Jan Arnoldus Schouten
January Arnoldus Schouten ( born August 28, 1883 Amsterdam ( Nieuweramstel ); † January 20, 1971 in Epe, The Netherlands) was a Dutch mathematician, in particular dealt with the differential geometry and is considered one of the founders of Tensorkalküls.
Life and work
Schouten came from a well known family of shipbuilders and studied electrical engineering at the Technical University Delft and worked for several years in this profession. After an inheritance, which made him independent, he began to study mathematics at Leiden University, where he received his doctorate in 1914 on tensor analysis ( by him "Direct Analysis of Affinoren " called ). In the same year he became professor of mathematics in Delft. In 1943 he resigned his professorship and retired ( in the same year he was divorced ). 1948 to 1953 he served as Professor Director of the Mathematics Research Center in Amsterdam. Schouten was also a savvy investor and managed the finances of the Dutch Mathematical Society. Like others before him, he had violent clashes with the topologists and Intuitionists Luitzen Egbertus January Brouwer, eg on the publication of the magazine " Compositio Mathematica ".
Schouten built said of him Ricci calculus building of tensor analysis, and applied it in physics at ( General Theory of Relativity, he wrote, for example, an essay cosmologist Alexander Alexandrovich Friedmann unified field theories and corresponded with Wolfgang Pauli ). He discovered independently in 1915 by Tullio Levi -Civita the Levi- Civita connection in Riemannian geometry, but published his discovery a year after Levi -Civita. In a subsequent priority dispute his compatriot Brouwer even took position against him. In the 1920s and 1930s, he took after Hubert backers a central role as mediator between mathematicians and physicists Albert Einstein and the other investigated generalizations of the theory of relativity ( Unified field theories ).
He also studied projective and conformal differential geometry ( he discovered the Kähler manifolds, two years before Erich Kähler ).
In 1922 he published his book The Ricci calculus on tensor analysis, in which he used the more elegant methods of Gregorio Ricci and Levi- Civita Curbastro held its initial very cumbersome notation - Schouten reported to have said later to Hermann Weyl, he could the author of this work - namely his early work on the tensor calculus - strangle.
Schouten was President of the International Congress of Mathematicians in 1954 in Amsterdam.
Among his doctoral students included Albert Nijenhuis and Dirk Struik, Schouten spread the ideas, especially in the United States. John Haantjes was also his student, assistant and close collaborator.
Writings
- Basics of vector and Affinoranalysis. Teubner, Leipzig, 1914.
- On the Determination of the Principle Laws of Statistical Astronomy. Kirchner, Amsterdam 1918.
- The Ricci calculus. Julius Springer, Berlin 1924, English 2nd Edition 1954
- Dirk Struik: Introduction to the new methods of differential geometry. 2 volumes, Noordhoff, Groningen 1935-38.
- With W. Van der Kulk Pfaff 's Problem and Its Generalizations. Chelsea Publishing Co., New York 1969.
- Tensor Analysis for Physicists. 2nd Edition, Dover Publications, New York, 1989.