube twice the volume of a given cube, nor to construct a square equal in area to a given circle. Mathematicians had vainly attempted to solve all of these problems since the time of the ancient Greeks. Niels Henrik Abel (August 5, 1802–April 6, 1829), Norwegian mathematician, was born in Nedstrand, near Finnøy where his father acted as rector. ... Galois at the age of fifteen from the pencil of a classmate. ... The tone or style of this article or section may not be appropriate for Wikipedia. ...

Abel and Galois's investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory, and the associated fields of abstract algebra. In the 20th century physicists and other scientists have seen group theory as the ideal way to study symmetry. Group theory is that branch of mathematics concerned with the study of groups. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... Sphere symmetry group o. ...

In the later 19th century, Georg Cantor established the first foundations of set theory, which enabled the rigorous treatment of the notion of infinity and has become the common language of nearly all mathematics. Cantor's set theory, and the rise of mathematical logic in the hands of Peano, L. E. J. Brouwer, David Hilbert, Bertrand Russell, and A.N. Whitehead, initiated a long running debate on the foundations of mathematics. Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845[1] – January 6, 1918) was a German mathematician. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Mathematical logic is a major area of mathematics, which grew out of symbolic logic. ... Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher. ... Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, and measure theory and complex analysis. ... | name = David Hilbert | image = Hilbert1912. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Alfred North Whitehead Alfred North Whitehead (February 15, 1861 _ December 30, 1947) was a British philosopher and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. ... Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...

The 19th century saw the founding of a number of national mathematical societies: the London Mathematical Society in 1865, the Société Mathématique de France in 1872, the Circolo Mathematico di Palermo in 1884, the Edinburgh Mathematical Society in 1883, and the American Mathematical Society in 1888. The London Mathematical Society (LMS) is the leading mathematical society in England. ... The Société Mathématique de France (SMF) is the main professional society of French mathematicians. ... The Edinburgh Mathematical Society is the leading mathematical society in Scotland. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...

20th century

A map illustrating the Four Color Theorem

The 20th century saw mathematics become a major profession. Every year, thousands of new Ph.D.s in mathematics are awarded, and jobs are available in both teaching and industry. In earlier centuries, there were few creative mathematicians in the world at any one time. For the most part, mathematicians were either born to wealth, like Napier, or supported by wealthy patrons, like Gauss. A few, like Fourier, derived meager livelihoods from teaching in universities. Niels Henrik Abel, unable to obtain a position, died in poverty of malnutrition and tuberculosis at the age of twenty-six. Example of a four-colored map The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such... For other people with the same name, see John Napier (disambiguation). ... Look up Gauss in Wiktionary, the free dictionary. ... Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Niels Henrik Abel (August 5, 1802–April 6, 1829), Norwegian mathematician, was born in Nedstrand, near Finnøy where his father acted as rector. ...

In a 1900 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems in mathematics. These problems, spanning many areas of mathematics, formed a central focus for much of 20th century mathematics. Today, 10 have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not. The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... | name = David Hilbert | image = Hilbert1912. ... Hilberts problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. ...

Famous historical conjectures were finally proved. In 1976, Wolfgang Haken and Kenneth Appel used a computer to prove the four color theorem. Andrew Wiles, building on the work of others, proved Fermat's Last Theorem in 1995. Paul Cohen and Kurt Gödel proved that the continuum hypothesis is independent of (could neither be proved nor disproved from) the standard axioms of set theory. Wolfgang Haken (born June 21, 1928) is a mathematician who specialized in topology, in particular 3-manifolds. ... Kenneth Appel (born 1932) is a mathematician who, in 1976 with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem. ... Example of a four-colored map The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such... For the French mathematician with work in the area of elliptic curves, see André Weil. ... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ... Paul Joseph Cohen (April 2, 1934 – March 23, 2007[1]) was an American mathematician. ... Kurt Gödel (IPA: ) (April 28, 1906 Brünn, Austria-Hungary (now Brno, Czech Republic) – January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ... In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. ... In mathematical logic, a statement S is independent of a theory T if it is impossible to prove S from T and it is impossible to prove not S from T. Many interesting statements in set theory are independent of ZF. It is possible for the statement S is independent... The Zermelo-Fraenkel axioms of set theory (ZF) are the standard axioms of axiomatic set theory on which, together with the axiom of choice, all of ordinary mathematics is based in modern formulations. ...

Mathematical collaborations of unprecedented size and scope took place. A famous example is the classification of finite simple groups (also called the "enormous theorem"), whose proof between 1955 and 1983 required 500-odd journal articles by about 100 authors, and filling tens of thousands of pages. A group of French mathematicians, including Jean Dieudonné and André Weil, publishing under the pseudonym "Nicolas Bourbaki," attempted to exposit all of known mathematics as a coherent rigorous whole. The resulting several dozen volumes has had a controversial influence on mathematical education.^[45] The classification of the finite simple groups is a vast body of work in mathematics, mostly published between around 1955 and 1983, which is thought to classify all of the finite simple groups. ... Jean-Alexandre-Eugène Dieudonné (July 1, 1906 - November 29, 1992) was a French mathematician, known for research in abstract algebra and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a... André Weil (May 6, 1906 - August 6, 1998) (pronounced [1]) was one of the greatest mathematicians of the 20th century, whether measured by his research work, its influence on future work, exposition or breadth. ... For other uses, see Alias. ... This article is about the group of mathematicians named Nicolas Bourbaki. ...

Entire new areas of mathematics such as mathematical logic, topology, complexity theory, and game theory changed the kinds of questions that could be answered by mathematical methods. Mathematical logic is a major area of mathematics, which grew out of symbolic logic. ... For other uses, see Topology (disambiguation). ... As a branch of the theory of computation in computer science, computational complexity theory investigates the problems related to the amounts of resources required for the execution of algorithms (e. ... For other uses, see Game theory (disambiguation) and Game (disambiguation). ...

At the same time, deep insights were made about the limitations to mathematics. In 1929 and 1930, it was proved the truth or falsity of all statements formulated about the natural numbers plus one of addition and multiplication, was decidable, i.e., could be determined by algorithm. In 1931, Kurt Gödel found that this was not the case for the natural numbers plus both addition and multiplication; this system, known as Peano arithmetic, was in fact incompletable. (Peano arithmetic is adequate for a good deal of number theory, including the notion of prime number.) A consequence of Gödel's two incompleteness theorems is that in any mathematical system that includes Peano arithmetic (including all of analysis and geometry), truth necessarily outruns proof; there are true statements that cannot be proved within the system. Hence mathematics cannot be reduced to mathematical logic, and David Hilbert's dream of making all of mathematics complete and consistent died. In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i. ... The word decidable has formal meaning in computability theory, the theory of formal languages, and mathematical logic. ... Kurt Gödel (IPA: ) (April 28, 1906 Brünn, Austria-Hungary (now Brno, Czech Republic) – January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher. ... In mathematics, the Peano axioms (or Peano postulates) are a set of first-order axioms proposed by Giuseppe Peano which determine the theory of Peano arithmetic (also known as first-order arithmetic). ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. ... Analysis has its beginnings in the rigorous formulation of calculus. ... For other uses, see Geometry (disambiguation). ... In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. ... | name = David Hilbert | image = Hilbert1912. ...

One of the more colorful figures in 20th century mathematics was Srinivasa Aiyangar Ramanujan (1887–1920) who, despite being largely self-educated, conjectured or proved over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also made major investigations in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory. Ramanujan Srinivasa Aiyangar Ramanujan (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. ... It has been suggested that this article or section be merged with Integer partition. ... In mathematics and applications, particularly the analysis of algorithms, asymptotic analysis is a method of classifying limiting behaviour, by concentrating on some trend. ... In mathematics, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. ... The Gamma function along part of the real axis In mathematics, the Gamma function (represented by the capitalized Greek letter Γ) is an extension of the factorial function to real and complex numbers. ... Modular form - Wikipedia /**/ @import /skins-1. ... In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a limit. ... In mathematics, a hypergeometric series is a power series in which the ratios of successive coefficients k is a rational function of k. ... In number theory, the prime number theorem (PNT) describes the approximate, asymptotic distribution of the prime numbers. ...

See also

• List of important publications in mathematics
• History of algebra
• History of calculus
• History of combinatorics
• History of geometry
• History of logic
• History of mathematical notation
• History of statistics
• History of trigonometry
• History of writing numbers

This is a list of important publications in mathematics, organized by field. ... Elementary algebra is the branch of mathematics that deals with solving for the operands of arithmetic equations. ... Table of Geometry, from the 1728 Cyclopaedia. ... Mathematic notation comprises the symbols used in expressing mathematical expressions, equations, and formulas. ... The history of trigonometry and of trigonometric functions may span about 4000 years. ... Pre-history Tallies carved from wood, bone, and stone have been used since prehistoric times. ...

References

St. ... The Bible (From Greek βιβλια—biblia, meaning books, which in turn is derived from βυβλος—byblos meaning papyrus, from the ancient Phoenician city of Byblos which exported papyrus) is the sacred scripture of Christianity. ... St Marys College Bute Medical School St Leonards College[5][6] Affiliations 1994 Group Website http://www. ... For other uses, see LSU. Louisiana State University and Agricultural and Mechanical College, generally known as Louisiana State University or LSU, is a public, coeducational university located in Baton Rouge, Louisiana and the main campus of the Louisiana State University System. ... Springer Science+Business Media or Springer (IPA: ) is a worldwide publishing company based in Germany which focuses on academic journals and books in the fields of science, technology, mathematics, and medicine. ... Founded in 1967, OCLC Online Computer Library Center is a nonprofit, membership, computer library service and research organization dedicated to the public purposes of furthering access to the worlds information and reducing information costs. ... Pearson can mean Pearson PLC the media conglomerate. ... This article is about the capital of France. ... Springer Science+Business Media or Springer (IPA: ) is a worldwide publishing company based in Germany which focuses on academic journals and books in the fields of science, technology, mathematics, and medicine. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...

Further reading

Paul Erdős (Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 – September 20, 1996), was an immensely prolific (and famously eccentric) Hungarian-born mathematician. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... University of St Andrews The University of St Andrews was founded between 1410-1413 and is the oldest university in Scotland and the third oldest in the United Kingdom. ... Stephen Mack Stigler is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago[1]. Stigler received his Ph. ... Pearson can mean Pearson PLC the media conglomerate. ...

External links

• MacTutor History of Mathematics archive (John J. O'Connor and Edmund F. Robertson; University of St Andrews, Scotland). An award-winning website containing detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the history of mathematics.
• History of Mathematics Home Page (David E. Joyce; Clark University). Articles on various topics in the history of mathematics with an extensive bibliography.
• The History of Mathematics (David R. Wilkins; Trinity College, Dublin). Collections of material on the mathematics between the 17th and 19th century.
• History of Mathematics (Simon Fraser University).
• Earliest Known Uses of Some of the Words of Mathematics (Jeff Miller). Contains information on the earliest known uses of terms used in mathematics.
• Earliest Uses of Various Mathematical Symbols (Jeff Miller). Contains information on the history of mathematical notations.
• Mathematical Words: Origins and Sources (John Aldrich, University of Southampton) Discusses the origins of the modern mathematical word stock.
• Biographies of Women Mathematicians (Larry Riddle; Agnes Scott College).
• Mathematicians of the African Diaspora (Scott W. Williams; University at Buffalo).
• Fred Rickey's History of Mathematics Page
• A Bibliography of Collected Works and Correspondence of Mathematicians (Steven W. Rockey; Cornell University Library).
• Mathourism - Places with a mathematical historic interest

Journals

• Convergence, the Mathematical Association of America's online Math History Magazine

Directories

• Links to Web Sites on the History of Mathematics (The British Society for the History of Mathematics)
• History of Mathematics Math Archives (University of Tennessee, Knoxville)
• History/Biography The Math Forum (Drexel University)
• History of Mathematics (Courtright Memorial Library).
• History of Mathematics Web Sites (David Calvis; Baldwin-Wallace College)
• History of mathematics at the Open Directory Project
• Historia de las Matemáticas (Universidad de La La guna)
• História da Matemática (Universidade de Coimbra)
• Using History in Math Class
• Mathematical Resources: History of Mathematics (Bruno Kevius)
• History of Mathematics (Roberta Tucci)

The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ... The Open Directory Project (ODP), also known as dmoz (from , its original domain name), is a multilingual open content directory of World Wide Web links owned by Netscape that is constructed and maintained by a community of volunteer editors. ...