Background
József Kürschák was born on March 14, 1864, in Buda (now Budapest), Hungary. His father, András Kürschák, an artisan, died when his son was six; the boy was very carefully brought up by his mother, the former Jozefa Teller.
Budapest University of Technology and Economics, Budapest, Hungary
Kürschák's mathematical talent appeared in secondary school, after which he attended Budapest University of Technology and Economics (1881-1886), which, although a technical school, also trained teachers of mathematics and physics. There he was a student of Gyula Kőnig and Jenő Hunyady. After graduating, he taught for two years at Rozsnyo, Slovakia. In 1888 he moved to Budapest, where he worked toward the Ph.D., which he received in 1890.
1928
University of Szeged, Szeged, Hungary
Mathematical conference at the University of Szeged, 1928. The first person in the middle row from left to right is József Kürschák.
Budapest University of Technology and Economics, Budapest, Hungary
Kürschák's mathematical talent appeared in secondary school, after which he attended Budapest University of Technology and Economics (1881-1886), which, although a technical school, also trained teachers of mathematics and physics. There he was a student of Gyula Kőnig and Jenő Hunyady. After graduating, he taught for two years at Rozsnyo, Slovakia. In 1888 he moved to Budapest, where he worked toward the Ph.D., which he received in 1890.
Hungarian Academy of Sciences, Budapest, Hungary
In 1897 Kürschák was elected a corresponding, and in 1914 an ordinary, member of the Hungarian Academy of Sciences.
educator mathematician scientist
József Kürschák was born on March 14, 1864, in Buda (now Budapest), Hungary. His father, András Kürschák, an artisan, died when his son was six; the boy was very carefully brought up by his mother, the former Jozefa Teller.
Kürschák's mathematical talent appeared in secondary school, after which he attended Budapest University of Technology and Economics (1881-1886), which, although a technical school, also trained teachers of mathematics and physics. There he was a student of Gyula Kőnig and Jenő Hunyady. After graduating, he taught for two years at Rozsnyo, Slovakia. In 1888 he moved to Budapest, where he worked toward the Ph.D., which he received in 1890.
In 1891 Kürschák was appointed to teach at the Technical University, where he served successively as a lecturer, assistant professor, and professor (1900) until his death.
Kürschák's first paper (1887) concerned the extremal properties of polygons inscribed in and circumscribed about a circle and proved the existence of the extremum. Another paper (1902) showed, in connection with Hilbert’s Grundlagen der Geometric, the sufficiency of the ruler and of a fixed distance for all discrete constructions. Meanwhile, in extending a result of Julius Valyi’s, Kürschák had turned to the investigation of the differential equations of the calculus of variations (1889, 1894, 1896), proved their invariance under contact transformations (1903), and gave the necessary and sufficient conditions - thereby generalizing a result of A. Hirsch’s - for second-order differential expressions to provide the equation belonging to the variation of a multiple integral (1905). These investigations also furthered his interest in linear algebra, aroused by Eugen von Hunyady, an early exponent of algebraic geometry in Hungary, and led to a series of papers on determinants and matrices.
Kürschák’s main achievement, however, is the founding of the theory of valuations (1912). Inspired by the algebraic studies of Julius Konig and by the fundamental work of E. Steinitz on abstract fields, as well as by K. Hensel’s theory of p-adic numbers, Kiirschak succeeded in generalizing the concept of absolute value by employing a “valuation,” which made possible the introduction of such notions as convergence, fundamental sequence, distance function, and limits into the theory of abstract fields. He proved that any field with a valuation on it can be extended by the adjunction of new elements to a “perfect” (i.e., closed and dense in itself) field which is at the same time algebraically closed. Kurschak’s valuation and his method were later developed, mainly by Alexander Ostrowski, into a consistent and highly important arithmetical theory of fields.
In 1897 Kürschák was elected a corresponding, and in 1914 an ordinary, member of the Hungarian Academy of Sciences.
Kürschák’s mathematical interests were wide, and he had the ability to deal with various kinds of problems. He was also a versatile and thought-provoking teacher.
Kürschák probably was married, but his wife's name is not known.