Encyclopedia > List of important publications in mathematics
This is a list of important publications in mathematics, organized by field. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
Some reasons why a particular publication might be regarded as important:
- Topic creator – A publication that created a new topic
- Breakthrough – A publication that changed scientific knowledge significantly
- Introduction – A publication that is a good introduction or survey of a topic
- Influence – A publication which has significantly influenced the world
- Latest and greatest – The current most advanced result in a topic
Early manuscripts
These are publications that are not necessarily relevant to a mathematician nowadays, but are nonetheless important publications in the history of mathematics. The Compendious Book on Calculation by Completion and Balancing The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge -- the deductive study of quantity, structure, space and change. ...
Description: It is one of the oldest mathematical texts, dating to the Second Intermediate Period of ancient Egypt. It was copied by the scribe Ahmes (properly Ahmose) from an older Middle Kingdom papyrus. It laid the foundations of Egyptian mathematics and in turn, later influenced Greek and Hellenistic mathematics. Besides describing how to obtain an approximation of π only missing the mark by under one per cent, it is describes one of the earliest attempts at squaring the circle and in the process provides persuasive evidence against the theory that the Egyptians deliberately built their pyramids to enshrine the value of π in the proportions. Even though it would be a strong overstatement to suggest that the papyrus represents even rudimentary attempts at analytical geometry, Ahmes did make use of a kind of an analogue of the cotangent. 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. ...
Ahmes (more accurately Ahmose) was an Egyptian scribe who lived during the Second Intermediate Period. ...
Illustration of a 15th century scribe This is about scribe, the profession. ...
The Second Intermediate Period marks a period when Ancient Egypt once again fell into disarray between the end of the Middle Kingdom, and the start of the New Kingdom. ...
Khafres Pyramid (4th dynasty) and Great Sphinx of Giza (c. ...
Ahmes (more accurately Ahmose) was an Egyptian scribe who lived during the Second Intermediate Period. ...
This name may refer to (amongst others): Ahmose I, a pharaoh of ancient Egypt and founder of the Eighteenth dynasty. ...
The Middle Kingdom is: a old name for China a period in the History of Ancient Egypt, the Middle Kingdom of Egypt This is a disambiguation page — a navigational aid which lists pages that might otherwise share the same title. ...
Papyrus plant Cyperus papyrus at Kew Gardens, London Papyrus is an early form of paper made from the pith of the papyrus plant, Cyperus papyrus, a wetland sedge that grows to 5 meters (15 ft) in height and was once abundant in the Nile Delta of Egypt. ...
This article or section is in need of attention from an expert on the subject. ...
Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BCE to the 5th century CE around the Eastern shores of the Mediterranean. ...
This square and circle have the same area. ...
This article or section does not cite its references or sources. ...
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. ...
Importance: Topic creator, Breakthrough, Influence
Description: Although the only mathematical tools at its author's disposal were what we might now consider secondary-school geometry, he used those methods with rare brilliance, explicitly using infinitesimals to solve problems that would now be treated by integral calculus. Among those problems were that of the center of gravity of a solid hemisphere, that of the center of gravity of a frustum of a circular paraboloid, and that of the area of a region bounded by a parabola and one of its secant lines. Contrary to historically ignorant statements found in some 20th-century calculus textbooks, he did not use anything like Riemann sums, either in the work embodied in this palimpsest or in any of his other works. For explicit details of the method used, see how Archimedes used infinitesimals. The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse. ...
Archimedes of Syracuse. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...
This article or section may contain original research or unverified claims. ...
Wikisource has an original article from the 1911 Encyclopædia Britannica about: Parabola A parabola The parabola (from the Greek: παÏαβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ...
In mathematics, a Riemann sum is a method for approximating the values of integrals. ...
The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ...
Online version: Online version The Sand Reckoner is probably the most accessible work of Archimedes, in some sense, it is the first research-expository paper. ...
Archimedes of Syracuse. ...
Description: The first known (European) system of number-naming that can be expanded beyond the needs of everyday life. A numeral is a symbol or group of symbols that represents a number. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
Description: Written around the 8th century BC, this is one of the oldest geometrical texts. It laid the foundations of Indian mathematics and was influential in South Asia and its surrounding regions, and perhaps even Greece. Among the important geometrical discoveries included in this text are: the earliest list of Pythagorean triples discovered algebraically, the earliest statement of the Pythagorean theorem, the earliest geometrical proof of the Pythagorean theorem, geometric solutions of linear equations, several approximations of π, the first use of irrational numbers, and an accurate computation of the square root of 2, correct to a remarkable five decimal places. Though this was primarily a goemetrical text, it also contained some important algebraic developments, including the earliest use of quadratic equations of the forms ax2 = c and ax2 + bx = c, and integral solutions of simultaneous Diophantine equations with upto four unknowns. Baudhayana, (circa 800 BC), was a Vedic Indian mathematician/scribe. ...
The Sulba Sutras or Sulva Sutras are a text of Vedic mathematics. ...
Baudhayana, (circa 800 BC), was a Vedic Indian mathematician/scribe. ...
(2nd millennium BC - 1st millennium BC - 1st millennium) Events and trends Ruins of the training grounds at Olympia, Greece. ...
The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BC) and Vedic civilization (1500-500 BC) to modern India (21st century AD). ...
Map of South Asia (see note on Kashmir) South Asia, also known as Southern Asia, is a southern geopolitical region of the Asian continent comprising territories on and in proximity to the Indian subcontinent. ...
The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BC) and Vedic civilization (1500-500 BC) to modern India (21st century AD). ...
Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
In mathematics, a Diophantine equation is a polynomial equation that only allows the variables to be integers. ...
Importance: Topic creator, Breakthrough, Influence
Publication data: c. 300 BC 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 Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems...
Euclid (also referred to as Euclid of Alexandria) (Greek: ) (c. ...
Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 350s BC 340s BC 330s BC 320s BC 310s BC - 300s BC - 290s BC 280s BC 270s BC 260s BC 250s BC Years: 305 BC 304 BC 303 BC 302 BC 301 BC - 300 BC - 299 BC 298 BC...
Online version: Interactive Java version
Description: This is often regarded as not only the most important work in geometry but one of the most important works in mathematics. It contains many important results in geometry, number theory and the first algorithm as well. The Elements is still a valuable resource and a good introduction to algorithm. More than any specific result in the publication, it seems that the major achievement of this publication is the popularization of logic and mathematical proof as a method of solving problems. Table of Geometry, from the 1728 Cyclopaedia. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Importance: Topic creator, Breakthrough, Influence, Introduction, Latest and greatest (though it is one of the first, some of the results are still the latest)
Description: This was a Chinese mathematics book, mostly geometric, composed during the Han Dynasty, perhaps as early as 200 BC. It remained the most important textbook in China and East Asia for over a thousand years, similar to the position of Euclid's Elements in Europe. Among its contents: Linear problems solved using the principle known later in the West as the rule of false position. Problems with several unknowns, solved by a principle similar to Gaussian elimination. Problems involving the principle known in the West as the Pythagorean theorem. The earliest solution of a matrix using a method equivalent to the modern method. The Nine Chapters on the Mathematical Art (ä¹ç« ç®—è¡“) 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...
Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
The Han Dynasty (Traditional Chinese: ; Simplified Chinese: ; Hanyu Pinyin: ; Wade-Giles: Han Chau; 206 BC–AD 220) followed the Qin Dynasty and preceded the Three Kingdoms in China. ...
Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 250s BC 240s BC 230s BC 220s BC 210s BC - 200s BC - 190s BC 180s BC 170s BC 160s BC 150s BC Years: 205 BC 204 BC 203 BC 202 BC 201 BC - 200 BC - 199 BC 198 BC...
East Asia is a subregion of Asia that can be defined in either geographical or cultural terms. ...
In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method. ...
In mathematics, Gaussian elimination or Gauss–Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (for many, Gaussian elimination is regarded as the front half of the complete Gauss–Jordan elimination), is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining...
In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ...
In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...
Importance: Topic creator, Breakthrough, Influence
Description: La Géométrie was published in 1637 and written by René Descartes. The book was influential in developing the Cartesian coordinate system and specifically discussed the representation of points of a plane, via real numbers; and the representation of curves, via equations. La Géométrie was published in 1637 and written by René Descartes. ...
René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. ...
This article is concerned with the production of books, magazines, and other literary material (whether in printed or electronic formats). ...
Events February 3 - Tulipmania collapses in Netherlands by government order February 15 - Ferdinand III becomes Holy Roman Emperor December 17 - Shimabara Rebellion erupts in Japan Pierre de Fermat makes a marginal claim to have proof of what would become known as Fermats last theorem. ...
A Specimen of typeset fonts and languages, by William Caslon, letter founder; from the 1728 Cyclopaedia. ...
René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. ...
Fig. ...
A spatial point is an entity with a location in space but no extent (volume, area or length). ...
Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ...
In mathematics, the set of real numbers, denoted R, or in blackboard bold , is the set of all rational and irrational numbers. ...
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
An equation is a mathematical statement, in symbols, that two things are the same. ...
Importance: Topic creator, Breakthrough, Influence
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Description: Published in 1879, the title Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modelled on that of arithmetic, of pure thought". Frege's motivation for developing his formal logical system was similar to Leibniz's desire for a calculus ratiocinator. Frege defines a logical calculus to support his research in the foundations of mathematics. Begriffsschrift is both the name of the book and the calculus defined therein. Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. ...
Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. ...
1879 (MDCCCLXXIX) was a common year starting on Wednesday (see link for calendar). ...
In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
Arithmetic or arithmetics (from the Greek word αÏιθμός = number) is the oldest and simplest branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ...
Thought or thinking is a mental process which allows beings to model the world, and so to deal with it effectively according to their goals, plans, ends and desires. ...
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. ...
The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ...
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. ...
Importance: Arguably the most significant publication in logic since Aristotle. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was an ancient Greek philosopher, a student of Plato and teacher of Alexander the Great. ...
Description: First published in 1895, the Formulario mathematico was the first mathematical book written entirely in a formalized language. It contained a description of mathematical logic and many important theorems in other branches of mathematics. Many of the notations introduced in the book are now in common use. Formulario Mathematico (interlingua: Formulation of mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. ...
Giuseppe Peano Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ...
1895 (MDCCCXCV) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day-slower Julian calendar). ...
In mathematics, logic, and computer science, a formal language is a set of finite-length words (i. ...
Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
Importance:Influence
Description: The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Bertrand Russell and Alfred North Whitehead and published in 1910-1913. It is an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. The questions remained whether a contradiction could be derived from the Principia's axioms, and whether there exists a mathematical statement which could neither be proven nor disproven in the system. These questions were settled, in a rather surprising way, by Gödel's incompleteness theorem in 1931. The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ...
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ...
Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England– December 30, 1947 Cambridge, Massachusetts, USA) was an English mathematician who became an American philosopher. ...
Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ...
Alfred North Whitehead, OM (February 15, 1861 Ramsgate, Kent, England– December 30, 1947 Cambridge, Massachusetts, USA) was an English mathematician who became an American philosopher. ...
1910 (MCMX) was a common year starting on Saturday (see link for calendar) of the Gregorian calendar or a common year starting on Sunday of the 13-day slower Julian calendar. ...
1913 (MCMXIII) was a common year starting on Wednesday. ...
Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ...
Importance: Influence
(Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38 (1931).) In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
Kurt Gödel Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
Online version: Online version
Description: In mathematical logic, Gödel's incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1930. The first incompleteness theorem states: Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
Kurt Gödel Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
1930 (MCMXXX) was a common year starting on Wednesday (link is to a full 1930 calendar). ...
For any formal system such that (1) it is ω-consistent (omega-consistent), (2) it has a recursively definable set of axioms and rules of derivation, and (3) every recursive relation of natural numbers is definable in it, there exists a formula of the system such that, according to the intended interpretation of the system, it expresses a truth about natural numbers and yet it is not a theorem of the system. In mathematical logic, an omega-consistent (or ω-consistent) theory is a theory (collection of sentences) that is not only consistent (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. ...
In computability theory a countable set is called recursive, computable or decidable if we can construct an algorithm which terminates after a finite amount of time and decides whether a given element belongs to the set or not. ...
For the algebra software named Axiom, see Axiom computer algebra system. ...
In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...
See: Recursion Recursively enumerable language Recursively enumerable set Recursive filter Recursive function Recursive set Primitive recursive function This is a disambiguation page — a list of pages that otherwise might share the same title. ...
In mathematics, a mathematical object X of some type T is definable, if there exists some predicate P(x) which is expressible using a finite string of mathematical symbols drawn from a finite language, such that P(X) is true and P(Y) is false for all Y of type...
A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ...
Importance: Breakthrough, Influence
See the list of publications in information theory. To meet Wikipedias quality standards, this article or section may require cleanup. ...
This is a list of important publications in computer science, organized by field. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Description: The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and adds important new results of his own. The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ...
(30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
(30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
The Union Jack, flag of the newly formed United Kingdom of Great Britain and Ireland. ...
Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parliament of Toulouse and a mathematician who is given credit for the development of modern calculus. ...
Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ...
Joseph-Louis Lagrange Joseph-Louis Lagrange, comte de lEmpire (January 25, 1736 – April 10, 1813; b. ...
Adrien-Marie Legendre (September 18, 1752–January 10, 1833) was a French mathematician. ...
Importance: Breakthrough, Influence
Description: On the Number of Primes Less Than a Given Magnitude (or Über die Anzahl der Primzahlen unter einer gegebenen Grösse) is a seminal 8-page paper by Bernhard Riemann published in the November 1859 edition of the Monthly Reports of the Berlin Academy. Although it is the only paper he ever published on number theory, it contains ideas which influenced dozens of researchers during the late 19th century and up to the present day. The paper consists primarily of definitions, heuristic arguments, sketches of proofs, and the application of powerful analytic methods; all of these have become essential concepts and tools of modern analytic number theory. On the Number of Primes Less Than a Given Magnitude (or Über die Anzahl der Primzahlen unter einer gegebenen Grösse) is a seminal 8-page paper by Bernhard Riemann published in the November 1859 edition of the Monthly Reports of the Berlin Academy. ...
Bernhard Riemann. ...
Bernhard Riemann. ...
1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ...
Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...
Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ...
Importance: Breakthrough, Influence
Description: Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. The Vorlesungen can be seen as a watershed between the classical number theory of Fermat, Jacobi and Gauss, and the modern number theory of Dedekind, Riemann and Hilbert. Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understanding of group theory Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. ...
Peter Gustav Lejeune Dirichlet. ...
Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ...
Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Peter Gustav Lejeune Dirichlet. ...
Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ...
Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parliament of Toulouse and a mathematician who is given credit for the development of modern calculus. ...
Karl Gustav Jacob Jacobi Carl Gustav Jacob Jacobi (December 10, 1804 - February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ...
(30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
Bernhard Riemann. ...
David Hilbert David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ...
Group theory is that branch of mathematics concerned with the study of groups. ...
Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ...
Importance: Breakthrough, Influence
Number Theory, An approach through history from Hammurapi to Legendre Description:An historical study of number theory, written by one of the 20th century's greatest researchers in the field. The book covers some thirty six centuries of arithmetical work but the bulk of it is devoted to a detailed study and exposition of the work of Fermat, Euler, Lagrange, and Legendre. The author wishes to take the reader into the workshop of his subjects to share their successes and failures. A rare opportunity to see the historical development of a subject through the mind of one of its greatest practitioners. André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ...
Importance:
An Introduction to the Theory of Numbers Description:This book was first published in 1938, and is still in print, with the lastest edition being the 5th (1980). It is likely that almost every serious student and researcher into number theory has consulted this book, and probably has it on their bookshelf. It was not intended to be a textbook, and is rather an introduction to a wide range of differing areas of number theory which would now almost certainly be covered in separate volumes. The writing style has long been regarded as exemplary, and the approach gives insight into a variety of areas without requiring much more than a good grounding in algebra, calculus and complex numbers. G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
Sir Edward Maitland Wright (February 13, 1906 - February 2, 2005) was an English mathematician, and collaborator with G.H. Hardy. ...
Importance:
Calculus is a central branch of mathematics. ...
Description: Written in India in 1501, this was the world's first calculus text. "This work laid the foundation for a complete system of fluxions" (Charles Whish, 1835) and served as a summary of the Kerala School's achievements in calculus, trigonometry and mathematical analysis, most of which were earlier discovered by the 14th century mathematician Madhava. It's possible that this text influenced the later development of calculus in Europe. Some of its important developments in calculus include: the fundamental ideas of differentiation and integration, the derivative, differential equations, term by term integration, numerical integration by means of infinite series, the relationship between the area of a curve and its integral, and the mean value theorem. Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series of sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence. Yuktibhasa (Malayalam:à´¯àµà´•àµà´¤à´¿à´à´¾à´· ; meaning — rationale language ) also known as Ganita Yuktibhasa (compendium of astronomical rationale) is a major treatise on Mathematics and Astronomy, written by Indian astronomer Jyesthadeva of the Kerala School of Mathematics in AD 1530. ...
Jyestadeva (1500-1610), was an astronomer of the Kerala school founded by Madhava of Sangamagrama and a student of Damodara. ...
1501 was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar. ...
| Come and take it, slogan of the Texas Revolution 1835 was a common year starting on Thursday (see link for calendar). ...
The Kerala School was a school of mathematics and astronomy founded by Madhava in Kerala (in South India) which included as its prominent members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. ...
Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ...
Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...
This 14th-century statue from south India depicts the gods Shiva (on the left) and Uma (on the right). ...
Madhava (माधव) of Sangamagrama (1350-1425) was a major mathematician from Kerala, in South India. ...
The Kerala School was a school of mathematics and astronomy founded by Madhava in Kerala (in South India) which included as its prominent members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. ...
In mathematics, a derivative is defined as the instantaneous rate of change of a function and the process of finding the derivative is called differentiation. ...
In calculus, the integral of a function is a generalization of area, mass, volume and total. ...
In mathematics, a derivative is defined as the instantaneous rate of change of a function and the process of finding the derivative is called differentiation. ...
Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...
For any function that is continuous on [a, b] and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining the endpoints of the interval [a, b] is parallel to the tangent at c. ...
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. ...
As the degree of the Taylor series rises, it approaches the correct function. ...
In mathematics, a Fourier series of a periodic function, named in honor of Joseph Fourier (1768-1830), represents the function as a sum of periodic functions of the form where e is Eulers number and i the imaginary unit. ...
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 word tangent has two distinct, but etymologically-related meanings: one in geometry, and one in trigonometry. ...
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. ...
Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
Note: A theta probe is a device for measuring soil moisture. ...
The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence. ...
Importance: Topic creator, Breakthrough, Influence
Description: The Philosophiae Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on July 5, 1687. Perhaps the most influential scientific book ever published, it contains the statement of Newton's laws of motion forming the foundation of classical mechanics as well as his law of universal gravitation. He derives Kepler's laws for the motion of the planets (which were first obtained empirically). In formulating his physical theories, Newton had developed a field of mathematics known as calculus. Newtons own copy of his Principia, with hand written corrections for the second edition. ...
Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ...
Latin is an ancient Indo-European language originally spoken in Latium, the region immediately surrounding Rome. ...
Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ...
July 5 is the 186th day of the year (187th in leap years) in the Gregorian Calendar, with 179 days remaining. ...
Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ...
Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...
Classical mechanics is a branch of physics which studies the deterministic motion of objects. ...
Gravity is a force of attraction that acts between bodies that have mass. ...
Johannes Keplers primary contributions to astronomy/astrophysics were the three laws of planetary motion. ...
The eight planets and three dwarf planets of the Solar System. ...
Calculus is a central branch of mathematics. ...
Up to the publication of this book, mathematics was only used to describe nature. This is the first instance when mathematics is used to explain nature. Here was born the practice, now so standard we identify it with science, of explaining nature by postulating mathematical axioms and demonstrating that their conclusion are observable phenomena. In other words, the greatness of the Principia is not only in developing a number of fundamental theories in physics and mathematics but first and foremost (amply demonstrated in the title!) in the very linking of science and mathematics. The influence of this book is so deep that nowadays we find this link obvious and cannot imagine doing science in any other way.
Importance: Topic creator, Breakthrough, Influence
Newton's Principia for the Common Reader Description: An exposition, using modern notation and language, of a large part of Newton's above-cited masterwork. Mathematical and physical language and notation have evolved considerably since Newton's time, making it difficult for a modern reader to read Newton's original work even in translation from the original Latin. Chandrasekhar's labor of love makes it possible for a modern reader, familiar with the modern treatment of algebra, geometry and calculus to appreciate Newton's genius through following his work as he originally conceived it. Subrahmanyan Chandrasekhar (October 19, 1910 – August 21, 1995) was an Indian-American physicist, astrophysicist and mathematician. ...
Importance: Interpretation for the modern reader of a great classic of mathematics and science
Description: Introductions to differential and integral calculus in a single and many variables respectively. Calculus is a central branch of mathematics. ...
Michael Spivaks Calculus on Manifolds is a text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. ...
Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. ...
Importance: Introduction
Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ...
Description: Method of Fluxions was a book written by Isaac Newton. The book was completed in 1671, and published in 1736. Method of Fluxions was a book by Isaac Newton. ...
Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ...
Sir Isaac Newton, FRS (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ...
Events May 9 - Thomas Blood, disguised as a clergyman, attempts to steal the Crown Jewels from the Tower of London. ...
Events January 26 - Stanislaus I of Poland abdicates his throne. ...
Within this book, Newton describes a method (the Newton-Raphson method) for finding the real zeroes of a function. In numerical analysis, Newtons method (or the Newton-Raphson method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function. ...
Partial plot of a function f. ...
Importance: Topic creator, Breakthrough, Influence
Game theory is a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...
John Maynard Smith Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ...
John Maynard Smith Professor John Maynard Smith, F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ...
(Theory of Games and Economic Behavior, 3rd ed., Princeton University Press 1953) In 1944 Princeton University Press published Theory of Games and Economic Behavior, a book by the mathematician John von Neumann and economist Oskar Morgenstern. ...
Description: This book led to the investigation of modern game theory as a prominent branch of mathematics. This profound work contained the method -- alluded to above -- for finding optimal solutions for two-person zero-sum games. Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ...
John von Neumann in the 1940s. ...
Importance: Influence, Topic creator, Breakthrough
Description: The book is in two, {0,1|}, parts. The zeroth part is about numbers, the first part about games - both the values of games and also some real games that can be played such as Nim, Hackenbush, Col and Snort amongst the many described. On Numbers and Games is a mathematics book by John Horton Conway. ...
John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ...
Nim is a two-player mathematical game of strategy in which players take turns removing objects from distinct heaps. ...
Hackenbush is a two-player partisan mathematical game that consists of several colored line segments connected to the ground. ...
Several map-coloring games are studied in Combinatorial game theory. ...
Importance:
Description: A compendium of information on mathematical games. It was first published in 1982 in two volumes, one focusing on Combinatorial game theory and surreal numbers, and the other concentrating on a number of specific games. Winning Ways for your Mathematical Plays (ISBN 1568811306) by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games. ...
Elwyn Ralph Berlekamp is professor of mathematics at University of California, Berkeley. ...
John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ...
Richard Kenneth Guy (born 1916) is a Professor Emeritus in the Department of Mathematics at the University of Calgary. ...
Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics. ...
1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ...
Combinatorial game theory (CGT) is a mathematical theory that only studies two-player games which have a position which the players take turns changing in defined ways or moves to achieve a defined winning condition. ...
In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similiar to superreal numbers and hyperreal numbers. ...
Importance:
It has been suggested that Fractal animation be merged into this article or section. ...
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension Description: A discussion of self-similar curves that have fractional dimensions between 1 and 2. These curves are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. Shows Mandelbrot's early thinking on fractals, and is an example of the linking of mathematical objects with natural forms that was a theme of much of his later work. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension is a paper by mathematician Benoît Mandelbrot, first published in Science in 1967. ...
Benoît Mandelbrot in 2006 Benoît B. Mandelbrot (born November 20, 1924) is a French mathematician, best known as the father of fractal geometry. Benoît Mandelbrot was born in Poland, but his family moved to France when he was a child; he is a French citizen and was...
Importance:
Textbooks
Online version: Online version A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. ...
G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
Description: A classic textbook in introductory mathematical analysis, written by G. H. Hardy. It was first published in 1908, and went through many editions. It was intended to help reform mathematics teaching in the UK, and more specifically in the University of Cambridge, and in schools preparing pupils to study mathematics at Cambridge. As such, it was aimed directly at "scholarship level" students — the top 10% to 20% by ability. The book contains a large number of difficult problems. The content covers introductory calculus and the theory of infinite series. Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ...
G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ...
The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ...
Calculus is a central branch of mathematics. ...
In mathematics, a series is a sum of a sequence of terms. ...
Importance:
- Richard Rusczyk and Sandor Lehoczky
Description: The Art of Problem Solving began as a set of two books coauthored by Richard Rusczyk and Sandor Lehoczky. The books, which are about 750 pages together, are for students who are interested in math and/or compete in math competitions. The Art of Problem Solving began as a set of two books coauthored by Richard Rusczyk and Sandor Lehoczky. ...
Importance:
Metalogic: an Introduction to the Metatheory of Standard First Order Logic Description: An excellent introduction to the mathematical theory of logical formal systems, covering completeness-proofs, consistency-proofs, and so on and even set-theory. In logic, mathematics, and computer science, a formal system is a formal grammar used for modelling purposes. ...
In mathematics and related technical fields, a mathematical object is complete if nothing needs to be added to it. ...
Consistency has several technical meanings: In NASCAR Racing, consistency is a term coined by NASCAR drivers about the frequency of finishing well in the top ten or top five each race as it helps to get enough points to make the Chase For The Cup and win the Nextel Cup...
Importance:
Popular writing
Description: Gödel, Escher, Bach: an Eternal Golden Braid is a Pulitzer Prize-winning book, first published in 1979 by Basic Books. It is a book about how the creative achievements of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach interweave. As the author states: "I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book." GEB cover Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, published in 1979 by Basic Books. ...
Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ...
Importance:
The World of Mathematics Description: The World of Mathematics was specially designed to make mathematics more accessible to the inexperienced. It comprises nontechnical essays on every aspect of the vast subject, including articles by and about scores of eminent mathematicians, as well as literary figures, economists, biologists, and many other eminent thinkers. Includes the work of Archimedes, Galileo, Descartes, Newton, Gregor Mendel, Edmund Halley, Jonathan Swift, John Maynard Keynes, Henri Poincaré, Lewis Carroll, George Boole, Bertrand Russell, Alfred North Whitehead, John von Neumann, and many others. In addition, an informative commentary by distinguished scholar James R. Newman precedes each essay or group of essays, explaining their relevance and context in the history and development of mathematics. Originally published in 1956, it does not include many of the exciting discoveries of the later years of the 20th century but it has no equal as a general historical survey of important topics and applications. James Roy Newman was a mathematician and mathematical historian. ...
Importance:Introduction
Arithmetic or arithmetics (from the Greek word αÏιθμός = number) is the oldest and simplest branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ...
Arithmetick: or, The Grounde of Arts Description: Written in 1542, it was the first really popular arithmetic book written in the English Language. Robert Recorde (c. ...
Importance:
Description: An early and popular English arithmetic textbook published in America in the eighteenth century. The book reached from the introductory topics to the advanced in five sections. The Schoolmasters Assistant, Being a Compendium of Arithmetic both Practical and Theoretical was an early and popular English arithmetic textbook, written by Thomas Dilworth and published in America in the eighteenth century. ...
The Reverend Mr. ...
Motto: (traditional) In God We Trust (official, 1956–present) Anthem: The Star-Spangled Banner Capital Washington, D.C. Largest city New York City Official language(s) None at the federal level; English de facto Government Federal Republic - President George W. Bush (R) - Vice President Dick Cheney (R) Independence - Declared - Recognized...
(17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ...
Importance:
Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ...
Moderne Algebra Description: The first introductory textbook (graduate level) expounding the abstract approach to algebra developed by Emil Artin and Emmy Noether. First published in German in 1931 by Springer Verlag. A later English translation was published in 1949 by Frederick Ungar Publishing Company. Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician. ...
Importance: Influence
Algebra Description: A definitive introductory text for abstract algebra using a category theoretic approach. Both a rigorous introduction from first principles, and a reasonably comprehensive survey of the field. Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ...
Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA - November 22, 1996, Water Mill, New York, USA) was an American mathematician. ...
In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. ...
Importance: Introduction
Abstract Algebra - David Dummit and Richard Foote
Description: A clear and concise introduction to abstract algebra, beginning with material suitable for undergraduates, and ranging through to cover graduate level topics in some detail.
Importance: Introduction
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems of linear equations. ...
Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...
Faisceaux Algébriques Cohérents Publication data: Annals of Mathematics, 1955 Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ...
Description: FAC, as it is usually called, first introduced the use of sheaves into algebraic geometry. Serre introduced Cech cohomology of sheaves in this paper, and, despite its technical deficiencies, revolutionized algebraic geometry. For example, the long exact sequence in sheaf cohomology allows one to show that some surjective maps of sheaves induce surjective maps on sections; specifically, these are the maps whose kernel (as a sheaf) has a vanishing first cohomology group. Before FAC, this was next to impossible. While Grothendieck's derived functor cohomology has replaced Cech cohomology for technical reasons, actual calculations, such as of the cohomology of projective space, are usually carried out by Cech techniques, and for this reason Serre's paper remains important even today. In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and...
Čech cohomology is a particular type of cohomology in mathematics. ...
In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. ...
Importance: Topic creator, Breakthrough, Influence
Description: In mathematics, algebraic geometry and analytic geometry are closely related subjects, where analytic geometry is the theory of complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. A (mathematical) theory of the relationship between the two was put in place during the early part of the 1950s, as part of the business of laying the foundations of algebraic geometry to include, for example, techniques from Hodge theory. (NB While analytic geometry as use of Cartesian coordinates is also in a sense included in the scope of algebraic geometry, that is not the topic being discussed in this article.) The major paper consolidating the theory was Géometrie Algébrique et Géométrie Analytique by Serre, now usually referred to as GAGA. A GAGA-style result would now mean any theorem of comparison, allowing passage between a category of objects from algebraic geometry, and their morphisms, and a well-defined subcategory of analytic geometry objects and holomorphic mappings. In mathematics, algebraic geometry and analytic geometry are two closely related subjects. ...
Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ...
Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...
Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ...
In differential geometry, a complex manifold is a manifold such that every neighborhood looks like the complex n-space. ...
Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ...
In mathematics, an analytic function is a function that is locally given by a convergent power series. ...
The theory of functions of several complex variables is the branch of mathematics dealing with functions f(z1, z2, ... , zn) on the space Cn of n-tuples of complex numbers. ...
In mathematics, Hodge theory is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric...
Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ...
Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ...
Importance: Topic creator, Breakthrough, Influence
Written with the assistance of Jean Dieudonne, this is Grothendieck's exposition of his reworking of the foundations of algebraic geometry. It has become the most important foundational work in modern algebraic geometry. The approach expounded in EGA, as these books are known, transformed the field and led to monumental advances. The Éléments de géométrie algébrique (Elements of Algebraic Geometry) by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, are an unfinished 1500-page treatise, in French, on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut...
Alexander Grothendieck (Berlin, March 28, 1928) is one of the most important mathematicians of the 20th century. ...
Importance: Seminal work which revolutionized the field
These seminar notes on Grothendieck's reworking of the foundations of algebraic geometry report on work done at IHÉS starting in the 1960s. SGA 1 dates from the seminars of 1960-1961, and the last in the series, SGA 7, dates from 1967–1969. In contrast to EGA, which is intended to set foundations, SGA describes ongoing research as it unfolded in Grothendieck’s seminar; as a result, it is quite difficult to read, since many of the more elementary and foundational results were relegated to EGA. One of the major results building on the results in SGA is Pierre Deligne's proof of the Weil conjectures in the 1970s. Other authors who worked on one or several volumes of SGA include Michel Raynaud, Michael Artin, Jean-Pierre Serre, Jean Verdier, Pierre Deligne, and Nicholas Katz. In mathematics, Alexander Grothendiecks Séminaire de géométrie algébrique was a unique phenomenon of research and publication outside of the main mathematical journals, reporting on work done starting from 1960 and centred on the IHÉS near Paris (the official title was the seminar of Bois...
Alexander Grothendieck (Berlin, March 28, 1928) is one of the most important mathematicians of the 20th century. ...
IHÉS main building The Institut des Hautes Études Scientifiques (I.H.É.S.) is a French institute supporting advanced research in mathematics and theoretical physics. ...
Pierre Deligne, March 2005 Pierre Deligne (born 3 October 1944) is a Belgian mathematician. ...
In mathematics, the Weil conjectures, which had become theorems by 1975, were some highly-influential proposals from the late 1940s by Andre Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. ...
Michel Raynaud (June 16, 1938) is a French mathematician working in algebraic geometry. ...
Michael Artin is an American mathematician, known for his contributions to algebraic geometry. ...
Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ...
Pierre Deligne, March 2005 Pierre Deligne (born 3 October 1944) is a Belgian mathematician. ...
Nick Katz (Nicholas M. Katz) is an American mathematician, working in the fields of algebraic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. ...
Importance: Seminal work which revolutionized the field
Description: The first comprehensive introductory (graduate level) text in algebraic geometry that used the language of schemes and cohomology. Published in 1977, it lacks aspects of the scheme language which are nowadays considered central, like the functor of points. Algebraic Geometry is an influential algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977. ...
Robin Hartshorne (born 1938) is an American mathematician. ...
In mathematics, specifically in category theory, Hom-sets, i. ...
Importance: Breakthrough textbook, influence
Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. ...
Universal algebra - Wolfgang Wechler.
- Springer-Verlag.
Description:
Importance:
Universal Algebra (book) - Burris, Stanley N., and H.P. Sankappanavar, H. P., 1981. A Course in Universal Algebra. Springer-Verlag. ISBN 3-540-90578-2.
Description: Available free online. An introduction to universal algebra. Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. ...
Importance: Introduction
In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. ...
Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ...
Topologie Description: First published round 1935, this text was a pioneering "reference" text book in topology, already incorporating many modern concepts from set-theoretic topology, homological algebra and homotopy theory. Pavel Sergeevich Alexandrov (Па́вел Серге́евич Алекса́ндров, sometimes romanized Alexandroff or Aleksandrov) (born May 7, 1896 - died November 16, 1982) was a Russian mathematician. ...
Heinz Hopf (November 19, 1894 – June 3, 1971) was a mathematician born in Gräbschen, Germany. ...
Importance: Influence
General Topology Description:First published in the mid-1950's,for many years the only introductory graduate level textbook in the U.S.A. teaching the basics of point set, as opposed to algebraic, topology. Prior to this the material, essential for advanced study in many fields, was only available in bits and pieces from texts on other topics or journal articles. John Leroy Kelley (December 6, 1916 – November 26, 1999) was an American mathematician at University of California, Berkeley who worked in general topology and functional analysis. ...
Importance: Pioneering text. Influence.
A labeled graph with 6 vertices and 7 edges. ...
Elementary graph theory - Berge, Claude, Théorie des graphes et ses applications. Collection Universitaire de Mathématiques, II Dunod, Paris 1958, viii+277 pp. (English edition, Wiley 1961; Methuen & Co, New York 1962; Russian, Moscow 1961; Spanish, Mexico 1962; Roumanian, Bucharest 1969; Chinese, Shanghai 1963; Second printing of the 1962 first English edition. Dover, New York 2001)
- Chartrand, Gary, Introductory Graph Theory, Dover. ISBN 0-486-24775-9.
Claude Berge (June 5, 1926 – June 30, 2002) was a French mathematician active in discrete mathematics and more specifically combinatorics and graph_theory. ...
Frank Harary (March 11, 1921 - January 4, 2005) was a prolific American mathematician, who specialized in graph theory. ...
Enumerative graph theory - Harary, Frank, and Palmer, Edgar M., Graphical Enumeration, Academic Press, New York, NY, 1973.
Graph Homomorphisms - Hell, Pavol and Nešetřil, Jaroslav. Graphs and Homomorphisms (Oxford Lecture Series in Mathematics and Its Applications). Oxford University Press. ISBN 0-19-852817-5. 2004
Jaroslav Nešetřil. ...
Asymptotic and random graph theory - Palmer, Edgar M., Graphical Evolution: An Introduction to the Theory of Random Graphs, John Wiley & Sons, New York, NY, 1985.
Algorithmic graph theory - Even, Shimon, Graph Algorithms, Computer Science Press, Rockville, MD, 1979.
In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. ...
Description: Saunders Mac Lane, one of the founders of category theory, wrote this exposition to bring categories to the masses. Mac Lane does not get lost in pointless abstraction, but instead brings to the fore the important concepts that make category theory useful, such as adjoint functors and universal objects. His text is more comprehensive than most mathematicians will ever need, and consequently is also an excellent reference. Categories for the Working Mathematician is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. ...
Saunders Mac Lane (4 August 1909, Taftville, Connecticut - 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. ...
The existence of many pairs of adjoint functors is a major observation of the branch of mathematics known as category theory. ...
In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. ...
Importance: Introduction
Category Theory for Computing Science - Michael Barr and Charles Wells
Description: Slower-paced introduction than Mac Lane's, assuming much less math background. Suitable for budding computer-scientists, logicians, linguists, etc. 1999 edition contains extensive exercises and solutions.
Importance: Introduction
Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ...
Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ...
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...
Topology from the Differentiable Viewpoint Description: This short book introduces the main concepts of differential topology in Milnor's lucid and concise style. While the book does not cover very much, its topics are explained beautifully in a way that illuminates all their details. John Willard Milnor (b. ...
Importance: Influence
Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ...
Analysis situs - Henri Poincaré's major contribution to algebraic topology, Analysis situs, published in 1895, was the first real systematic look at topology.
Henri Poincaré, photograph from the frontispiece of the 1913 edition of Last Thoughts Jules Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [][1]), generally known as Henri Poincaré, was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ...
Analysis Situs is an influential mathematical paper (and a series of addendums) written by Henri Poincare. ...
Algebraic Topology Publication data: Cambridge University Press, 2002.
Online version: http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Description: This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature.
Importance: Introduction
A fractal is a geometric object which can be divided into parts, each of which is similar to the original object. ...
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. ...
- Matoušek, Jiri, Jaroslav Nešetřil (1998). Invitation to Discrete Mathematics. Oxford University Press. ISBN 0-19-850207-9.
- german: Matoušek, Jiri, Jaroslav Nešetřil, H. Mielke (translator) (2002). Diskrete Mathematik: Eine Entdeckungsreise. Springer. ISBN 3-540-42386-9.
- french: Matoušek, Jiri, Jaroslav Nešetřil (2006). Introduction aux mathématiques discrètes. Springer. ISBN 2-287-20010-X.)
Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. ...
Jaroslav Nešetřil. ...
Jaroslav Nešetřil. ...
Jaroslav Nešetřil. ...
Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...
Grundzüge der Mengenlehre Description: First published in 1914, this was the first comprehensive introduction to set theory. Besides the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Here Hausdorff presents and develops highly original material which was later to become the basis for those areas. Grundzüge der Mengenlehre (German: Basics of set theory) is an influential book on set theory written by Felix Hausdorff. ...
Felix Hausdorff Felix Hausdorff (November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory and functional analysis. ...
In mathematics, a measure is a function that assigns a number, e. ...
Importance: Influence, Introduction
Description: An undergraduate introduction to not-very-naive set theory which has lasted for decades. It is still considered by many to be the best introduction to set theory for beginners. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo-Fraenkel set theory and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: There are no long-winded discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals. Instead it tried, and succeeds, in being intelligible to someone who has never thought about set theory before. Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. ...
Paul Halmos Paul Richard Halmos (born March 3, 1916) is a Hungarian-born American mathematician who has written on probability theory, statistics, operator theory, ergodic theory, functional analysis (in particular, Hilbert spaces), and mathematical logic. ...
Zermelo-Fraenkel set theory, commonly abbreviated ZFC, is the most common form of axiomatic set theory, and as such is the most common foundation of mathematics. ...
In mathematics, a cardinal is called a large cardinal if it belongs to a class of cardinals, the existence of which provably cannot be proved within the standard axiomatic set theory ZFC, if one assumes ZFC itself is consistent. ...
Importance: Influence, Introduction
Cardinal and Ordinal Numbers Description:The nec plus ultra reference for basic facts about cardinal and ordinal numbers. If you have a question about the cardinality of sets occurring in everyday mathematics, the first place to look is this book, first published in the early 1950's but based on the author's lectures on the subject over the preceding 40 years. Wacław Franciszek Sierpiński, was born on March 14, 1882 in Warsaw and died on October 21, 1969 in Warsaw. ...
Importance: Influence, unique reference
The Consistency of the Continuum Hypothesis Description:Gödel proves the result of the title and also the consistency of the axiom of choice. Also, in the process, introduces the class L of constructible sets, a major influence in the development of axiomatic set theory. Kurt Gödel Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
In mathematics, the axiom of choice, or AC, is an axiom of set theory. ...
In mathematics, the constructible universe (or Gödels constructible universe), denoted L, is a particular class of sets which can be described entirely in terms of simpler sets. ...
Importance: Breakthrough, influence
Set Theory and the Continuum Hypothesis Description:Published in 1966, these lecture notes from a course at Stanford University made accessible to the general mathematical community Cohen's breakthrough work proving the independence of the continuum hypothesis. In proving this Cohen introduced the concept of forcing which led to many other major results in axiomatic set theory. Paul Joseph Cohen (born April 2, 1934) is an American mathematician. ...
Importance: Breakthrough, influence
Set Theory: An Introduction to Independence Proofs Description: This book is not really for beginners, but graduate students with some minimal experience in set theory and formal logic will find it a valuable self-teaching tool, particularly in regard to forcing. It is far easier to read than a true reference work such as Jech, Set Theory. It may be the best textbook from which to learn forcing, though it has the disadvantage that the exposition of forcing relies somewhat on the earlier presentation of Martin's axiom. Kenneth Kunen is a professor of mathematics at the University of Wisconsin who works in set theory and its applications to various areas of mathematics, such as set-theoretic topology and measure theory. ...
In axiomatic set theory, forcing is a technique, invented by Paul Cohen, for proving consistency and independence results with respect to the Zermelo-Fraenkel axioms. ...
Importance: Textbook, reference
In mathematics, the term optimization refers to the study of problems that have the form Given: a function f : A R from some set A to the real numbers Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A (minimization) or such that...
The New Variational Method Description: Kantorovich wrote the first paper on production planning, which used Linear Programs as the model. He proposed the simplex algorithm as a systematic procedure to solve these Linear Programs. He received the Nobel prize for this work in 1975. Leonid V. Kantorovich. ...
Importance:
Decomposition Principle for Linear Programs. Description: Dantzig's is considered the father of Linear Programming in the western world. He independently invented the simplex algorithm. Dantzig and Wolfe worked on decomposition algorithms for large scale linear programs in factory and production planning. George Bernard Dantzig (8 November 1914 – 13 May 2005) was a mathematician who introduced the simplex algorithm and is considered the Father of linear programming. He was the recipient of many honors, including the National Medal of Science in 1975, the John von Neumann Theory Prize in 1974. ...
In mathematical optimization theory, the simplex algorithm of George Dantzig is a popular technique for numerical solution of the linear programming problem. ...
Importance:
Network Flows and General Matchings - Ford, L., & Fulkerson, D.
- Flows in Networks. Prentice-Hall, 1962.
Description: Ford and Fulkerson paper on Network Flows. The algorithm along with many ideas on flow-based models can be found in their book. This book is supposedly very well written. 1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ...
Importance:
Paths, trees and Flowers - J. Edmonds.
- Canadian Journal of Mathematics, 17:449–467, 1965.
Description:
Importance:
The complexity of theorem proving procedures - S. A. Cook
- Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (1971), pp. 151--158.
Description: This paper introduced the concept of NP-Completeness and proved that Boolean satisfiability problem (SAT) is NP-Complete. Stephen A. Cook is a noted computer scientist. ...
In complexity theory, the NP-complete problems are the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
In complexity theory, the NP-complete problems are the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use...
Importance: Topic creator, Breakthrough, Influence
Reducibility among combinatorial problems - R. M. Karp
- In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85-103. Plenum Press, New York, NY, 1972.
Description: This paper showed that 21 different problems are NP-Complete and showed the importance of the concept. Richard M. Karp (born 1935) is a computer scientist, notable for research in the theory of algorithms, for which he received a Turing Award in 1985. ...
In complexity theory, the NP-complete problems are the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use...
Importance: Influence
How good is the simplex algorithm? - V. Klee and G. J. Minty
- In: O. Shisha (ed.) Inequalities III, Academic Press (1972) 159–175.
Description: Klee and Minty gave example showing that simplex method can take exponentially many steps to solve a linear program if it chooses the greedy ascent rule.
Importance:
Linear Programming and Polynomial time algorithms - L. Khachiyan
- Doklady Akademii Nauk SSSR 244 (1979) pp. 1093–1096 (Russian).
Description: Khachiyan's work on Ellipsoid method. Leonid Khachiyan Leonid Khachiyan (May 3, 1952 - April 29, 2005) was a Russian-born mathematician who taught Computer Science at Rutgers University. ...
Importance: This was the first polynomial time algorithm for Linear programming.
New polynomial-time algorithm for linear programming - Karmarkar, N.
- Combinatorica 4, 373–395, 1984.
Description: Karmarkars path-breaking work on Interior-Point algorithms for Linear Programming. 1984 (MCMLXXXIV) was a leap year starting on Sunday of the Gregorian calendar. ...
Importance:
Interior Point Polynomial Algorithms in Convex Programming - Yurii NESTEROV and A. NEMIROVSKY.
- Philadelphia : Society for Industrial and Applied Mathematics, 1994. (SIAM Studies in Applied Mathematics).
Description: Nesterov and Nemirovski's work on Self-concordant barriers and Interior-Point Methods for general convex programming. All their series of papers (both individual and combined) is compiled more coherently in the following "bible" of convex optimization.
Importance:
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