Ernst Kummer

Ernst Kummer

box width = 300px
name = Ernst Kummer

image_width = 220px
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
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 functions
prizes =
religion =
footnotes =

Ernst Eduard Kummer (29 January 1810 - 14 May 1893) was a German mathematician. Highly 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). He retired from teaching and from mathematics in 1890 and died three years later in Berlin.

Contributions to mathematics

Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (contiguity relations). The Kummer surface results from taking the quotient of a two-dimensional 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 and Fermat's last theorem

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 p-adic 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 "n"th root to a field already containing a primitive "n"th root of unity. This is a significant extension of the theory of quadratic extensions, and the genus theory of quadratic forms (linked to the 2-torsion of the class group). As such, it is still foundational for class field theory.

Kummer surface

Kummer also found the Kummer surface, which is a special case of André Weil's K3 surfaces (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 Calabi-Yau manifolds of dimension two, and have played an important role in string theory.


* 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

* [ Mathworld, proof of infinite number of primes]
* [ Biography of Ernst Kummer]

NAME= Kummer, Ernst
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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