- Ernst Kummer
Infobox_Scientist

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name = Ernst Kummer

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caption = Ernst Eduard Kummer

birth_date = birth date|1810|1|29|df=y

birth_place =Sorau ,Brandenburg ,Prussia

death_date = death date and age|1893|5|14|1810|1|29|df=y

death_place =Berlin ,Germany

residence =

nationality =

field = Mathematician

work_institution =University of Berlin University of Breslau

Gewerbeinstitut

alma_mater =University of Halle-Wittenberg

doctoral_advisor =Heinrich Scherk

doctoral_students =Georg Frobenius

Lazarus Fuchs

Hermann Schwarz Georg Cantor

nowrap|Hans Carl Friedrich von Mangoldt

known_for =Bessel function s

prizes =

religion =

footnotes =**Ernst Eduard Kummer**(29 January 1810 -14 May 1893 ) was a Germanmathematician . Highly skilled inapplied mathematics , Kummer trained German army officers inballistics ; afterwards, he taught for 10 years in a "Gymnasium" (the German equivalent of high school), where he inspired the mathematical career ofLeopold Kronecker .Kummer was born in

Sorau ,Brandenburg (then part ofPrussia ). He retired from teaching and from mathematics in 1890 and died three years later inBerlin .**Contributions to mathematics**Kummer made several contributions to mathematics in different areas; he codified some of the relations between different

hypergeometric series (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). See alsoKummer's function ,Kummer ring andKummer sum .**Kummer and Fermat's last theorem**Kummer also proved

Fermat's last theorem for a considerable class of prime exponents (seeregular prime ,ideal class group ). His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term 'ideal' arose here. He studied what were later calledKummer extension s of fields: that is, extensions generated by adjoining an "n"th root to a field already containing a primitive "n"throot of unity . This is a significant extension of the theory of quadratic extensions, and the genus theory ofquadratic form s (linked to the 2-torsion of the class group). As such, it is still foundational forclass field theory .**Kummer surface**Kummer also found the Kummer surface, which is a special case of

André Weil 'sK3 surface s (named after the peak in theHimalayas 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 theCalabi-Yau manifold s of dimension two, and have played an important role instring theory .**References*** Eric Temple Bell, "Men of Mathematics", Simon and Schuster, New York: 1986.

* R. W. H. T. Hudson, "Kummer's Quartic Surface", Cambridge, [1905] rept. 1990.

* "Ernst Kummer," in "Dictionary of Scientific Biography", ed. C. Gillispie, NY: Scribners 1970-90.

**External links***

* [*http://primes.utm.edu/notes/proofs/infinite/kummers.html Mathworld, proof of infinite number of primes*]

* [*http://fermatslasttheorem.blogspot.com/2006/01/ernst-eduard-kummer.html Biography of Ernst Kummer*]Persondata

NAME= Kummer, Ernst

ALTERNATIVE NAMES=

SHORT DESCRIPTION= German Mathematician

DATE OF BIRTH=29 January 1810

PLACE OF BIRTH=Sorau ,Brandenburg ,Prussia

DATE OF DEATH=14 May 1893

PLACE OF DEATH=Berlin ,Germany

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