Ernst Kummer  

Ernst Eduard Kummer


Born  29
January 1810 Sorau, Brandenburg, Prussia 
Died  14
May 1893 (aged 83) Berlin, Germany 
Residence  Germany 
Nationality  German 
Fields  Mathematician 
Institutions  University of Berlin University of Breslau Gewerbeinstitut 
Alma mater  University of HalleWittenberg 
Doctoral advisor  Heinrich Scherk 
Doctoral students  Georg Frobenius Lazarus Fuchs Hermann Schwarz Georg Cantor Hans Carl Friedrich von Mangoldt 
Known for  Bessel functions, 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.
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 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. The daughter Marie married the mathematician Hermann Schwarz. Kummer retired from teaching and from mathematics in 1890 and died three years later in Berlin.
Contents 
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). 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 padic 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 2torsion of the class group). As such, it is still foundational for class field theory.
Kummer also found the Kummer surface, which is a special case of André Weil's K3 surfaces , possibly named after the peak in the Himalayas discovered around the time of Weil's work. Another explanation is that K3 stands for the trio of mathematicians Kummer, Kodaira, and Kähler. K3 surfaces are the CalabiYau manifolds of dimension two, and have played an important role in string theory.
Ernst Kummer  

Born 
29 January 1810 Sorau, Brandenburg, Prussia 
Died 
14 May 1893 (aged 83) Berlin, German Empire 
Residence  Germany 
Nationality  German 
Fields  Mathematician 
Institutions 
University of Berlin University of Breslau Gewerbeinstitut 
Alma mater  University of HalleWittenberg 
Doctoral advisor  Heinrich Scherk 
Doctoral students 
Georg Frobenius Lazarus Fuchs Hermann Schwarz Georg Cantor Hans Carl Friedrich von Mangoldt 
Known for  Bessel functions, 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.
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 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. The daughter Marie married the mathematician Hermann Schwarz. Kummer retired from teaching and from mathematics in 1890 and died three years later in Berlin.
Contents 
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). 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 padic 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 2torsion of the class group). As such, it is still foundational for class field theory.
Kummer also found the Kummer surface, which is a special case of André Weil's K3 surfaces , possibly named after the peak in the Himalayas discovered around the time of Weil's work. Another explanation is that K3 stands for the trio of mathematicians Kummer, Kodaira, and Kähler. K3 surfaces are the CalabiYau manifolds of dimension two, and have played an important role in string theory.
