Ernst Eduard Kummer

Ernst Kummer and the Introduction of Ideal Numbers

Ernst Kummer and the Introduction of Ideal Numbers

On January 29, 1810, German mathematician Ernst Eduard Kummer was born. One of his major contributions is the introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields.He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes.…
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Karl Weierstrass – the Father of Modern Analysis

Karl Weierstrass – the Father of Modern Analysis

On February 19, 1897, German mathematician Karl Theodor Wilhelm Weierstrass passed away. Weierstrass often is cited as the “father of modern analysis“. He formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. “… it is true that a mathematician who is not somewhat of a poet, will never be a…
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Pierre de Fermat and his Last Problem

Pierre de Fermat and his Last Problem

On January 12, 1665, French lawyer and amateur mathematician Pierre de Fermat, famous for his research in number theory, analytical geometry and probability theory, passed away. He is best known for Fermat’s Last Theorem, which he described in a note at the margin of a copy of Diophantus’ Arithmetica.[4] Pierre de Fermat – Early Years Born on August 17, 1601, into a wealthy French family, Pierre de Fermat grew up in Beaumont…
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Sophus Lie and the Theory of Continuous Symmetry

Sophus Lie and the Theory of Continuous Symmetry

On December 17, 1842, Norwegian mathematician Sophus Lie was born. Lie largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations. He made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. “In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group,…
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Felix Klein and the Klein-Bottle

Felix Klein and the Klein-Bottle

On April 25, 1849, German mathematician and mathematics educator Felix Klein was born. Klein is known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day. Klein also devised the Klein-bottle, a one-sided surface which, if traveled upon, could…
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God made the integers, all the rest is the work of man – Leopold Kronecker

God made the integers, all the rest is the work of man – Leopold Kronecker

On December 7, 1823, German mathematician Leopold Kronecker was born, who worked on number theory and algebra. He criticized Cantor’s work on set theory, and his most cited quote says, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk” (traditionally rendered: “God made natural numbers; all else is the work of man“.) Leopold Kronecker – Early Life Leopold Kronecker was born in Liegnitz, Prussia (now Legnica, Poland) in a wealthy Jewish…
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