Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time

A mathematician is a person whose primary area of study and research is mathematics. In other words, a mathematician is a person who contributes to the field of mathematics. People who apply mathematics to other fields, but do not contribute directly to mathematics, are generally not considered mathematicians. Image File history File links Picture of Leonhard Euler by Emanuel Handmann. ... Image File history File links Picture of Leonhard Euler by Emanuel Handmann. ... Leonhard Euler by Emanuel Handmann. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ...

Overview

Unlike the other sciences, fundamental research in much of mathematics does not consist of performing experiments. Rather, mathematics is about problem-solving, where truths are deduced from other known truths. Computer experiments and other numerical evidence can result in new problems and are sometimes used to solve them, though most of the time they are just used as indicators that the work is on the right track - numerical evidence is not proof to a mathematician. In the end mathematics research is about constructing proofs of theorems, and most journals would reject a paper consisting solely of numerical data. Some outstanding open problems in mathematics, such as the Birch and Swinnerton-Dyer conjecture, developed after analyzing numerical work on a computer. In mathematics, the Birch and Swinnerton-Dyer conjecture relates the rank of the abelian group of points over a number field of an elliptic curve E to the order of zero of the associated L-function L(E, s) at s = 1. ...

Not only is calculation not a big part of some areas of mathematics research, but people who have had an important influence on mathematics do not necessarily have any extraordinary ability in adding or multiplying numbers. For instance, Albert Einstein, whose ideas had a significant impact in geometry, had great difficulties with mathematics when he was a youth. See mental calculators to read about prodigies performing impressive mental calculations. Albert Einstein, photographed in 1947 by Oren J. Turner. ... Mental calculators are people with a prodigious ability in some area of mental calculation, such as multiplying large numbers or factoring large numbers. ...

Fields of work

Mathematicians are employed by private firms in various capacities or as professors at universities or other educational institutions, by research organizations, or by military or civilian government agencies. [1] The largest employer of mathematicians in the United States, for instance, is the National Security Agency. Finally, because mathematics is useful in a wide range of fields, many who consider themselves mathematicians are involved in other subjects, such as physics and computer science. A professor giving a lecture The meaning of the word professor (Latin: one who claims publicly to be an expert) varies. ... Representation of a university class, 1350s. ... Image:Security Agency seal. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ...   Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

Mathematics can be divided into many different areas, but broadly speaking mathematicians speak of pure mathematics and applied mathematics. Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. ...

Pure mathematics traditionally includes algebra, geometry, and (some areas of) analysis, while applied mathematics involved the use of differential equations or other aspects of analysis to solve practical problems. Throughout the physical and social sciences and the business world, much use is made of probability and statistics. However, with the advent of the computer, even parts of algebra (number theory and combinatorics) and geometry (elliptic curves) are used in applied situations. The word probability derives from the Latin probare (to prove, or to test). ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ...

Problems in mathematics

Some people incorrectly believe mathematics is fully understood, but the publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical physics). One of the most exciting recent developements was the proof of Fermat's Last Theorem, following 350 years of the brightest mathematical minds attempting to settle the problem. Proceedings of the National Academy of Sciences. ... Computer science (informally, CS or compsci) is, in its most general sense, the study of computation and information processing, both in hardware and in software. ... Theoretical physics employs mathematical models and abstractions, as opposed to experimental processes, in an attempt to understand Nature. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats Last Theorem (edition of 1670). ...

There are many famous open problems in mathematics, many dating back tens if not hundreds of years. Some examples include the Riemann hypothesis (from 1859), the Poincaré conjecture (1904) and Goldbach's Conjecture (1742). Unsolved problems in mathematics: Is the real part of a non-trivial zero of the Riemann zeta function always ½? In mathematics, the Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous unsolved problems. ... 1859 (MDCCCLIX) is a common year starting on Saturday of the Gregorian calendar (or a common year starting on Monday of the Julian calendar). ... In mathematics, the Poincaré conjecture (see Henri Poincaré for pronunciation) is a conjecture about the characterisation of the three-dimensional sphere amongst 3-manifolds. ... 1904 (MCMIV) was a leap year starting on a Friday (link will take you to calendar). ... In mathematics, Goldbachs conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. ... // Events January 24 - Charles VII Albert becomes Holy Roman Emperor. ...

Motivation

Mathematicians are typically interested not in calculating, but in finding and describing patterns, or creating proofs that justify a theorem mathematically. Problems have come from physics, economics, games, computer science and generalizations of earlier mathematics. Some problems are simply created for the challenge of solving them. Although much mathematics is not immediately useful, history has shown that eventually applications are found. For example, number theory originally seemed to be without purpose to the real world, but after the development of computers it gained important applications to algorithms and cryptography. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ... GAMES Magazine is a United States based magazine devoted to games published by GAMES Publications, a division of Kappa Publishing Group. ...   Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Flowcharts are often used to represent algorithms. ... The German Lorenz cipher machine, used in World War II for encryption of high-level messages. ...

There are no Nobel Prizes awarded to mathematicians. The award that is generally viewed as having the highest prestige in mathematics is the Fields Medal. This medal, sometimes described as the "Nobel Prize of Mathematics" is awarded once every four years to up to four young (under 40 years old) awardees at a time. Other prominent prizes include the Abel Prize, the Wolf Prize, the Schock Prize, and the Nevanlinna Prize. Sir Edward Appletons medal Photographs of Nobel Prize Medals. ... The Fields Medal is a prize awarded to up to four mathematicians not over forty years of age at each International Congress of the International Mathematical Union (therefore once every four years). ... The Abel Prize is awarded annually by the King of Norway to outstanding mathematicians. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ... The Schock Prizes were instituted by the will of philosopher and artist Rolf Schock (1933-1986). ... The Nevanlinna Prize is a prize for major contributions to mathematical aspects of computer science. ...

Differences

Mathematicians differ from philosophers in that the primary questions of mathematics are assumed (for the most part) to transcend the context of the human mind; the idea that "2+2=4 is a true statement" is assumed to exist without requiring a human mind to state the problem. Not all mathematicians would strictly agree with the above; the philosophy of mathematics contains several viewpoints on this question. Nonetheless, many of the great philosophers were mathematicians, such as Rene Descartes. A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense(s), if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to answering these questions will... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ...

Whereas physical theories in the sciences are usually assumed to be an approximation of truth, mathematical statements are an attempt at capturing truth. If a certain statement is believed to be true by mathematicians (typically as special cases are confirmed to some degree) but has neither been proven nor disproven to logically follow from some set of assumptions, it is called a conjecture, as opposed to the ultimate goal, a theorem that is proven true. Physical theories may be expected to change whenever new information about our physical world is discovered. Mathematics changes in a different way: new ideas don't falsify old ones, but rather are used to generalize what was known before to capture a broader range of phenomena. For instance, calculus (in one variable) generalizes to multivariable calculus, which generalizes to analysis on manifolds. The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint without making what was proved before in any way incorrect. While a theorem, once proved, is true forever, our understanding of what the theorem really means gains in profundity as the mathematics around the theorem grows. A mathematician feels that a theorem is better understood when it can be extended to apply in a broader setting than previously known. For instance, Fermat's little theorem for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups. An approximation is an inexact representation of something that is still close enough to be useful. ... In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. ... Calculus is a central branch of mathematics, developed from algebra and geometry. ... Multivariable calculus is the extension of calculus in one variable to calculus in several variables: the functions which are differentiated and integrated involve several variables rather than one variable. ... On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... Fermats little theorem (not to be confused with Fermats last theorem) states that if p is a prime number, then for any integer a, This means that if you start with a number, initialized to 1, and repeatedly multiply, for a total of p multiplications, that number by... In number theory, Eulers theorem (also known as the Fermat-Euler theorem or Eulers totient theorem) states that if n is a positive integer and a is coprime to n, then aφ(n) ≡ 1 (mod n) where φ(n) is Eulers totient function and mod denotes the congruence... In mathematics, most commonly, Lagranges theorem states that if G is a finite group and H is a subgroup of G, then the order (that is, the number of elements) of H divides the order of G. This can be shown using the concept of left cosets of H...

Demographics

As is the case in many scientific disciplines, the majority of mathematicians are male. There was a little change after World War II. Among the prominent female mathematicians are Emmy Noether (1882 - 1935), Sophie Germain (1776 - 1831), Sofia Kovalevskaya (1850 - 1891), Rózsa Péter (1905 - 1977), Julia Robinson (1919 - 1985), Mary Ellen Rudin, Eva Tardos, Émilie du Châtelet, Mary Cartwright, Hypatia of Alexandria and Marianna Csörnyei. Emmy Noether (born Nöther) (March 23, 1882 – April 14, 1935) was a talented mathematician of the early 20th century, with penetrating insights that she used to develop elegant abstractions which she formalized and published. ... 1882 (MDCCCLXXXII) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar or a common year starting on Tuesday of the 12-day slower Julian calendar. ... 1935 (MCMXXXV) was a common year starting on Tuesday (link will take you to calendar). ... Marie-Sophie Germain (April 1, 1776 – June 27, 1831) was a French mathematician, and one of the most important mathematicians of all time. ... This article is about the year 1776. ... Leopold I 1831 was a common year starting on Saturday (see link for calendar). ... Sofia Vasilyevna Kovalevskaya (Софья Васильевна Ковалевская) (January 15, 1850 – February 10, 1891) was the first major Russian female mathematician and a student of Karl Weierstrass in Berlin. ... 1850 was a common year starting on Tuesday (see link for calendar). ... 1891 (MDCCCXCI) was a common year starting on Thursday (see link for calendar). ... Rózsa Péter, (February 17, 1905–February 16, 1977) was a Hungarian mathematician. ... 1905 (MCMV) was a common year starting on Sunday (see link for calendar). ... For the album by Ash, see 1977 (album). ... Julia Hall Bowman Robinson (December 8, 1919 - July 30, 1985) was an American mathematician, born in Saint Louis, Missouri. ... 1919 (MCMXIX) was a common year starting on Wednesday (see link for calendar). ... This article is about the year. ... Mary Ellen Rudin (born December 7, 1924, Hillsboro, Texas) is an American mathematician. ... Éva Tardos, mathematician, winner of the Fulkerson Prize (1988), professor of Computer Science at Cornell University. ... Emilie du Chatelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet-Laumont (December 17, 1706 - September 10, 1749) was a French mathematician, physicist and author. ... Dame Mary Cartwright was a leading British mathematician of the 20th century. ... Hypatia redirects here. ... Marianna Csörnyei (born in Budapest on October 8, 1975) is a Hungarian mathematician. ...

Doctoral degree statistics for mathematicians in the United States

The number of doctoral degrees awarded each year in the United States has ranged from 750 to 1230 over the past 35 years.[2] In the early seventies degree awards were at their peak, followed by a decline throughout the seventies, a rise through the eighties and another peak through the nineties. Unemployment for new doctoral recipients peaked at 10.7% in 1994 but was as low as 3.3% by 2000. The percentage of female doctoral recipients increased from 15% in 1980 to 30% in 2000.

As of 2000 there are approximately 21,000 full-time faculty positions at colleges and universities in the United States. Of these positions about 36% are at institutions whose highest degree granted in mathematics is a bachelor's degree, 23% at institutions that offer a master's degree and 41% at institutions offering a doctoral degree.

The median age for doctoral recipients in 1999-2000 was 30 and the mean age was 31.7.

Quotes

Wikiquote has a collection of quotations related to:

Mathematician

The following are quotes about mathematicians, or by mathematicians. Image File history File links Wikiquote-logo-en. ... Wikiquote logo Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ...

A mathematician is a machine for turning coffee into theorems.

—Alfréd Rényi [3]

Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. (Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)

—Johann Wolfgang von Goethe

Some humans are mathematicians; others aren't.

—Jane Goodall (1971) In the Shadow of Man

"I'm not a magician, I'm a mathemagician!"

—Simpsons

Coffee Coffee is a beverage, served hot or with ice, prepared from the roasted seeds of the coffee plant. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... Alfréd Rényi (March 20, 1921 – February 1, 1970) was a Hungarian mathematician who made contributions in combinatorics and graph theory but mostly in probability theory. ... Johann Wolfgang von Goethe. ... Trinomial name Homo sapiens sapiens Linnaeus, 1758 Humans, or human beings, are bipedal primates belonging to the mammalian species Homo sapiens (Latin for wise man or knowing man) under the family Hominidae (the great apes). ... Jane Goodall Dame Jane Goodall, DBE (born April 3, 1934) is an English primatologist, ethologist and anthropologist, probably best-known for conducting a forty-five year study of chimpanzee social and family life, as director of the Jane Goodall Institute in Gombe Stream National Park in Tanzania. ... 1971 (MCMLXXI) was a common year starting on Friday (the link is to a full 1971 calendar). ... The Simpsons. ...

See also

• Mental calculator
• List of mathematicians
• List of amateur mathematicians
• Astronomers, Physicists, Philosophers, Scientists
• American Mathematical Society
• Mathematical Association of America
• Mathematical joke

Mental calculators are people with a prodigious ability in some area of mental calculation, such as multiplying large numbers or factoring large numbers. ... The famous mathematicians are listed below in English alphabetical transliteration order (by surname). ... This is a list of people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. ... An astronomer or astrophysicist is a scientist whose area of research is astronomy or astrophysics. ... Many famous physicists of the 20th and 21st century are found on the list of recipients of the Nobel Prize in physics. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... The physicist Albert Einstein is probably historys most widely recognized scientist. ... 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. ... The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. ... Some mathematical humor is as simple and crude as using mathematical symbols to write Sex is fun A mathematical joke is a form of professional humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. ...

References

• A Mathematician's Apology, by G. H. Hardy. Memoir, with foreword by C. P. Snow.
  • Reprint edition, Cambridge University Press, 1992; ISBN 0521427061
  • First edition, 1940
• Dunham, William. The Mathematical Universe. John Wiley 1994.

A Mathematicians Apology is a 1940 essay by British mathematician G. H. Hardy (ISBN 0521427061). ... 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. ... C. P. Snow, born Charles Percy Snow, (1905-1980) was a scientist and novelist. ...

External links

• The MacTutor History of Mathematics archive, a very complete list of detailed biographies.
• The Mathematics Genealogy Project, which allows to follow the succession of thesis advisors for most mathematicians, living or dead.