Alexander Nikolayevich Korkin

Alexander Nikolayevich Korkin ( Russian Александр Николаевич Коркин * February 19 ^jul. / 3. March  1837 ^greg. In Schidowinowo, Province of Vologda ; † August 19 ^jul. / 1. September  1908 ^greg. In St. Petersburg ) was a Russian mathematician who mainly dealt with partial differential equations and the geometry of numbers.

Live and act

Although Korkin's father was a wealthy farmer and merchant, he was also a serf in the province of Vologda, about 700 km east of St. Petersburg. He was tutored in the provincial capital of Vologda by Alexander Ivanitsky, a student of Bunjakowski . From 1847 he attended the local grammar school after his father had bought him free. He was a very good student and studied from 1854 at the University of St. Petersburg with Tschebyschow , Osip Iwanowitsch Somow and Bunjakowski mathematics and physics. Since his father had died shortly before and left him penniless, he had to finance his living through private lessons. An essay on the calculus of variations brought him the gold medal of the university in 1856. In 1858 he graduated as a future mathematics teacher and began to teach at the cadet school after he bought himself another amount of money. In 1860 he received his doctorate from Chebyshev and, after winning a competition, began teaching at the university. Due to political unrest, the university was closed shortly afterwards and Korkin was sent abroad to continue studying. In 1862 he visited Paris , where he heard Joseph Liouville , Gabriel Lamé and Joseph Bertrand , and a year later Ernst Eduard Kummer and Karl Weierstrass in Berlin . In 1867 he completed his habilitation in St. Petersburg with a thesis on partial differential equations. In 1868 he became associate professor at the university, in 1873 professor, which he remained until his death. At the same time he taught analysis at the Naval Academy from 1864 to 1900 (as successor to Bunjakowski).

Korkin mainly worked on partial differential equations, but is best known today for his collaboration with his student Yegor Ivanovich Zolotaryov on integral positive definite quadratic forms in several variables (1872, 1873, 1877). They solved a problem from Charles Hermite , who asked about the upper bounds for the minima of such forms as a function of the coefficients and with a fixed discriminant (determinant of the symmetric coefficient matrix). In their first paper of 1872 on quadratic forms in four variables, they refuted a conjecture by Hermite about this upper bound and gave the upper bound instead . Quadratic forms whose minima were relative maxima (again depending on the coefficients) were called extremal by them. For quadratic forms in variables, they showed in 1873 that Hermite's conjectured upper bound was indeed the bound on the minima of some extremal forms, but not all. Korkin also looked at iteration, particularly Abel's functional equation . ${\displaystyle D}$ ${\displaystyle D^{\frac {1}{4}}}$ ${\displaystyle n}$

Korkin's tomb in Saint Petersburg

A definition for the reducedness of a base of a lattice is named after Korkin and Solotarjow (an alternative definition comes from Hermann Minkowski ). With Solotarjew he determined the closest packing of spheres on the grid in 4 and 5 dimensions.

Among his students were Alexei Nikolayevich Krylov , who also succeeded him at the Naval Academy, Dmitrij Grawe and Boris Nikolayevich Delone .

literature

• Delone: The Petersburg School of Number Theory .
• Opolka, Scharlau : From Fermat to Minkowski , Springer 1980
• Daniel S. Alexander: A history of complex dynamics: from Schröder to Fatou and Julia. (Aspects of Mathematics), Vieweg, Braunschweig 1994, ISBN 3-528-06520-6 . Sections 2.3 and 2.5 discuss Korkin's contribution.

Web links

• John J. O'Connor, Edmund F. Robertson :  Alexander Nikolajewitsch Korkin. In: MacTutor History of Mathematics archive .
• Biography (St. Petersburg State University, Russian) ( Memento from September 25, 2006 in the web archive archive.today )
• Article Alexander Nikolajewitsch Korkin in the Great Soviet Encyclopedia (BSE) , 3rd edition 1969–1978 (Russian)http: //vorlage_gse.test/1%3D064695~2a%3D~2b%3DAlexander%20Nikolajewitsch%20Korkin

Individual evidence

1. ↑ Eric Weis stone HyperSphere packings, tungsten Mathworld
2. ↑ Korkin, Zolotareff, Sur les formes quadratiques positives. Math. Ann., Vol. 11, 1877, pp. 242-292