# Ernst Kummer

Ernst Eduard Kummer ( born January 29, 1810 in Sorau, Lower Lusatia, † May 14, 1893 in Berlin) was a German mathematician and university teacher who dealt primarily with number theory, analysis and geometry.

## Life

Kummer was the son of a doctor who died when grief was three years old. He went into Sorau to high school and studied Protestant theology at the Friedrich - University of Halle, with the aim to become a priest, but changed after attending a lecture by Heinrich Ferdinand Scherk to mathematics. In 1831 he passed his state examination and was awarded his doctorate. After grief taught as a secondary school physics and mathematics first in Sorau and from 1832 to 1842 in Legnica. There Leopold Kronecker and Ferdinand Joachimsthal were among his pupils. He published in 1836 a paper on the hypergeometric differential equation in Crelle Journal, which led to a correspondence with Carl Gustav Jacobi and Dirichlet. On Dirichlet's proposal, he was admitted to the Berlin Academy of Sciences in 1839. In 1842 he was with the support of Jacobi and Dirichlet professor at the Silesian Friedrich Wilhelm University. During this time he turned to the theory of numbers. At the time of the Revolution of 1848/1849 he was rector of the University of Breslau. He represented politically conservative views and was an opponent of the revolution. In 1855, he became the successor of Dirichlet ( who moved to a chair in Göttingen ) on whose recommendation at the Friedrich- Wilhelms- University of Berlin. He attended in 1856 that Karl Weierstrass was also called to Berlin - he had a similar career as grief and had been for years a high school teacher -. , And supported the appointment of his former pupil Kronecker 1855 1857/58 and 1865/66 he was dean and 1868 / 69 he was rector of the University of Berlin. Kummer was known for his clear and lively lectures and chatted with Weierstrass in 1861, the first seminar of Pure Mathematics at the University of Berlin. He was a favorite among students high school teacher who also took care personally about his students. With Weierstrass and Kronecker, he established the Royal Commercial Institute, which in 1879 integrated in the TH Berlin. The friendly threesome Kummer- Weierstrass - Kronecker made Berlin for three decades one of the world's leading centers for mathematics, but it was around 1875, tensions between Weierstrass and Kronecker, which also affected grief, as he considered his friend Kronecker. In 1883 he retired because he felt that his memory faded.

From 1863 to 1878 he was secretary of the Department of Mathematics and Physics at the Berlin Academy of Sciences.

Among his doctoral students included Paul Bachmann, Heinrich Bruns, Gotthold Eisenstein ( the proposal of grief received an honorary doctorate in Breslau), Paul Du Bois- Reymond, Georg Cantor, Arthur Moritz Schoenflies, Friedrich Schur, Hermann Amandus Schwarz, Franz Mertens. He promoted mathematician Alfred Clebsch, who qualified as a professor in Berlin, and Lazarus Fuchs, who became his successor in Berlin.

## Work

Grief dealt first with analysis and specifically the hypergeometric differential equation and hypergeometric series in following testing of Carl Friedrich Gauss.

He was known primarily as a number theorist. He dealt with cyclotomic bodies and resulted in 1847 in the study of the ring of integers in an ideal numbers, which later became the Ideal Theory by Richard Dedekind and Kronecker, was one of the foundations of the development of abstract algebra. He lived a perfect figures to ensure these generalized numerical concepts the unique prime factorization in cyclotomic bodies. A motive was the Fermat 's conjecture, in the various proof attempts in the early 19th century failed (in particular grief recognized ) because they mistakenly proceeded from a unique prime factorization in cyclotomic bodies. Kummer was able to prove Fermat 's conjecture with his theory for a ( infinitely ) large number of exponents, such that normal by so-called prime numbers are divisible ( by the prime numbers below 100 are, for example, only three non- regular). But his motivation for the study of number theory were primarily the higher reciprocity laws ( generalizations of the quadratic reciprocity law on higher powers ), whose investigation Gauss and Jacobi ( and Eisenstein ) began and one of the main themes in the development of algebraic number theory were. In 1857 he received the Grand Prize of the Paris Academy of Sciences for his number-theoretic work. The price was originally awarded for work to resolve Fermat 's conjecture - grief kept him for his great progress in this area, without that he had submitted a job. Soon after, he was a correspondent for the Academie des Sciences in 1863 and Fellow of the Royal Society.

Later on, he dealt with radiation systems in connection to William Rowan Hamilton and algebraic geometry (Kummer surface 1864). He wrote about ballistics and taught the subject at the Institute of War.

There are two named after him guesses:

- The assumption of grief and Vandiver that p does not divide the class number of the maximal real sub- body of the p-th cyclotomic field was numerically confirmed by grief for prime numbers up to 200 ( and then later confirmed by Vandiver to 600 and up to much higher numbers, by David Harvey to about ), but remains unresolved.
- Another conjecture of grief over the distribution of values of special cubic Gaußsummen was disproved in 1979 by Roger Heath- Brown and Samuel Patterson.

## Private

Grief of the daughter of Nathan Mendelssohn and Henriette born Izzy was born in his first marriage in 1840 with Ottilie Mendelssohn, married. Ottilie was the cousin of Rebecca Mendelssohn Bartholdy, the wife of the mathematician Peter Gustav Lejeune Dirichlet. His first wife died in 1848. His second wife Bertha, daughter of the reform pedagogues Ludwig Cauer, was the cousin of his first wife. Overall, he had 13 children. The daughter Marie married the mathematician Hermann Amandus Schwarz.