Ernst Kummer | |
|---|---|
 | |
| Born | Ernst Eduard Kummer (1810-01-29)29 January 1810 |
| Died | 14 May 1893(1893-05-14) (aged 83) Berlin,Brandenburg,Germany |
| 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 Germanmathematician. Skilled inapplied mathematics, Kummer trained German army officers inballistics; afterwards, he taught for 10 years in agymnasium, the German equivalent of high school, where he inspired the mathematical career ofLeopold Kronecker.
Kummer was born inSorau,Brandenburg (then part ofPrussia). He was awarded a PhD from theUniversity of Halle in 1831 for writing a prize-winning mathematical essay (De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis), which was published a year later.
In 1840, Kummer married Ottilie Mendelssohn, daughter of Nathan Mendelssohn and Henriette Itzig. Ottilie was a cousin ofFelix Mendelssohn and his sister Rebecca Mendelssohn Bartholdy, the wife of the mathematicianPeter 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 mathematicianHermann Schwarz. Kummer retired from teaching and from mathematics in 1890 and died three years later in Berlin.
Kummer made several contributions to mathematics in different areas; he codified some of the relations between differenthypergeometric series, known as contiguity relations. TheKummer surface results from taking the quotient of a two-dimensionalabelian variety by the cyclic group {1, −1} (an earlyorbifold: it has 16 singular points, and its geometry was intensively studied in the nineteenth century).
Kummer also provedFermat's Last Theorem for a considerable class of prime exponents (seeregular prime,ideal class group). His methods were closer, perhaps, top-adic ones than toideal theory as understood later, though the term 'ideal' was invented by Kummer. He studied what were later calledKummer extensions offields: that is, extensions generated by adjoining annth root to a field already containing a primitiventhroot of unity. This is a significant extension of the theory of quadratic extensions, and the genus theory ofquadratic forms (linked to the 2-torsion of the class group). As such, it is still foundational forclass field theory.
Kummer further conducted research inballistics and, jointly withWilliam Rowan Hamilton he investigatedray systems.[1]
Media related toErnst Kummer at Wikimedia Commons
