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Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a gymnasium, the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker.
Kummer was born in Sorau, Brandenburg (then part of Prussia). Kummer was first married to Ottilie Mendelssohn, daughter of Nathan Mendelssohn and Henriette Itzig. Ottilie was a cousin of Felix Mendelssohn and his sister Rebecca Mendelssohn Bartholdy, the wife of the mathematician Peter Gustav Lejeune Dirichlet. His second wife, Bertha, was a maternal cousin of Ottilie. Overall, he had 13 children. His daughter Marie married the mathematician Hermann Schwarz. Kummer retired from teaching and from mathematics in 1890 and died three years later in Berlin.
Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series, known as contiguity relations. The Kummer surface results from taking the quotient of a two-dimensional abelian variety by the cyclic group {1, −1} (an early orbifold: it has 16 singular points, and its geometry was intensively studied in the nineteenth century).
Kummer also proved Fermat's last theorem for a considerable class of prime exponents (see regular prime, ideal class group). His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term 'ideal' arose here. He studied what were later called Kummer extensions of fields: that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. This is a significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms (linked to the 2-torsion of the class group). As such, it is still foundational for class field theory.
Kingdom of Prussia, Gdańsk, Lutheranism, House of Hohenzollern, Hamburg
Logic, Set theory, Statistics, Number theory, Mathematical logic
Berlin, North Rhine-Westphalia, Hamburg, France, United Kingdom
Berlin, German Empire, Margraviate of Brandenburg, Hamburg, German Confederation
Erich Kähler, Mathematics, K2, String theory, Ernst Kummer
Mathematics, Carl Friedrich Gauss, University of Oxford, Bilateral hypergeometric series, Leonhard Euler
Berlin, Abraham Mendelssohn Bartholdy, Felix Mendelssohn, Joseph Mendelssohn, Moses Mendelssohn
Moscow, Russia, Mathematics, Berlin, Chess
Number theory, Fermat's last theorem, Ernst Kummer, Cyclotomic polynomial, Carl Friedrich Gauss