Great Figures in Mathematics

Thu, 22 Sep 2022 23:06:37 +0900

Fermat (P. de Fermat, 1601-1665)

A representative French mathematician of the 17th century. He laid the foundation for analytic geometry, probability theory, and differential calculus. He is also the founder of number theory.

Diophantus (Diophantus, c. 207-c. 291)

A Greek mathematician. Famous for the introduction of symbolic notation and the study of rational solutions. His representative work is “Arithmetica”. The field of finding rational solutions to equations is called Diophantine analysis.

Euler (L. Euler, 1707-1783)

The king of mathematics born in Switzerland. He made achievements in every conceivable area of mathematics. He left behind over 700 papers and 45 books.

Legendre (A. M. Legendre, 1752-1833)

A French mathematician. He left numerous achievements in number theory, elliptic integrals, and the problem of gravitational attraction. The term “number theory” originates from his main work, “Essai sur la théorie des nombres”.

Kummer (E. E. Kummer, 1810-1893)

A German mathematician. He achieved great success by applying the number theory of cyclotomic fields to Fermat’s Last Theorem.

Descartes (R. Descartes, 1596-1650)

A highly original French philosopher. His representative works include “Discourse on the Method”, “Geometry”, and “The World”.

Pascal (B. Pascal, 1623-1662)

A French philosopher known for his research in probability theory and fluids. Later, he joined the Jansenists and engaged in religious activities. “Pensées” is his work from that time.

Bachet (C. G. Bachet, 1581-1638)

A French nobleman who studied number puzzles as a hobby. He published a Latin translation of Diophantus’s “Arithmetica” and included his own research as annotations.

Wallis (J. Wallis, 1616-1703)

An English mathematician. In his main work “Arithmetica Infinitorum”, he gave a mathematical form to the concept of limits, contributing to the foundation of calculus.

Brouncker (W. Brouncker, 1620-1684)

An Irish nobleman. The first President of the Royal Society (British Academy). A mathematics enthusiast who interacted with Wallis and others.

Lagrange (J. L. Lagrange, 1736-1813)

An Italian-born French mathematician. He served as the Director of Mathematics at the Berlin Academy as Euler’s successor. He made major achievements in number theory, analytical mechanics, and more.

Siegel (C. L. Siegel, 1896-1981)

A German number theorist. He made numerous contributions to the analytic theory of numbers.

Fibonacci (L. Fibonacci, c. 1175-c. 1250)

An Italian mathematician. In his main work “Liber Abaci”, he used Hindu-Arabic numerals and worked to popularize them. He also discussed congruent numbers in “Liber Quadratorum”.

Baker (A. Baker, 1939-)

An English number theorist. For his contributions to transcendental number theory, he was awarded the Fields Medal along with Heisuke Hironaka.

Poincaré (J. Poincaré, 1854-1912)

A French mathematician known as the last universal mathematician. He left behind outstanding works in automorphic functions, non-Euclidean geometry, differential equations, celestial mechanics, electrodynamics, and scientific essays.

Mordell (L. J. Mordell, 1888-1972)

An American-born mathematician. His parents were immigrants from Lithuania. He published numerous papers on Diophantine equations, but Mordell’s theorem in the theory of elliptic curves is especially famous. Weil extended this to the case of general algebraic curves, leading to an explosive development in arithmetic algebraic geometry.

Weil (A. Weil, 1906-)

A French mathematician of Jewish descent. In his youth, he took an interest in Fermat’s problem and fundamentally revised algebraic geometry with the aim of applying it to number theory, providing a rigorous foundation. He is also known for his writings on the history of mathematics.

Mersenne (M. Mersenne, 1588-1648)

A French Minim friar. He facilitated correspondence among mathematicians in various places. The numbers known as Mersenne numbers were actually conceived by Fermat.

Roberval (G. P. de Roberval, 1602-1675)

A French mathematician. He was almost the only person at the time who held a professorship as a mathematician, and is known for his research on the cycloid.

Abel (N. H. Abel, 1802-1829)

A Norwegian mathematician. He made outstanding achievements such as proving the insolvability of the general quintic equation, the theory of elliptic functions, and the theory of Abelian integrals, but died at a young age.

Jacobi (K. G. Jacob, 1804-1851)

A German mathematician of Jewish descent. He left major achievements in the theory of elliptic functions, theta functions, differential equations, and the calculus of variations. He introduced Abel’s work to the world. He is also known for stating that the purpose of science is for “the honor of the human spirit,” rejecting utilitarianism.

Gauss (C. F. Gauss, 1777-1855)

The king of mathematics born in Germany. Known for his research in number theory, non-Euclidean geometry, geodesy, hypergeometric series, the theory of surfaces, and geomagnetism. He was a perfectionist who is said to have not published his results unless they were perfected to the point where the scaffolding was invisible. His main work is “Disquisitiones Arithmeticae”.

Lamé (G. Lamé, 1795-1870)

A French mathematician. Contributed to the theory of elasticity, heat conduction, etc.

Liouville (J. Liouville, 1809-1882)

A French mathematician. Contributed to differential equations, transcendental number theory, and complex analysis.

Cauchy (A. L. Cauchy, 1789-1857)

A French mathematician. Highly prolific, with many achievements in theoretical physics and mathematics. In France, he is said to be respected as much as Gauss.

Galois (E. Galois, 1811-1832)

A French mathematician. He elucidated Abel’s theorem that equations of degree 5 or higher generally cannot be solved algebraically by introducing the concept of a group. He died young in a duel, which is now known to have been triggered by a trivial issue involving a woman.

Hensel (K. Hensel, 1861-1941)

A German mathematician. A student of Kronecker. He introduced the theory of p-adic numbers (p-adic analysis) into number theory by applying function-theoretic methods.

Hasse (H. Hasse, 1898-1979)

A German mathematician. A student of Hensel, he contributed to the foundation of p-adic analysis and its applications. His work includes the development of class field theory and research on the L-functions of elliptic curves.

Kronecker (L. Kronecker, 1823-1891)

A German mathematician of Jewish descent. Contributed to the theory of elliptic functions, number theory, etc. Known for advocating the arithmetization of mathematics, but his highly subjective personality led him to unfairly criticize his colleague Weierstrass at the University of Berlin and hinder Cantor’s employment, which has given his life a negative image.

Hilbert (D. Hilbert, 1862-1943)

A German mathematician. Left a massive footprint in every field of mathematics, including invariant theory, algebraic number theory, and the foundations of mathematics. The 23 problems he proposed at the International Congress of Mathematicians in Paris (1900) had a major impact on the development of mathematics.

Riemann (B. Riemann, 1826-1866)

A German mathematician. Made profound contributions to the very foundations of mathematics, such as the concept of Riemann surfaces in complex analysis and Riemannian geometry.

Faltings (G. Faltings, 1954-)

A German mathematician. Resolved the Mordell conjecture in 1983.

Wiles (A. Wiles, 1953-)

An English-born mathematician. A leading figure in this field who made major contributions through his research on Iwasawa’s main conjecture, the Birch and Swinnerton-Dyer conjecture, and famously proving Fermat’s Last Theorem.

References

Fermat’s Last Theorem Solved! From Euler to Wiles’ Proof, Kodansha

Mathematician on kenji.blog