Ernst Kummer

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Ernst Kummer
ErnstKummer.jpg
Ernst Eduard Kummer
Born (1810-01-29)29 January 1810
Sorau, Prussia
Died 14 May 1893(1893-05-14) (aged 83)
Berlin, Brandenburg, Germany
Residence Germany
Nationality Prussian
Fields Mathematician
Institutions University of Berlin
Humboldt-Universität zu Berlin
University of Breslau
Gewerbeinstitut
Lomonosov University
Alma mater University of Halle-Wittenberg
Doctoral advisor Heinrich Scherk
Doctoral students Gotthold Eisenstein
Georg Frobenius
Lazarus Fuchs
Hermann Schwarz
Georg Cantor
Hans Carl Friedrich von Mangoldt
Adolf Piltz
Known for Bessel functions, Kummer theory, Kummer surface, and other contributions

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.

Life[edit]

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.

Mathematics[edit]

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). See also Kummer's function, Kummer ring and Kummer sum.

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.

Publications[edit]

See also[edit]

References[edit]

  1. ^ a b Mazur, Barry (1977). "Review: Kummer, Collected Papers". Bull. Amer. Math. Soc. 83 (5): 976–988. doi:10.1090/s0002-9904-1977-14343-7. 
  • Eric Temple Bell, Men of Mathematics, Simon and Schuster, New York: 1986.
  • R. W. H. T. Hudson, Kummer's Quartic Surface, Cambridge, [1905] rept. 1990.
  • "Ernst Kummer," in Dictionary of Scientific Biography, ed. C. Gillispie, NY: Scribners 1970–90.

External links[edit]