Jurjen Koksma

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Jurjen Ferdinand Koksma (born April 21, 1904 , Schoterland ; † December 17, 1964 , Amsterdam ) was a Dutch mathematician who worked in the field of analytical number theory , especially Diophantine approximation .

Koksma received his doctorate in 1930 from the University of Groningen on the subject of Over stelsels Diophantische ongelijkheden (On systems of Diophantine inequalities). His doctoral supervisor was Johannes van der Corput . After a six-month stay in Göttingen, Koksma became a professor at the Free University of Amsterdam in October 1930 , where, together with the physicist Johannes Gerardus Sizoo, he began to set up the newly founded faculties of mathematics and physics. In 1938 and 1953 he was Rector Magnificus of the Free University, in 1954 main organizer of the International Congress of Mathematicians in Amsterdam and from 1954 to 1961 secretary of the natural science department of the Royal Netherlands Academy of Sciences .

In 1946, together with the mathematicians and physicists van Dantzig , van der Corput , Kramers , Minnaert , and Schouten , Koksma founded the mathematical center ( Mathematisch Centrum ) in Amsterdam, which is now called Centrum Wiskunde & Informatica (CWI).

Koksma's best-known work is the book Diophantine Approximations , which was published in 1936 in the series Results of Mathematics and its Frontier Areas at Julius Springer Verlag in Berlin and gave a comprehensive overview of the current state of research.

Title page of Koksma's main work

In 1939 he introduced an equivalent class division of real and complex numbers according to transcendent properties to that of Kurt Mahler (who defined S, T, U classes in 1932).

In 1942 Koksma proved the inequality named after him, which was generalized to several dimensions by Edmund Hlawka in 1961 and still plays a major role in the treatment of numerical integration methods with quasi-random numbers (see also uniform distribution modulo 1 , discrepancy and Monte Carlo algorithm ).

Koksma's students include Nicolaas Govert de Bruijn and Lauwerens Kuipers.

Jurjen Koksma had two brothers who were also mathematicians: Jan Koksma (doctorate in 1937 in Groningen) and Marten Koksma. Koksma married Grietje van der Stouwe in 1933, they had five sons and two daughters.

Fonts

Koksma's list of publications contains around 50 mathematical articles, as well as his main work

  • Diophantine Approximations , Springer, Results of Mathematics and its Frontier Areas, 1936 (reprints 1950, 1974, 2002)

and a conference proceedings (together with Lauwerens Kuipers)

  • Asymptotic distribution modulo 1 , Nuffic International Summer School, 1962 (P. Noordhoff, Groningen 1964).

His first two writings date from 1930, namely the

  • Dissertation: Over stelsels Diophantische ongelijkheden (137 pages) and the
  • Inaugural address at the Free University of Amsterdam: Benaderingsproblemen bij irrationale getallen (19 pages).

Koksma's co-authors were (in chronological order) Johannes van der Corput , Jan Popken , Barend Meulenbeld, István Gál ( Steven Gaal ), Paul Erdős , Raphaël Salem and Gerrit Lekkerkerker . He wrote in roughly equal proportions in Dutch, German, French and English - although he only used German until 1942 and English only from 1943.

literature

Individual evidence

  1. ↑ See Arie van Deursen, pp. 183/84.
  2. ↑ See Arie van Deursen, pp. 511/12
  3. ↑ See Joseph I. Naus: A Conversation with Johannes HB Kemperman. In: Statistical Science , Vol. 15, No. 4 (2000), pp. 396-408. This describes the situation at the Free University of Amsterdam from 1941 to 1945 and the early days of the Mathematical Center. Although Kemperman worked primarily in the field of statistics, he also wrote a series of research articles with van der Corput in 1949.
  4. ↑ About this book, for example, Paul Erdős says: Problems and results on diophantine approximations. In: Compositio Mathematica , Volume 16 (1964), pp. 52-65: "The older literature on this subject (until about 1935) is treated in the excellent book of Koksma. The more recent literature is discussed in a very interesting paper of Cigler and Helmberg. “This refers to the article Johann Cigler / G. Helmberg: Recent developments in the theory of equal distribution. In: Annual report of the DMV , 64 (1961).
  5. ↑ JF Koksma: Een algemeene stelling uit de theorie der gelijkmatige verdeeling modulo 1. In: Mathematica B (Zutphen) , Volume 11 (1942/1943), pp. 7-11.
  6. ↑ See e.g. B. Harald Niederreiter: Random Number Generation and Quasi-Monte Carlo Methods. SIAM (1992)
  7. ^ Kuipers wrote the book Uniform Distribution of Sequences , John Wiley, New York (1974) together with Harald Niederreiter .
  8. ↑ Source: Zentralblatt der Mathematik
  9. ↑ There are 65 articles if one counts partial articles that have appeared in successive issues of a magazine as separate articles (examples are the four articles with B. Meulenbeld from 1942, “Sur le théorème de Minkowski, ..., I-IV "). 7 of the 50 articles are introductory, the remaining research articles. Sources: Mathematical Reviews (MR), Zentralblatt der Mathematik (Zbl) and Yearbook on the Progress of Mathematics (JFM).
  10. ↑ Koksma's articles were reviewed in the Mathematical Reviews (MR), Zentralblatt der Mathematik (Zbl) and Yearbook on the Progress of Mathematics (JFM) - among others - by the following mathematicians: Kurt Mahler , Vojtěch Jarník , Theodor Schneider , Hendrik Kloosterman , Oskar Perron , Edmund Hlawka , Raphaël Salem , Paul Erdős , John Cassels , Georg Feigl , Antoni Zygmund , Ivan M. Niven , Steven Gaal , William LeVeque , Hildegard Rothe-Ille , Donald Spencer , Peter Szüsz, which is an interesting insight into number theory Research supplies from 1930 to early 50's.
personal data
SURNAME Koksma, Jurjen
ALTERNATIVE NAMES Koksma, Jurjen Ferdinand (full name)
BRIEF DESCRIPTION Dutch mathematician
DATE OF BIRTH April 21, 1904
PLACE OF BIRTH Scotland
DATE OF DEATH 17th December 1964
Place of death Amsterdam