List of eminent mathematicians

This list of important mathematicians represents a selection of mathematicians from antiquity to the present day. The selection of mathematicians is based on their scientific achievements or their level of awareness, on the basis of which they are shown interest in mathematical historical considerations in schools or universities.

Until well into the time of the Renaissance , mathematicians as scholars were mostly focused on several sciences; they were often philosophers , engineers , astronomers and astrologers at the same time . This polyhistorism gave way over the centuries, so that at the time of rationalism mathematicians often only studied and pursued a second science. Usually theology or physics was chosen as a further field of activity because of their thematic relationship . This development has continued since the 19th century, so that today's mathematicians often only conduct research in a few sub-areas of mathematics.

Antiquity

	Name (life data)	Research area
	Thales of Miletus * around 624 BC In Miletus, Asia Minor † around 546 BC Chr.	Thales was a Greek natural philosopher, statesman, mathematician, astronomer and engineer. According to tradition, he is said to have proven geometric theorems for the first time based on definitions and assumptions with the help of symmetry considerations. Thales sought a rational explanation of the world. The Thales' sentence is named after him.
	Pythagoras of Samos * around 570 BC BC † after 510 BC Chr.	Pythagoras was a mathematician, philosopher and founder of the secret society of the Pythagoreans . The Pythagorean theorem , named after him by Euclid , was known much earlier.
	Eudoxos of Knidos * 410 or 408 BC BC † 355 or 347 BC Chr.	Eudoxos was a Greek mathematician , astronomer , geographer, and doctor . He summarized the concepts of number , length, spatial and temporal expansion under one umbrella term and laid the basis for the doctrine of sizes . His theory of size already contains the Archimedean axiom and irrational relationships. He developed the exhaustion method and determined the volume of the pyramid and the cone .
	Euclid of Alexandria * approx. 365 BC BC probably in Alexandria or Athens † approx. 300 BC Chr.	Euclid tried to build up mathematics and especially geometry axiomatically . In his important 13-volume textbook " The Elements " he summarized the mathematical knowledge known at the time. According to him, are Euclidean geometry and the Euclidean algorithm named.
	Archimedes of Syracuse around 287 BC BC probably in Syracuse in Sicily † 212 BC Chr. Ibid	Archimedes was a Greek mathematician, physicist and engineer and is considered the most important mathematician of the ancient world. He proved that the circumference of a circle is related to its diameter in the same way as the area of the circle to the square of the radius, the ratio is now referred to as π (Pi) , and he calculated the area under a parabola. The Archimedean axiom is named after him .
	Apollonios of Perge * 262 BC In Perge † 190 BC In Alexandria	In his most important work Konika (“About conic sections”), Apollonios von Perge devoted himself to in-depth investigations into the problems of conic sections , limit value determinations and extreme value problems . Among other things, the circle of Apollonios is named after him.
	Diophant of Alexandria dates of life uncertain between 100 BC and 350 AD	Diophant of Alexandria was a Greek mathematician about whom very little is known. One knows his works, of which the multi-volume Arithmetika is the best known. He dealt with solving algebraic equations with several unknowns. Today, algebraic equations for which integer solutions are sought are called Diophantine equations .
	Pappos life dates uncertain 4th century AD	Pappos lived in Alexandria and is considered to be one of the last great mathematicians of antiquity, who was particularly concerned with geometry ( Pappos' theorem ) and left a mathematical collection . He was also familiar with the Guldin rules . He was also an astronomer.

middle Ages

In the period that is called the Middle Ages from a Eurocentric point of view, scholars from the Arab-Persian region in particular produced new knowledge and further developed the mathematics of the Greeks and Indians. It was only in the late Middle Ages that parts of Islamic mathematics gradually gained acceptance in Christian Europe. The most important mathematical achievement of Islamic mathematicians lies in the founding of today's algebra .

	Name (life data)	Research area
	Aryabhata * 476 in Ashmaka † around 550	Aryabhata was an Indian polymath, mathematician, and astronomer. It is believed that the concept of the number 0 (zero) goes back to Aryabhata, although it is not until Brahmagupta that the zero is obviously treated as a separate number. Aryabhata determined the circle number Pi very precisely to 3.1416 for that time and seems to have already suspected that it was an irrational number.
	Brahmagupta * 598 † 668	Brahmagupta also worked as an astronomer in India. He established rules for arithmetic with negative numbers and also used the number 0 for calculation. The Brahmagupta phrase was named after him.
	al-Khwarizmi * around 780 † between 835 and 850	Al-Chwarizmi was a Persian mathematician, astronomer, and geographer. He is considered to be one of the most important mathematicians because, unlike Diophantus, he was not concerned with number theory, but with algebra as an elementary form of investigation. Al-Chwarizmi introduced the number zero (Arabic: sifr) from the Indian into the Arabic number system and thus into all modern number systems. In his books he gave systematic approaches to solving linear and quadratic equations . The term "algebra" goes back to the translation of his book Hisab al-Jabr wa-l-muqabala .
	Thabit ibn Qurra * 826 in Harran; † February 18, 901 in Baghdad	Thabit ibn Qurra (lat. Thebit) dealt with the generalization of the Pythagorean theorem , the parallels axiom , magic squares and number theory , his theorem on friendly numbers is known .
	Al-Battani * between 850 and 869 in Harran † 929 in Qasr al-Jiss near Samarra	Al-Battani is considered a great mathematician and astronomer of the Islamic Middle Ages. He taught the Arab world the basics of Indian mathematics and the concept of zero . Above all, however, Al-Battani's contribution to trigonometry is significant , in which he was the first to use the sinus instead of the tendons . He was the first to find and prove the law of sines , as well as that the tangent represents the ratio of sine to cosine .
	Abu'l Wafa * June 10, 940 in Buzjan † July 15, 998 in Baghdad	Abu'l Wafa made significant contributions to trigonometry. He was the first to introduce the functions of secans and cosecans and was also the first to use the tangent function . He also suggested defining the trigonometric functions using the unit circle . In addition, he simplified the ancient methods of spherical trigonometry and proved the law of sines for general spherical triangles.
	Alhazen * around 965 in Basra † 1039/40 in Cairo	al-Hasan ibn al-Haitham (lat.Alhazen) was an Arab mathematician, optician and astronomer, he mainly dealt with problems of geometry and through an early application of complete induction he found a formula for the sum of fourth powers and was thus able to do that for the first time Calculate the volume of the paraboloid . Furthermore, he was able to solve the Alhazen problem named after him by geometrically calculating with conic sections in a spherical mirror the point from which an object is projected from a given distance to a given image.
	Omar Khayyam * around 1048 in Nishapur, Province Khorasan † 1123	ʿOmar Chayyām was a Persian mathematician and astronomer who found the solution to cubic equations and their roots through geometric representation. He mainly dealt with the parallel and the irrational numbers . He also created a long dominant work of algebra .
	Leonardo Fibonacci * around 1180 † after 1241	Leonardo da Pisa, called Fibonacci, is considered the most important European mathematician of the Middle Ages. The Fibonacci numbers named after him , which form the Fibonacci sequence , are best known today . By studying the geometry of Euclid, Fibonacci laid down the "summa" of his mathematical knowledge in his main work, the Liber abbaci .
	Li Ye * 1192 in Tahsing, today Beijing † 1279 in the province of Hopeh	Li Ye was a Chinese mathematician in the Song Dynasty . He left behind two important books on the calculation of circles and on calculation methods for reducing geometric problems and other tasks to algebraic equations. His solution method is very similar to the approach that became known much later as the Horner scheme .
	Zhu Shijie * around 1260 † around 1320	Zhu Shijie was one of the most important Chinese mathematicians. Zhu covers about 260 problems in the fields of arithmetic and algebra. His second book The Precious Mirror of the Four Elements from 1303 brought Chinese algebra to the highest level. It includes an explanation of his four element method that can be used to represent algebraic equations with four unknowns. Zhu also explained how to find square roots and added the understanding of series and sequence. At the beginning of the book there is a picture that shows the representation of the binomial coefficients , now called Pascal's triangle .
	al-Kashi * around 1380 in Kashan † June 22, 1429 in Samarkand	In his work ar-Risala al-Muhitiya he determined the circumference of the unit circle ( i.e. twice the number of circles π) from the 3 * 228-corner to 9 sexagesimal places: 6; 16,59,28,01,34,51,46, 14.50, which he converted to 16 decimal places. This is one of the oldest documents on calculating with decimal fractions. He advocated the replacement of fractions in the sexagesimal system with decimal fractions. To make it easier to predict planetary locations , he built a kind of analog computer , the Tabaq-al-Manateq , which was constructed like an astrolabe . In France, the cosine phrase is called Théorème d'Al-Kashi in his honor .
	Regiomontanus * June 6, 1436 in Königsberg in Lower Franconia † July 6, 1476 in Rome	Johannes Müller from Königsberg, later called Regiomontanus, was a mathematician, astronomer and publisher of the late Middle Ages. Regiomontanus is considered the founder of modern trigonometry and an early reformer of the Julian calendar .

Early modern age

	Name (life data)	Research area
	Michael Stifel * around 1487 in Esslingen am Neckar † April 19, 1567 in Jena	Michael Stifel was a German theologian, mathematician and reformer. The Arithmetica integra , published in 1554 , which deals with negative numbers, exponents and sequences of numbers, is considered to be Stifel's main mathematical work . He was the first to deal with logarithms and wrote several arithmetic books for everyday use.
	Gerolamo Cardano * September 24, 1501 in Pavia † September 21, 1576 in Rome	Gerolamo Cardano was an Italian doctor, philosopher and mathematician. Cardano made important discoveries in relation to both probability and complex numbers . Cardano found a general approach to solving cubic equations, the Cardan formulas named after him . The cardan joint is named after him.
	François Viète * 1540 in Fontenay-le-Comte † December 13, 1603 in Paris	François Viète (Vieta) was a French lawyer and mathematician. The use of letters as variables in mathematical notation goes back to Viète . Actually, mathematics was just a sideline for him, but he became one of the most important and influential mathematicians of his time. In addition, he excelled in the field of trigonometry and did valuable preparatory work for the subsequent elaboration of the infinitesimal calculus. The Vieta phrase is named after him.
	Johannes Kepler * December 27, 1571 in Weil der Stadt † November 15, 1630 in Regensburg	Johannes Kepler was a German natural philosopher, mathematician, astronomer, astrologer and optician. He dealt with the general theory of polygons and polyhedra. He discovered several previously unknown spatial structures and constructed them from scratch, including the regular four-sided star. Johannes Kepler also gave the definition of the antiprism . In addition, he developed the Kepler barrel rule named after him , which allows approximate numerical integration. His most important achievement is the discovery of the laws of planetary motion named after him in ellipses with the sun as the focal point.
	John Wallis * December 3, 1616 in Ashford, Kent † November 8, 1703 in Oxford	John Wallis was an English mathematician. Wallis contributed in his works to the development of the infinitesimal calculus before Newton. In 1656 he led in Arithmetica Infinitorum , in which he published studies on infinite series, the Wallis product .
	Pierre de Fermat * around the end of 1607 in Beaumont-de-Lomagne † January 12, 1665 in Castres	Pierre de Fermat was a French mathematician and lawyer. Fermat made important contributions to number theory , probability theory, variational and differential calculus . After him u. a. named the Fermat numbers as well as the small and large Fermatsche theorem . The latter could only be proven very elaborately in 1993 by Andrew Wiles .
	René Descartes * March 31, 1596 in La Haye / Touraine, France † February 11, 1650 in Stockholm, Sweden	René Descartes was a French philosopher, mathematician and natural scientist. He is best known for his contributions to geometry. The Cartesian coordinate system named after him probably does not go back to him. Around 1640 he made a contribution to solving the tangent problem of differential calculus .
	Blaise Pascal * June 19, 1623 in Clermont-Ferrand † August 19, 1662 in Paris	Blaise Pascal was a French mathematician, physicist, man of letters and philosopher. Pascal provided a number of elementary insights. He dealt with the calculation of probability and examined especially dice games . According to him, this is Pascal's Triangle named, which, however, was not discovered by him; in addition, Pascal's theorem, hexagons inscribed over a conic section.
	Seki Takakazu * 1637/1642? in Fujioka † October 24, 1708	Seki Takakazu was a Japanese mathematician. Takakazu discovered many theorems and theories that were discovered shortly before or only shortly after independently in Europe, and is considered the most important mathematician of Wasan . He made an important contribution to the discovery of determinants . In his work Kaiindai no ho , published in 1685, he describes an old Chinese method for calculating the zeros of polynomials and extends it to find all real zeros. He also discovered the Bernoulli numbers before Bernoulli.
	Jakob I Bernoulli * January 6, 1655 in Basel † August 16, 1705 there	Jakob I Bernoulli was a Swiss mathematician and physicist. He contributed significantly to the development of probability theory as well as to the calculus of variations and to the investigation of power series . Among other things, the Bernoulli numbers are named after him. He is one of the most famous representatives of the Bernoulli family of scholars .
	Gottfried Wilhelm Leibniz * July 1, 1646 in Leipzig † November 14, 1716 in Hanover	Gottfried Wilhelm Leibniz was a German philosopher and scientist, mathematician, diplomat, physicist, historian and librarian. In 1672 Leibniz constructed a calculating machine that could multiply, divide and take the square root. In the years 1672 to 1676 Leibniz developed the fundamentals of infinitesimal calculus . In Leibniz is still common today in differential notation and the integral sign back. He also found the Leibniz criterion named after him , a mathematical convergence criterion for infinite series , and the Leibniz formula , which is used to calculate the determinant of matrices . ${\ displaystyle \ textstyle {\ frac {{\ text {d}} y} {{\ text {d}} x}}}$ ${\ displaystyle \ textstyle \ int {\ text {d}} x}$
	Isaac Newton * January 4, 1643 in Woolsthorpe-by-Colsterworth in Lincolnshire † March 31, 1727 in Kensington	Isaac Newton was an English physicist, mathematician, astronomer, alchemist, philosopher, and administrator. Independently of Leibniz, Newton founded the infinitesimal calculus and made important contributions to algebra . After Newton, in mathematics, among other things, the Newton method is named, and in physics Newtonian mechanics, with the help of which u. a. Kepler's laws could be derived mathematically.
	Johann I Bernoulli * August 6, 1667 in Basel † January 1, 1748 there	Johann I Bernoulli was the younger brother of Jakob I Bernoulli. His areas of work included series , differential equations , curves from the point of view of geometric and mechanical issues, such as the problem of the brachistochrones . Johann I Bernoulli's most famous pupil was Leonhard Euler.
	Leonhard Euler * April 15, 1707 in Basel † September 18, 1783 in Saint Petersburg	Leonhard Euler was one of the most important mathematicians of all; he wrote a total of 866 publications and his foundational results created new fields in mathematics. Much of today's mathematical symbolism goes back to Euler. In addition to differential and integral calculus, he dealt with differential equations, differential geometry, differential equations , elliptic integrals and the theory of the gamma and beta function . A number of mathematical terms and sentences are named after him. The Euler number e = 2.7182818284590452 ... among the best known.
	Joseph-Louis Lagrange * January 25, 1736 in Turin † April 10, 1813 in Paris	Joseph-Louis Lagrange was an Italian mathematician and astronomer. He worked on the three-body problem of celestial mechanics, the calculus of variations and the theory of complex functions. Lagrange made contributions to the theory of equations in algebra and to the theory of quadratic forms in number theory. The Lagrangian function, which is particularly important in mechanics, comes from him, among others.
	Gaspard Monge * May 9, 1746 in Beaune † July 28, 1818 in Paris	Gaspard Monge was a French mathematician and physicist. He took part in the French Revolution and played an important political role in the republic in 1792. Monge is the founder of the École polytechnique in Paris and has made a name for himself mathematically primarily through the introduction of descriptive geometry .
	Pierre-Simon Laplace * March 28, 1749 in Beaumont-en-Auge in Normandy † March 5, 1827 in Paris	Pierre-Simon Laplace was a French mathematician and astronomer. He was active in many areas of mathematics. He is particularly known for his treatises on probability and game theory . Laplace was the interior minister of France at the time of Napoleon . In addition to a few sentences, the Laplace transformation and the Laplace equation are named after him.
	Adrien-Marie Legendre * September 18, 1752 in Paris † January 9, 1833 there	Adrien-Marie Legendre was a French mathematician. He worked on elliptical integrals and conducted studies on elliptical spheroids. Independently of Carl Friedrich Gauß, he discovered the least squares method in 1806 . Legendre gave a simple proof of the irrationality of π and proved for the first time that π² is also irrational. The Legendre polynomials and the Legendre symbol for square residues or non-residues in number theory are named after him.
	Jean Baptiste Joseph Fourier * March 21, 1768 at Auxerre † May 16, 1830 in Paris	Jean Baptiste Joseph Fourier was a French mathematician and physicist. He dealt with the propagation of heat in solids and found the so-called Fourier series with the help of which he could establish Fourier's law . With the Fourier analysis or Fourier transformation , he laid the foundation for progress in modern physics, it is now crucial in digital communications and communications engineering .

19th century

In the 19th century, mathematics began to develop as an abstract science of its own, detached from physics, for example. New branches of mathematics developed such as B. the function theory . A new strictness in the mathematical argumentation is also characteristic . Cauchy justifies the flawless definition of the limit value and thus placed the analysis on a rigorous basis. Thanks to the authority of Carl Friedrich Gauß , the complex numbers found their full recognition in mathematics. ${\ displaystyle \ epsilon}$

The set theory founded by Georg Cantor and the development of the fundamentals of formal logic, among others by George Boole in England and by Ernst Schröder and Gottlob Frege from Germany, initiated the development of mathematics in the 19th century, the full implications of which only became apparent in the 19th century 20th century began to have an impact.

	Name (life data)	Research area
	Carl Friedrich Gauß * April 30, 1777 in Braunschweig † February 23, 1855 in Göttingen	Carl Friedrich Gauß was a German mathematician, astronomer, geodesist and physicist. Gauss is considered one of the greatest mathematicians in history and was honored for his scientific work during his lifetime. He dealt with almost all areas of mathematics and recognized the benefits of complex numbers very early on . Already in his youth he discovered the constructability of the regular seventeenth-corner with compass and ruler. A large number of procedures, terms and sentences were named after Gauss, e.g. B. the Gaussian elimination method and the Gaussian number plane . The Carl Friedrich Gauß Prize , named after him, is awarded every four years for work in the field of applied mathematics.
	Bernard Bolzano * October 5, 1781 in Prague † December 18, 1848 there	Bernard Bolzano was a Bohemian philosopher, theologian and mathematician. Bolzano carried out basic research in the field of analysis . He was probably the first to construct a function that is continuous everywhere but nowhere differentiable . The Bolzano-Weierstrasse sentence is named after him.
	Augustin-Louis Cauchy * August 21, 1789 in Paris † May 23, 1857 in Sceaux	Augustin-Louis Cauchy was a French mathematician. Cauchy is considered a pioneer of analysis, who further developed the foundations established by Leibniz and Newton and also formally proved the fundamental statements. Many central theorems come from him, especially in function theory . His nearly 800 publications by and large cover the entire spectrum of mathematics of the time. The Cauchy sequences are named after him, as well as the Cauchy-Riemann differential equations, Cauchy's integral theorem and Cauchy's integral formula.
	August Ferdinand Möbius * November 17, 1790 in Schulpforte near Naumburg (Saale) † September 26, 1868 in Leipzig	August Ferdinand Möbius was a German mathematician and astronomer. Möbius wrote numerous extensive treatises and writings on astronomy, geometry and statics . He made valuable contributions to analytical geometry , including a. with the introduction of the homogeneous coordinates and the duality principle, as well as with the geometry of the circular relationships. He is considered a pioneer in topology . The Möbius strip named after him has also become known outside of mathematics.
	Nikolai Ivanovich Lobachevsky * December 1, 1792 in Nizhny Novgorod † February 24, 1856 in Kazan	Nikolai Ivanovich Lobachevsky was a Russian mathematician. He was the first to publish a work that defines a non-Euclidean geometry . In this he also developed a non-Euclidean trigonometry. Another important mathematical achievement of Lobachevsky is the method he developed for the approximate determination of the zeros of polynomials of the nth degree.
	Niels Henrik Abel * August 5, 1802 on the island of Finnøy † April 6, 1829 in Froland	Niels Henrik Abel was a Norwegian mathematician. Abel reformulated the theory of the elliptic integral into the theory of elliptic functions using their inverse functions. He extended the theory to Riemannian surfaces of the higher sex and introduced Abelian integrals . This gave rise to a theory of Abelian functions, to which Abel himself made no contribution. In algebra , the Abelian groups are named after him. The Abel Prize for extraordinary mathematical work is also awarded in his honor .
	Carl Gustav Jakob Jacobi * December 10, 1804 in Potsdam † February 18, 1851 in Berlin	Carl Gustav Jakob Jacobi was a German mathematician. Jacobi's most important work is his theory of elliptic functions; these are doubly periodic meromorphic functions of a complex variable. In this context he introduced the theta functions as brilliantly converging series, and with their help derived new theorems of number theory about sums of squares. He continued to deal with the so-called quadruple periodic functions and carried out studies on the division of circles and on number theoretic applications. The Jacobi matrix (also known as the “functional matrix ”) is named after Jacobi .
	Peter Gustav Lejeune Dirichlet * February 13, 1805 in Düren † May 5, 1859 in Göttingen	Peter Gustav Lejeune Dirichlet was a German mathematician. Dirichlet worked mainly in the fields of analysis and number theory. He proved the convergence of Fourier series and the existence of an infinite number of prime numbers in arithmetic progressions. The Dirichlet set of units of units in algebraic number fields is named after him . Dirichlet took over the chair from Carl Friedrich Gauß after his death in Göttingen .
	Évariste Galois * October 25, 1811 in Bourg-la-Reine † May 31, 1832 in Paris	Évariste Galois was a French mathematician. Despite the short lifespan of 20 years (he fell in a duel), Galois gained posthumous recognition for his work on solving algebraic equations , known as the Galois theory . Fundamental propositions of the group theory - beginning with him - come from him.
	Karl Weierstrasse * October 31, 1815 in Ostenfelde in the Münsterland † February 19, 1897 in Berlin	Karl Weierstrass was a German mathematician who made outstanding contributions to the logically well-founded processing of analysis, such as the - definition of continuity. He also made important contributions to the theory of elliptic functions, differential geometry and calculus of variations. Bolzano-Weierstrass's theorem on bounded number sequences was named after him in analysis , as well as Weierstrass's elliptic functions and Weierstrass '(later Stone-Weierstrass') approximation theorem. ${\ displaystyle \ epsilon}$ ${\ displaystyle \ delta}$
	Pafnuti Lwowitsch Tschebyschow * May 16, 1821 in the village of Okatowo near Moscow † December 8, 1894 in Saint Petersburg	Pafnuti Lwowitsch Tschebyschow (also written Tschebyshev) was an important Russian mathematician of the 19th century. Chebyshev worked in the fields of interpolation , approximation theory , function theory , probability theory, number theory, mechanics and ballistics . The Chebyshev polynomials are named after him . When trying to prove the prime number theorem, he achieved an important partial result.
	Arthur Cayley * August 16, 1821 in Richmond upon Thames, Surrey † January 26, 1895 in Cambridge	Arthur Cayley was an English mathematician . He dealt with a great many areas of mathematics from analysis , algebra , geometry to astronomy and mechanics, but is best known for his role in the introduction of the abstract group concept .
	Charles Hermite * December 24, 1822 in Dieuze (Lorraine) † January 14, 1901 in Paris	Charles Hermite was a French mathematician. Hermite worked in number theory and algebra, on orthogonal polynomials and elliptic functions. Hermite achieved particular fame when he proved in 1873 that Euler's number e is transcendent . Hermite has taught at various Paris universities. His students included Gösta Mittag-Leffler , Jacques Hadamard, and Henri Poincaré . In honor of Hermite u. a. named the Hermitian polynomial .
	Leopold Kronecker * December 7, 1823 in Liegnitz † December 29, 1891 in Berlin	Leopold Kronecker was one of the most important German mathematicians. His research made fundamental contributions to algebra and number theory, but also to analysis and function theory. In the course of time he became a follower of finitism and tried to define mathematics only on the basis of natural numbers . His saying became known: "God made the whole numbers, everything else is human work."
	Bernhard Riemann * September 17, 1826 in Breselenz near Dannenberg † July 20, 1866 in Selasca on Lake Maggiore	Bernhard Riemann was a German mathematician. Riemann was active in the fields of analysis, differential geometry , mathematical physics and analytical number theory . The Riemann Hypothesis named after him is one of the most important unsolved problems in mathematics . The complex-valued Riemann ζ function plays an important role in analytic number theory. The Riemann surfaces, the Riemann geometry and within these the Riemann metric are named after him . After Dirichlet died in 1859, Riemann continued the succession to the chair of Carl Friedrich Gauß .
	Richard Dedekind * October 6, 1831 in Braunschweig † February 12, 1916 there	Richard Dedekind was a German mathematician. Dedekind, who did his doctorate under Gauss, dealt with the clear decomposition of ideals into prime ideals. The important concept of the ideal in a ring, an analogue to the normal divisor of a group, comes from him. A Dedekind cut is a decomposition of the rational numbers into two non-empty subsets A and B, so that every element of A is smaller than every element of B. With the help of these cuts, Dedekind provided one of the exact introductions of the field of real numbers. He also made a decisive contribution to the axiomatics of natural numbers, which Peano later referred to. The definition of an infinite set is named after him, as a set for which a bijective mapping to a real subset exists.
	Georg Cantor * March 3, 1845 in Saint Petersburg † January 6, 1918 in Halle (Saale)	Georg Cantor was a German mathematician. Cantor made important contributions to modern mathematics, in particular he is the founder of set theory . Cantor laid the foundations of the later of 1870 with the so-called point set Benoît Mandelbrot so called fractals . The Cantor point set follows the principle of the infinite repetition of self-similar processes. The Cantor set is considered to be the oldest fractal ever. In honor of Cantor, the Georg Cantor Medal of the same name is awarded for outstanding mathematical work.
	Felix Klein * April 25, 1849 in Düsseldorf † June 22, 1925 in Göttingen	Felix Klein was a German mathematician. Klein achieved significant results in geometry in the 19th century . He has also made an outstanding contribution to the application of mathematics and mathematics didactics . In addition, he was active in the field of function theory. The Klein bottle , the Klein group of four and above all the Klein model of non-Euclidean (hyperbolic) geometry are named after him .
	Sofja Wassiljewna Kowalewskaja January 15, 1850 in Moscow † February 10, 1891 in Stockholm	Sofja Kowalewskaja was a Russian mathematician and the first ever female mathematics professor (1889 Stockholm). Kovalevskaya took private lessons from Weierstrasse because women were not allowed to study at the time. In 1886 she succeeded in solving a special case of the problem of the rotation of solid bodies around a fixed point.
	Henri Poincaré * April 29, 1854 in Nancy † July 17, 1912 in Paris	Henri Poincaré was a French mathematician, theoretical physicist, and philosopher. He developed the theory of automorphic functions and is considered the founder of algebraic topology . Other areas of his work were algebraic geometry and number theory. The Poincaré conjecture has long been considered the most important unsolved problem in topology. Named after him is u. a. the conformal but not conformal Poincaré model of non-Euclidean geometry.

20th century

In order to avoid redundancies, only those mathematicians are included here who have proven to be particularly influential for the further development of mathematics. For other important mathematicians of the 20th century see also Fields Medal and Abel Prize .

	Name (life data)	Research area
	David Hilbert * January 23, 1862 in Königsberg, East Prussia † February 14, 1943 in Göttingen	David Hilbert was one of the most important mathematicians. His work is fundamental in most branches of mathematics and mathematical physics. Much of his work established independent research areas. In 1900 Hilbert presented an influential list of 23 unsolved math problems . Hilbert is considered to be the founder and most exposed representative of the direction of formalism in mathematics. He called for mathematics to be based entirely on a system of axioms that should be demonstrably free of contradictions. This endeavor became known as the Hilbert's program .
	Hermann Minkowski * June 22, 1864 in Aleksotas, then Russia (now Kaunas / Lithuania) † January 12, 1909 in Göttingen	Hermann Minkowski was a German mathematician and physicist. Minkowski expanded the geometry of numbers, where he did pioneering work. His major work on it appeared in 1896 and in full in 1910. It also includes work on convex bodies. In 1907 his second major number-theoretical work, Diophantine Approximations , appeared, in which he gave applications of his geometry of numbers. The Minkowski diagram he developed illustrates the properties of space and time in the special theory of relativity .
	Felix Hausdorff * November 8, 1868 in Breslau † January 26, 1942 in Bonn	Felix Hausdorff was a German mathematician. He is considered a co-founder of modern topology and made significant contributions to general and descriptive set theory, measure theory, functional analysis and algebra. In addition to his job, he also worked as a philosophical writer and man of letters under the pseudonym Paul Mongré. In the topology, the Hausdorff area is named after him.
	Henri Léon Lebesgue * June 28, 1875 in Beauvais † July 26, 1941 in Paris	Henri Léon Lebesgue was a French mathematician. Lebesgue expanded the concept of integral and thus founded the theory of measure . The Lebesgue measure and the Lebesgue integral are named after him . The Lebesgue measure generalized the measures previously used and, like the corresponding Lebesgue integral, became a standard tool in real analysis.
	Luitzen Egbertus Jan Brouwer * February 27, 1881 in Overschie, Netherlands † December 2, 1966 in Blaricum, Netherlands	Luitzen Egbertus Jan Brouwer created fundamental topological methods and concepts and founded intuitionism , which defines a stricter mathematical concept of truth. After him is Brouwer fixed point theorem named.
	Emmy Noether * March 23, 1882 in Erlangen † April 14, 1935 in Bryn Mawr in Pennsylvania, USA	Emmy Noether was a German mathematician and physicist. She is one of the founders of modern algebra. Noether's rings and modules are named after Emmy Noether, and Noether's normalization theorem also bears her name. In the last quarter of the 20th century, Noether's theorem developed into one of the most important foundations in physics.
	Hermann Weyl * November 9, 1885 in Elmshorn † December 8, 1955 in Zurich	Hermann Klaus Hugo Weyl was a German mathematician , physicist and philosopher who is considered to be one of the last mathematical universalists because of his wide range of interests from number theory to theoretical physics and philosophy.
	S. Ramanujan * December 22, 1887 in Erode, India † April 26, 1920 in Kumbakonam, India	S. Ramanujan was an Indian mathematician. Ramanujan was mainly concerned with number theory and has become famous for many sum formulas that contain constants such as the circle number, prime numbers and partition functions .
	Stefan Banach * March 30, 1892 in Cracow † August 31, 1945 in Lemberg	Stefan Banach was a Polish mathematician. He is considered the founder of modern functional analysis . In his doctoral thesis and in the monograph Théorie des opérations linéaires (theory of linear operations), he axiomatically defined those spaces that were later named after him, the Banach spaces . Banach put the final basis for functional analysis and proved many fundamental propositions about the Hahn-Banach theorem , the Banach fixed-point theorem and the uniform boundedness principle .
	Andrei Nikolajewitsch Kolmogorow * April 25, 1903 in Tambov † October 20, 1987 in Moscow	Andrei Kolmogorow was one of the most important mathematicians of the 20th century. He made significant contributions in the areas of probability theory and topology, he is considered to be the founder of algorithmic complexity theory . His most famous mathematical achievement was the axiomatization of probability theory.
	John von Neumann * December 28, 1903 in Budapest † February 8, 1957 in Washington, DC	John von Neumann was a mathematician of Austro-Hungarian origin. John von Neumann made outstanding contributions in many areas of mathematics. Von Neumann developed the theory of algebra of bounded operators in Hilbert spaces, the objects of which were later named after him, Von Neumann algebras and which are used today in quantum field theory and quantum statistics. Von Neumann was a consultant for the army and navy in the USA for ballistic issues and worked on the Manhattan project . He made a decisive contribution to the development of electronic calculating machines.
	Kurt Gödel * April 28, 1906 in Brno † January 14, 1978 in Princeton, New Jersey	Kurt Gödel was a mathematician and one of the most important logicians of the 20th century. He has made significant contributions in the area of predicate logic (decision problem) as well as the classical and intuitionistic propositional calculus . The basic theorems of logic that Gödel proved are named after him: Gödel's completeness theorem and Gödel's incompleteness theorem .
	André Weil * May 6, 1906 in Paris † August 6, 1998 in Princeton	André Weil was a French mathematician. The focus of his work was on the areas of algebraic geometry and number theory, between which he found surprising connections. Weil proved the Riemann Hypothesis for zeta functions on Abelian varieties. Weil formulated the Weil conjectures named after him . Also named after him is the Taniyama-Shimura-Weil conjecture , which states that elliptic curves over the rational numbers are parameterized by modular functions.
	Shiing-Shen Chern * October 28, 1911 in Jiaxing † December 3, 2004 in Tianjin	Shiing-Shen Chern was an American mathematician of Chinese descent whose work played a leading role in the field of differential geometry . He proved Gauss-Bonnet's theorem in the 1940s. The Chern classes (special characteristic classes of complex vector bundles) and the Chern-Simons theory (from a work with James Simons in 1974), which also has many applications in physics, since the invariant form of a Yang mill described in it, are named after him Gauge theory serves as an active functional of a topological quantum field theory.
	Alan Turing * June 23, 1912 in London † June 7, 1954 in Wilmslow	Alan Turing was a British logician, mathematician and cryptanalyst. He created a large part of the theoretical basis for modern information and computer technology . His contributions to theoretical biology also proved to be trend-setting . Today Turing is considered one of the most influential theorists of early computer development and computer science . The predictability model of the Turing machine that he developed forms one of the foundations of theoretical computer science .
	Paul Erdős * March 26, 1913 in Budapest † September 20, 1996 in Warsaw	Paul Erdős was one of the most important mathematicians of the 20th century. Paul Erdős worked with hundreds of colleagues ( Erdős number ) in the fields of combinatorics , graph theory and number theory. Erdős made numerous conjectures and offered cash prizes for the solution of many of them. Independently of Selberg , he succeeded in proving the prime number theorem without using function theory, i.e. only with real analysis.
	Jean-Pierre Serre * September 15, 1926 in Bages de Rosselló, France	Jean-Pierre Serre is one of the leading mathematicians of the 20th century and a pioneer of modern algebraic geometry , number theory and topology and recipient of the Fields Medal and the Abel Prize .
	Alexander Grothendieck * March 28, 1928 in Berlin † November 13, 2014 in Saint-Girons	Alexander Grothendieck was a French mathematician of German descent. He was the founder of his own school of algebraic geometry , the development of which he significantly influenced in the 1960s. In 1966 he was awarded the Fields Medal , generally recognized as the highest honor in mathematics . After he had largely withdrawn from his central position in mathematical life in Paris around 1970, he disappeared completely from the public eye in 1991. Few friends knew of his last whereabouts in the Pyrenees.
	Andrew Wiles * April 11, 1953 in Cambridge	Andrew Wiles is considered one of the most important mathematicians of our time. In 1984, together with the American mathematician Barry Mazur , he proved the main conjecture of the Iwasawa theory about the rational numbers, which he then extended to totally real bodies. In 1994 he and his student Richard Taylor succeeded in proving Fermat's great theorem .
	Grigori Jakowlewitsch Perelman * June 13, 1966 in Leningrad	Grigori Perelman is a Russian mathematician who made pioneering work, particularly in the field of topology . In 2002 he proved the Poincaré conjecture , making him the first and so far only mathematician to have solved one of the Millennium Problems . As a result, he became known far beyond specialist circles because he rejected both the prize money of 1 million dollars awarded for it and the Fields Medal awarded to him in 2006 . Perelman has been living in seclusion in St. Petersburg for many years .

literature

Hans Wußing , Wolfgang Arnold: Biographies of important mathematicians , Aulius Verlag & Deubner, ISBN 3-7614-1191-X
Ioan Mackenzie James : Remarkable Mathematicians: From Euler to Von Neumann , Cambridge University Press, ISBN 0-521-81777-3
Siegfried Gottwald (Ed.) U. a .: Lexicon of important mathematicians , Harri Deutsch publishing house, ISBN 3-323-00319-5

Web links

Individual evidence

↑ O'Connor, JJ; Robertson, EF (February 1996). "A history of calculus" . University of St Andrews
↑ according to other sources on February 23

This version was added to the selection of informative lists and portals on October 10, 2007 .

[1] O'Connor, JJ; Robertson, EF (February 1996). "A history of calculus" . University of St Andrews

[2] rding to other sources on February 23