Kummer, Ernst Edward

Kummer was born in the Prussian city of Zorau (now it is the city of Zary in Poland ), in the family of a doctor. At an early age he lost his father, but the heroic efforts of his mother helped a talented young man to get an education.

In 1828, Kummer entered Halle University , where he studied mathematics, theology and philosophy. In 1831 he graduated from the university. For one of the works on mathematical analysis, the university awarded him a doctorate. For the next 10 years, Kummer taught mathematics and physics at the Lignitz High School (now Lignice). Among his students was Kronecker , with whom he kept a friendship for life. At this time, Kummer attracted the attention of the scientific world by publishing several works on hypergeometric series. In 1839 he was elected to the Berlin Academy of Sciences .

In 1840 he married a cousin Dirichlet (she died in 1848). In 1842, on the recommendation of Dirichlet and Jacobi, Kummer received the chair of a professor of mathematics in Breslau (now Wroclaw ).

In 1855, Kummer moved to Berlin, where he taught at the University of Berlin . Kummer helped Weierstrass move there, after which the Berlin school of mathematics became one of the leading in Europe.

In 1890 he resigned and died 3 years later.

Kummer contributed to analysis , algebraic number theory , geometry, and theoretical mechanics.

In the analysis, he continued the work of Gauss on hypergeometric series. His name bears the famous sign of convergence.

Since 1837, in number theory, he has worked a lot on Fermat’s Great Theorem and proved it for a whole class of simple indicators. He did not solve the problem, but in the course of the study he received many valuable results, for example, discovered ideal numbers and described their unusual properties (1846). For these works he received the Grand Prize of the Paris Academy of Sciences (1857).

Kummer also proved the law of reciprocity for all power residues with a simple exponent. Only Hilbert managed to advance further after several decades.

Among the students of Kummer, in addition to the mentioned Kronecker , there were such well-known mathematicians as P. Dubois-Reymond , P. Gordan , K. G. A. Schwartz and G. Cantor .

• Algebraic number
• Fermat's Great Theorem
• Ideal number
• Kummer ring
• Kummer method
• Sign of Kummer
• Kummer Theory
• Error function

• Kolmogorov A.N., Yushkevich A.P. (Ed.) Mathematics of the 19th century. M .: Science.

• Volume 1 Mathematical Logic. Algebra. Number theory Probability theory. 1978. (link unavailable)
• Volume 2 Geometry. Theory of analytic functions. 1981. (link unavailable)

• John J. O'Connor and Edmund F. Robertson . Kummer, Ernst Edward (English) - biography in the MacTutor archive.

• Mathworld, proof of infinite number of primes
• Biography of Ernst Kummer