Ernst Kummer facts for kids
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Ernst Kummer



Born 
Ernst Eduard Kummer
29 January 1810 Sorau, Prussia

Died  14 May 1893 Berlin, Brandenburg, Germany

(aged 83)
Nationality  Prussian 
Alma mater  University of Halle (Ph.D., 1831) 
Known for  Bessel functions, Kummer theory, Kummer surface, and other contributions 
Scientific career  
Fields  Mathematics 
Institutions  University of Berlin University of Breslau Gewerbeinstitut Lomonosov University 
Thesis  De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis (1831/1832) 
Doctoral advisor  Heinrich Scherk 
Doctoral students  Gotthold Eisenstein Georg Frobenius Lazarus Fuchs Wilhelm Killing Adolf Kneser Franz Mertens Hermann Schwarz Georg Cantor Hans Carl Friedrich von Mangoldt Adolf Piltz Friedrich Prym 
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
Kummer was born in Sorau, Brandenburg (then part of Prussia). He was awarded a PhD from the University of Halle in 1831 for writing a prizewinning mathematical essay (De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis), which was eventually published a year later.
In 1840, Kummer married 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 (whom he married soon after the death of Ottilie in 1848), Bertha Cauer, 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
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 twodimensional 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 padic ones than to ideal theory as understood later, though the term 'ideal' was invented by Kummer. 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 2torsion of the class group). As such, it is still foundational for class field theory.
Kummer further conducted research in ballistics and, jointly with William Rowan Hamilton he investigated ray systems.
See also
In Spanish: Ernst Kummer para niños
 Kummer configuration
 Kummer's congruence
 Kummer series
 Kummer theory
 Kummer's theorem, on primepower divisors of binomial coefficients
 Kummer's function
 Kummer sum
 Kummer variety
 Kummer–Vandiver conjecture
 Kummer's transformation of series
 Ideal number
 Regular prime
 Reflection theorem
 Principalization
 25628 Kummer – asteroid named after Ernst Kummer