Affinor - Works By Schouten

Works By Schouten

Schouten's name appears in various mathematical entities and theorems, such as the Schouten tensor, the Schouten bracket and the Weyl–Schouten theorem.

He wrote Der Ricci-Kalkül in 1922 surveying the field of tensor analysis.

In 1931 he wrote a treatise on tensors and differential geometry. The second volume, on applications to differential geometry, was authored by his student Dirk Jan Struik.

Schouten collaborated with Élie Cartan on two articles as well as with many other eminent mathematicians such as Kentaro Yano (with whom he co-authored three papers). Through his student and co-author Dirk Struik his work influenced many mathematicians in the United States.

In the 1950s Schouten completely rewrote and updated the German version of Ricci-Kalkül and this was translated into English as Ricci Calculus. This covers everything that Schouten considered of value in tensor analysis. This included work on Lie groups and other topics and that had been much developed since the first edition.

Later Schouten wrote Tensor Analysis for Physicists attempting to present the subtleties of various aspects of tensor calculus for mathematically inclined physicists. It included Paul Dirac's matrix calculus. He still used part of his earlier affinor terminology.

Schouten, like Weyl and Cartan, was stimulated by Albert Einstein's theory of general relativity. He co-authored a paper with Alexander Aleksandrovich Friedmann of Petersburg and another with Václav Hlavatý. He interacted with Oswald Veblen of Princeton University, and corresponded with Wolfgang Pauli on spin space. (See H. Goenner, Living Review link below.)

Schouten was an effective university administrator and leader of mathematical societies. During his tenure as professor and as institute head he was involved in various controversies with the topologist and intuitionist mathematician L. E. J. Brouwer. He was a shrewd investor as well as mathematician and successfully managed the budget of the institute and Dutch mathematical society. He hosted the International Congress of Mathematicians in Amsterdam in early 1954, and gave the opening address. He died in Epe.

Following is a list of works by Schouten.

• Grundlagen der Vektor- und Affinoranalysis, Leipzig: Teubner, 1914.
• On the Determination of the Principle Laws of Statistical Astronomy, Amsterdam: Kirchner, 1918.
• Der Ricci-Kalkül, Berlin: Julius Springer, 1924.
• Einführung in die neueren Methoden der Differentialgeometrie, 2 vols., Gröningen: Noordhoff, 1935–8.
• Ricci Calculus 2d edition thoroughly revised and enlarged, New York: Springer-Verlag, 1954.
• With W. Van der Kulk, Pfaff's Problem and Its Generalizations, Clarendon Press, 1949; 2nd edn,, New York: Chelsea Publishing Co., 1969.
• Tensor Analysis for Physicists 2d edn., New York: Dover Publications, 1989.