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.

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 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.

Related Topics:
Fermat's last theorem - Regular prime - Ideal class group - P-adic - Ideal theory - Kummer extension - Fields - Root of unity - Quadratic form - Class field theory

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