| Ernst Kummer | |
 Ernst Eduard Kummer | |
| Born | 29 January 1810 Sorau, Brandenburg, Prussia |
|---|---|
| Died | 14 May 1893 (aged 83) Berlin, Germany |
| Residence |  Germany |
| Nationality | German |
| Fields | Mathematician |
| Institutions | 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 Hans Carl Friedrich von Mangoldt |
| Known for | Bessel functions |
Ernst Eduard Kummer (29 January 1810 - 14 May 1893) was a German mathematician. Events 904 - Sergius III comes out of retirement to take over the papacy from the deposed Antipope Christopher. Year 1810 ( MDCCCX) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common year Żary (Sorau is a town in western Poland with 39900 inhabitants (2006 Brandenburg ( Lower Sorbian: Bramborska; Upper Sorbian: Braniborska) is one of the sixteen states of Germany. Prussia ( Latin: Borussia, Prutenia; Prūsija Prūsija Prusy Old Prussian: Prūsa) was most recently a historic state Events 1264 - Battle of Lewes: Henry III of England is captured in France making Simon de Montfort the Year 1893 ( MDCCCXCIII) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Berlin is the capital city and one of sixteen states of Germany. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The University of Wrocław (Uniwersytet Wrocławski Universität Breslau Universitas Wratislaviensis is one of nine universities in Wrocław, Poland The Technical University of Berlin ( Berlin Institute of Technology, TUB, TU Berlin, German Technische Universität Berlin) is located Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The Martin Luther University of Halle-Wittenberg (Martin-Luther-Universität Halle-Wittenberg also referred to as MLU, is a public University in the cities of A doctorate is an Academic degree that indicates the highest level of academic achievement Heinrich Ferdinand Scherk ( 27 October, 1798 &ndash 4 October 1885) was a German mathematician notable for his work on Minimal surfaces Ferdinand Georg Frobenius ( October 26, 1849 – August 3, 1917) was a German Mathematician, best-known for his contributions Immanuel Lazarus Fuchs ( 5 May 1833 &ndash 26 April 1902) was a German Mathematician. See also Hermann Schwarz (philosopher (1864&ndash1951 A different Hermann Schwarz was a founder of Rohde & Schwarz, a German manufacturer Georg Ferdinand Ludwig Philipp Cantor ( – January 6 1918) was a German Mathematician, born in Russia. Hans Carl Friedrich von Mangoldt (1854–1925 was a German mathematician who contributed to the solution of the Prime number theorem. In Mathematics, Bessel functions, first defined by the Mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are Canonical Events 904 - Sergius III comes out of retirement to take over the papacy from the deposed Antipope Christopher. Year 1810 ( MDCCCX) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common year Events 1264 - Battle of Lewes: Henry III of England is captured in France making Simon de Montfort the Year 1893 ( MDCCCXCIII) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A mathematician is a person whose primary area of study and research is the field of Mathematics. 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. Applied mathematics is a branch of Mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains Ballistics ( gr βάλλειν ('ba'llein' "throw" is the science of Mechanics that deals with the motion behavior and effects of Projectiles A gymnasium (pronounced with ɡ- in several languages is a type of school providing Secondary education in some parts of Europe, comparable to English grammar Leopold Kronecker ( December 7, 1823 – December 29, 1891) was a German Mathematician and Logician who argued
Kummer was born in Sorau, Brandenburg (then part of Prussia). Żary (Sorau is a town in western Poland with 39900 inhabitants (2006 Brandenburg ( Lower Sorbian: Bramborska; Upper Sorbian: Braniborska) is one of the sixteen states of Germany. Prussia ( Latin: Borussia, Prutenia; Prūsija Prūsija Prusy Old Prussian: Prūsa) was most recently a historic state He retired from teaching and from mathematics in 1890 and died three years later in Berlin. Berlin is the capital city and one of sixteen states of Germany.
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Contributions to mathematics
Kummer made several contributions to mathematics in different areas; he codified some of the relations between different hypergeometric series (contiguity relations). In Mathematics, a hypergeometric series is a Power series in which the ratios of successive Coefficients k is a Rational function 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). In Mathematics, in the field of Complex manifolds a K3 surface is an important and interesting example of a compact complex surface ( Complex dimension In Mathematics, particularly in Algebraic geometry, Complex analysis and Number theory, an Abelian variety is a projective algebraic variety In the mathematical disciplines of Topology and Geometric group theory, an orbifold (for "orbit-manifold" is a generalization of a Manifold. The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar See also Kummer's function, Kummer ring and Kummer sum. In Mathematics, there are several functions known as Kummer's function. In Abstract algebra, a Kummer ring \mathbb{Z} is a Subring of the ring of Complex numbers, such that each of its elements has the 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
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). Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like In Number theory, a regular prime is a certain kind of Prime number. In Mathematics, the extent to which Unique factorization fails in the ring of integers of an Algebraic number field (or more generally any Dedekind domain His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term 'ideal' arose here. In Mathematics, the p -adic number systems were first described by Kurt Hensel in 1897 In Ring theory, a branch of Abstract algebra, an ideal is a special Subset of a ring. He studied what were later called Kummer extensions of fields: that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. In Mathematics, Kummer theory provides a description of certain types of Field extensions involving the adjunction of n th roots of elements of In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division In Mathematics, the n th roots of unity, or de Moivre numbers are all the Complex numbers that yield 1 when raised to a given power 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). In Mathematics, a quadratic form is a Homogeneous polynomial of degree two in a number of variables As such, it is still foundational for class field theory. In Mathematics, class field theory is a major branch of Algebraic number theory.
Kummer surface
Kummer also found the Kummer surface, which is a special case of Andre Weil's K3 surfaces (named after the peak in the Himalayas discovered around the time of Weil's work. André Weil should not be confused with two other mathematicians with similar names Hermann Weyl (1885-1955 who made substantial contributions In Mathematics, in the field of Complex manifolds a K3 surface is an important and interesting example of a compact complex surface ( Complex dimension Another explanation is that K3 stands for the trio of mathematicians Kummer, Kodaira, and Kähler). was a Japanese Mathematician known for distinguished work in Algebraic geometry and the theory of Complex manifolds and as the founder of the Japanese Erich Kähler ( 16 January 1906 - 31 May 2000) was a German Mathematician with wide-ranging geometrical interests K3 surfaces are the Calabi-Yau manifolds of dimension two, and have played an important role in string theory. In mathematics Calabi&ndashYau manifolds are compact Kähler manifolds whose Canonical bundle is trivial String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings
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
- O'Connor, John J. & Robertson, Edmund F. , “Ernst Kummer”, MacTutor History of Mathematics archive
- Mathworld, proof of infinite number of primes
- 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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