Ernst Kummer

Ernst Kummer

Infobox_Scientist
box width = 300px
name = Ernst Kummer

|300px
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
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 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.

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


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Ernst Kummer — Ernst Eduard Kummer in den 1870er Jahren. Ernst Eduard Kummer (* 29. Januar 1810 in Sorau; † 14. Mai 1893 in Berlin) war ein deutscher Mathematiker. Nach seinem Studium in Halle unterrichtete Kummer von 1832 bis 1842 am Gymnasium in Liegnitz, wo… …   Deutsch Wikipedia

  • Kummer — may refer to:* Ernst Kummer (1810 1893), mathematician * Kummer s function, one of two functions named for Ernst Kummer * Paul Kummer (1834–1912), taxonomist * Siegfried Adolf Kummer (1899 ?), mysticist * Wolfgang Kummer (bobsleigh), German… …   Wikipedia

  • Kummer sum — In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p , with p congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as… …   Wikipedia

  • Kummer theory — In mathematics, Kummer theory provides a description of certain types of field extensions involving the adjunction of n th roots of elements of the base field.The theory was originally developed by Ernst Kummer around the 1840s in his pioneering… …   Wikipedia

  • Kummer's function — In mathematics, there are several functions known as Kummer s function. One is known as the confluent hypergeometric function of Kummer. Another one, defined below, is related to the polylogarithm. Both are named for Ernst Kummer.Kummer s… …   Wikipedia

  • Ernst Eduard Kummer — in den 1870er Jahren. Ernst Eduard Kummer (* 29. Januar 1810 in Sorau; † 14. Mai 1893 in Berlin) war ein deutscher Mathematiker. Nach seinem Studium in Halle unterrichtete Kummer von 1832 bis 1842 am Gymnasium in Liegnitz, wo unte …   Deutsch Wikipedia

  • Ernst (Name) — Ernst ist ein männlicher Vorname. Inhaltsverzeichnis 1 Herkunft 2 Varianten 3 Namenstag 4 Bekannte Träger des Vornamens // …   Deutsch Wikipedia

  • Ernst Moritz Arndt — (* 26. Dezember 1769 in Groß Schoritz auf Rügen, damals Schwedisch Pommern; † 29. Januar 1860 in Bonn) war ein deutscher Schriftsteller und Abgeordneter der Frankfurter Nationalver …   Deutsch Wikipedia

  • Ernst Thälmann — Ernst Thälmann, 1932 Ernst Thälmann Denkmal in Weimar Ernst Frit …   Deutsch Wikipedia

  • Ernst Heinrich Bruns — (* 4. September 1848 in Berlin; † 23. September 1919 in Leipzig) war deutscher Mathematiker und Astronom, der auch zur Entwicklung der theoretischen Geodäsie beitrug. Bruns studierte zwischen 1866 und 1871 an der Universität Berlin Mathematik,… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”