Leonhard Euler is widely considered as one of the greatest mathematicians of all time

A mathematician is a person whose primary area of study and research is the field of mathematics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and

Problems in mathematics

The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals. For a broader class of publications which include scientific journals see Academic journal. One of the most exciting recent developments was the proof of Fermat's last theorem by Andrew Wiles, following 350 years of the brightest mathematical minds attempting to settle the problem. In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like Sir Andrew John Wiles KBE FRS (born 11 April 1953 is a British Mathematician and a professor at Princeton University

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) and Goldbach's conjecture (1742). The Riemann hypothesis (also called the Riemann zeta-hypothesis) first formulated by Bernhard Riemann in 1859 is one of the most famous and important unsolved Goldbach's conjecture is one of the oldest unsolved problems in Number theory and in all of Mathematics. The Millennium Prize Problems highlight longstanding, important problems in mathematics and offers a US$1,000,000 reward for solving any one of them. The Millennium Prize Problems are seven problems in Mathematics that were stated by the Clay Mathematics Institute in 2000 The United States dollar ( sign: $; code: USD) is the unit of Currency of the United States; it has also been One of these problems, the Poincaré conjecture (1904), was proven by Russian mathematician Grigori Perelman in a paper released in 2003; peer review was completed in 2006, and the proof was accepted as valid. In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among Grigori Yakovlevich Perelman (Григорий Яковлевич Перельман born 13 June 1966 in Leningrad, USSR (now St ^[1]

Motivation

Mathematicians are typically interested in finding and describing patterns, or finding (mathematical) proofs of theorems. Most problems and theorems come from within mathematics itself, or are inspired by theoretical physics. Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world To a lesser extent, problems have come from economics, games and computer science. Economics is the social science that studies the production distribution, and consumption of goods and services. A game is a structured activity, usually undertaken for Enjoyment and sometimes also used as an Educational tool Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their 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. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write"

There are no Nobel Prizes awarded to mathematicians. The Nobel Prize (Nobelpriset (Nobelprisen is a Swedish prize established in the 1895 will of Swedish chemist Alfred Nobel; it was first awarded in Peace, Literature The award that is generally viewed as having the highest prestige in mathematics is the Fields Medal. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical This medal, sometimes described as the "Nobel Prize of Mathematics", is awarded once every four years to as many as four young (under 40 years old) awardees at a time. Other prominent prizes include the Abel Prize, the Nemmers Prize, the Wolf Prize, the Schock Prize, and the Nevanlinna Prize. The Abel Prize is an international prize presented annually by the King of Norway to one or more outstanding Mathematicians The prize is named after Norwegian The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. The Rolf Schock Prizes were established and endowed by bequeath of philosopher and artist Rolf Schock (1933-1986 The Rolf Nevanlinna Prize is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information

Differences

Mathematics differs from natural sciences in that physical theories in the sciences are tested by experiments, while mathematical statements are supported by proofs which may be verified objectively by mathematicians. Science (from the Latin scientia, meaning " Knowledge " or "knowing" is the effort to discover, and increase human understanding If a certain statement is believed to be true by mathematicians (typically because special cases have been confirmed to some degree) but has neither been proven nor dis-proven, it is called a conjecture, as opposed to the ultimate goal: a theorem that is proven true. In Mathematics, a conjecture is a Mathematical statement which appears resourceful but has not been formally proven to be true under the rules of 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. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Multivariable calculus is the extension of Calculus in one Variable to calculus in several variables the functions which are differentiated and integrated involve A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be 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. Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with 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. Fermat's little theorem (not to be confused with Fermat's last theorem) states that if p is a Prime number, then for any Integer a In Number theory, Euler's theorem (also known as the Fermat-Euler theorem or Euler's totient theorem) states that if n is a positive Integer Lagrange's theorem, in the Mathematics of Group theory, states that for any Finite group G, the order (number of elements of

Demographics

Emmy Noether

While the majority of mathematicians are male, there have been some demographic changes since World War II. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including Some prominent female mathematicians are Ada Lovelace (1815 - 1852), Maria Gaetana Agnesi (1718-1799), Emmy Noether (1882 - 1935), Sophie Germain (1776 - 1831), Sofia Kovalevskaya (1850 - 1891), Rózsa Péter (1905 - 1977), Julia Robinson (1919 - 1985), Olga Taussky-Todd (1906 - 1995), Émilie du Châtelet (1706 – 1749), Mary Cartwright (1900 - 1998), and Hypatia of Alexandria (ca. Augusta Ada King Countess of Lovelace (10 December 1815 London England &ndash 27 November 1852 Marylebone, London England born Augusta Ada Byron, was the only Maria Gaetana Agnesi ( May 16, 1718 - January 9, 1799) was an Italian linguist mathematician and philosopher Amalie Emmy Noether, ˈnøːtɐ (23 March 1882 – 14 April 1935 was a German Mathematician known for her groundbreaking contributions to Abstract algebra and This article is about the mathematician Marie-Sophie Germain See also Sophie Germain primes Marie-Sophie Germain ( April 1, 1776 Sofia Vasilyevna Kovalevskaya (Софья Васильевна Ковалевская Julia Hall Bowman Robinson ( December 8, 1919 – July 30, 1985) was an American Mathematician, born in St Olga Taussky Todd ( August 30, 1906, Olomouc, then Austria-Hungary - October 7, 1995, Pasadena, California Gabrielle Émilie Le Tonnelier de Breteuil marquise du Châtelet ( December 17, 1706 &ndash September 10, 1749) was a French Dame Mary Lucy Cartwright DBE ( December 17, 1900 &ndash April 3, 1998) was a leading 20th-century British Mathematician Hypatia of Alexandria (haɪˈpeɪʃə ( Greek:; born between AD 350 and 370 – 415 was a Greek scholar from Alexandria in Egypt, considered 400 AD). The AMS and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

Doctoral degree statistics for mathematicians in the United States

The number of doctoral degrees in mathematics awarded each year in the United States has ranged from 750 to 1230 over the past 35 years. The United States of America —commonly referred to as the ^[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 in mathematics 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.

Quotations

The following are quotations about mathematicians, or by mathematicians.

A mathematician is a machine for turning coffee into theorems.

—Attributed to both Alfréd Rényi ^[3] and Paul Erdős

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. Alfréd Rényi (20 March 1921 &ndash 1 February 1970 was a Hungarian Mathematician who made contributions in Combinatorics and Graph theory Paul Erdős ( Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 &ndash (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. ˈjoːhan ˈvɔlfgaŋ fɔn ˈgøːtə (in English generally ˈgɝːtə 28 August 1749 22 March 1832 was a German writer

—Jane Goodall (1971) In the Shadow of Man

Each generation has its few great mathematicians. Dame Jane Goodall, DBE (born Valerie Jane Morris Goodall on 3 April 1934) is an English UN Messenger of Peace primatologist . . and [the others'] research harms no one.

—Alfred Adler, "Mathematics and Creativity"^[4]

Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. Alfred Adler ( February 7 1870 &ndash May 28 1937) was an Austrian medical doctor, psychologist and founder of

—Bertrand Russell, The Study of Mathematics

A mathematician, like a painter or poet, is a maker of patterns. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian If his patterns are more permanent than theirs, it is because they are made with ideas.

—G. H. Hardy, A Mathematician's Apology

Another roof, another proof. Godfrey Harold Hardy FRS ( February 7, 1877 Cranleigh, Surrey, England &ndash December 1, 1947

—Paul Erdős

Some of you may have met mathematicians and wondered how they got that way. Paul Erdős ( Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 &ndash

—Tom Lehrer

It is impossible to be a mathematician without being a poet in soul. Thomas Andrew "Tom" Lehrer (born April 9 1928)is an American Singer-songwriter, satirist, Pianist, and mathematician

—Sofia Kovalevskaya

See also

Notes

References

• A Mathematician's Apology, by G. H. Hardy. A Mathematician's Apology is a 1940 essay by British mathematician G Godfrey Harold Hardy FRS ( February 7, 1877 Cranleigh, Surrey, England &ndash December 1, 1947 Memoir, with foreword by C. P. Snow. Charles Percy Snow Baron Snow CBE ( 15 October 1905 &ndash 1 July 1980) was an English Physicist and Novelist
  • Reprint edition, Cambridge University Press, 1992; ISBN 0-521-42706-1
  • First edition, 1940
• Dunham, William. The Mathematical Universe. John Wiley 1994.
• Paul Halmos. Paul Richard Halmos ( March 3 1916 &mdash October 2 2006) was a Hungarian -born Jewish American Mathematician I Want to Be a Mathematician. Springer-Verlag 1985.

External links

• The MacTutor History of Mathematics archive. A comprehensive list of detailed biographies.
• The Mathematics Genealogy Project. Allows to follow the succession of thesis advisors for most mathematicians, living or dead.
• Occupational Outlook – Mathematicians. Information on the occupation of mathematician from the US Department of Labor.
• Unsolved Problems. A list of sixteen major unsolved problems in mathematics at MathWorld.
• Sloan Career Cornerstone Center: Careers in Mathematics. Although US-centric, a useful resource for anyone interested in a career as a mathematician. Learn what mathematicians do on a daily basis, where they work, how much they earn, and more.