“…It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and André Weil, as well as a proof of the Gauss-Bonnet-Chern theorem based on the Mathai-Quillen construction of Thom forms; the second part presents analytic proofs of the Poincaré-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. …”
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“…Indeed some of the most complex conventions of the mathematical mind have evolved from the study of basic problems of number theory. André Weil, one of the outstanding contributors to number theory, has written an historical exposition of this subject; his study examines texts that span roughly thirty-six centuries of arithmetical work — from an Old Babylonian tablet, datable to the time of Hammurapi to Legendre’s Essai sur la Théorie des Nombres (1798). …”
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“…The careers of a generation of pathbreakers in modern mathematics, such as S.Banach, B.L.van der Waerden and André Weil, were decisively affected by their becoming fellows of the Rockefeller-funded International Education Board in the 1920s. …”
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