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Encyclopedia > Mathematician
Leonhard Euler, considered one of the greatest mathematicians of all time
Leonhard Euler, considered 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. Image File history File links Download high resolution version (614x767, 96 KB) 1737 portrait by Johann Georg Brucker Summary From English Wikipedia: Leonhard Euler Source: http://www. ... Image File history File links Download high resolution version (614x767, 96 KB) 1737 portrait by Johann Georg Brucker Summary From English Wikipedia: Leonhard Euler Source: http://www. ... Leonhard Paul Euler (pronounced Oiler; IPA ) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...

Contents

Problems in mathematics

Some people incorrectly believe that mathematics has been fully understood, but the publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals. One of the most exciting recent developments was the proof of Fermat's last theorem, following 350 years of the brightest mathematical minds attempting to settle the problem. This article or section does not cite its references or sources. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ...


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 Millennium Prize Problems highlight longstanding, famous problems in mathematics and offers a US$1,000,000 reward for solving any one of them. 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.[1] 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. ... Goldbachs conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. ... The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts, and dedicated to increasing and disseminating mathematical knowledge. ... ISO 4217 Code USD User(s) the United States, the British Indian Ocean Territory,[1] the British Virgin Islands, East Timor, Ecuador, El Salvador, the Marshall Islands, Micronesia, Palau, Panama, Caicos Islands, and the insular areas of the United States Inflation 2. ... In mathematics, the Poincaré conjecture (IPA: [])[1] is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. ... Grigori Yakovlevich Perelman (Russian: ), born 13 June 1966 in Leningrad, USSR (now St. ...


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. This article needs additional references or sources for verification. ... This article needs additional references or sources for verification. ... GAMES Magazine is a United States based magazine devoted to games published by GAMES Publications, a division of Kappa Publishing Group. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... Flowcharts are often used to represent algorithms. ... The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Cryptography (or cryptology; derived from Greek κρυπτός kryptós hidden, and the verb γράφω gráfo write or λεγειν legein to speak) is the study of message secrecy. ...


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 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. Nobel Prize 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 Union, a meeting that takes place every four years. ... The Abel Prize is awarded annually by the King of Norway to outstanding mathematicians. ... The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. ... 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 scientists in that physical theories in the sciences are usually assumed to be an approximation of truth, while mathematical statements are an attempt at capturing truth. 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 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. This article does not cite any references or sources. ... It has been suggested that this article or section be merged with estimation. ... In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic. ... Calculus (from Latin, pebble or little stone) is a branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series, and constitutes a major part of modern university education. ... 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 techniques of abstract algebra, especially commutative algebra, with the language and the problematics of 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... Lagranges theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. Lagranges theorem is named after Joseph Lagrange. ...


Demographics

While the majority of mathematicians are male, there have been some demographic changes since World War II. Some 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, Marianna Csörnyei, Ingrid Daubechies and Nicole El Karoui. The AMS and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000... Amalie Emmy Noether [1] (March 23, 1882 – April 14, 1935) was a German-born mathematician, said by Einstein in eulogy to be [i]n the judgment of the most competent living mathematicians, [...] the most significant creative mathematical genius thus far produced since the higher education of women began. ... Sophie Germain Marie-Sophie Germain (April 1, 1776 – June 27, 1831), born to a middle-class merchant family in Paris, France, was an French mathematician. ... Sofia Vasilyevna Kovalevskaya (Russian Софья Васильевна Ковалевская), also known as Sonya Kovalevsky (January 15, 1850-February 10, 1891), was the first major Russian female mathematician, and also the first woman who was appointed to a full professorship in Europe 1889 (Sweden). ... Rózsa Péter, (February 17, 1905–February 16, 1977) was a Hungarian mathematician. ... Julia Hall Bowman Robinson (December 8, 1919 - July 30, 1985) was an American mathematician, born in Saint Louis, Missouri. ... 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. ... Émilie du Châtelet Émilie du Châtelet (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. ... An imagined portrait of Hypatia of Alexandria Hypatia of Alexandria (Greek: Υπατία; born between 350 and 370 AD – 415 AD) was a Greek Neoplatonist philosopher, the first notable woman in mathematics, and also taught in the fields of astronomy and astrology. ... Marianna Csörnyei (born in Budapest on October 8, 1975) is a Hungarian mathematician. ... Ingrid Daubechies (born August 17, 1954) is a Belgian physicist and mathematician. ...


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.[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

Wikiquote has a collection of quotations related to:
Mathematician

The following are quotations about mathematicians, or by mathematicians. Image File history File links This is a lossless scalable vector image. ... Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ...

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. (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
Each generation has its few great mathematicians...and [the others'] research harms no one.
—Alfred Adler, "Mathematics and Creativity"[1]
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.
Bertrand Russell, The Study of Mathematics
Another roof, another proof.
Paul Erdős
Some of you may have met mathematicians and wondered how they got that way.
Tom Lehrerhe was mad to do all this

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. ... Paul ErdÅ‘s, also ErdÅ‘s Pál, in English Paul Erdos or Paul Erdös (March 26, 1913 – September 20, 1996), was an immensely prolific (and famously eccentric) Hungarian-born mathematician. ...  , IPA: , (28 August 1749 – 22 March 1832) was a German polymath. ... This article needs additional references or sources for verification. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Paul ErdÅ‘s, also ErdÅ‘s Pál, in English Paul Erdos or Paul Erdös (March 26, 1913 – September 20, 1996), was an immensely prolific (and famously eccentric) Hungarian-born mathematician. ... Thomas Andrew (Tom) Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. ...

See also

This article does not cite any references or sources. ... Mathematicians by letter: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Requested mathematicians articles Lists of mathematicians (by country, etc. ... This is a list of female mathematicians who have made significant contributions to mathematics. ... 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 person whose area of interest 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. ... This article does not cite any references or sources. ... 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. ... This article or section does not cite its references or sources. ...

References

  • A Mathematician's Apology, by G. H. Hardy. Memoir, with foreword by C. P. Snow.
    • Reprint edition, Cambridge University Press, 1992; ISBN 0-521-42706-1
    • First edition, 1940
  • Dunham, William. The Mathematical Universe. John Wiley 1994.
  • Paul Halmos. I Want to Be a Mathematician. Springer-Verlag 1985.

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 English mathematician, known for his achievements in number theory and mathematical analysis. ... Charles Percy Snow, Baron Snow, CBE (15 October 1905–1 July 1980) was a scientist and novelist. ... Paul Halmos Paul Richard Halmos (March 3, 1916 — October 2, 2006) was a Hungarian-born American mathematician who wrote on probability theory, statistics, operator theory, ergodic theory, functional analysis (in particular, Hilbert spaces), and mathematical logic. ...

Notes

  1. ^ Alfred Adler, "Mathematics and Creativity," The New Yorker, 1972, reprinted in Timothy Ferris, ed., The World Treasury of Physics, Astronomy, and Mathematics, Back Bay Books, reprint, June 30, 1993, p, 435.

External links


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