Online Encyclopedia
Ernst Kummer
Ernst Eduard Kummer (29 January 1810 in Sorau , Brandenburg, Prussia - 14 May 1893 in Berlin, Germany) was a German mathematician. Highly 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. He retired from teaching and from mathematics in 1890.
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Contributions to mathematics
Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (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 and Fermat's Last Theorem
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 n-th root to a field already containing a primitive n-th 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.
References
- Eric Temple Bell, Men of Mathematics, Simon and Schuster, New York, 1986.
External link
- Source for more Ernst Kummer information http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Kummer.html