来自IHES教授Pierre Cartier写的关于他的一篇回忆录：http://www.xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf
Once he was received into a favorable milieu, in Nancy, where JeanDieudonn´e, Jean Delsarte, Roger Godement and Laurent Schwartz (all active members ofBourbaki) were attempting to go beyond Banach’s work, he revolutionized the subject,and even, in a certain sense, killed it. In his thesis, defended in 1953 and published in1955, he created from scratch a theory of tensor products for Banach spaces and theirgeneralizations, and invented the notion of “nuclear spaces”. This notion, created inorder to explain an important theorem of Laurent Schwartz on functional operators (the“kernel theorem”), was subsequently used by the Russian school around Gelfand, andbecame one of the keys of the application of techniques from probability theory to problemsfrom Mathematical Physics (statistical mechanics, “constructive” quantum field theory).Grothendieck left this subject, after a deep and dense article on metric inequalities, whichfed the research of an entire school (G. Pisier and his collaborators) for 40 years.
Once he was received into a favorable milieu, in Nancy, where JeanDieudonn´e, Jean Delsarte, Roger Godement and Laurent Schwartz (all active members ofBourbaki) were attempting to go beyond Banach’s work, he revolutionized the subject,and even, in a certain sense, killed it. In his thesis, defended in 1953 and published in1955, he created from scratch a theory of tensor products for Banach spaces and theirgeneralizations, and invented the notion of “nuclear spaces”. This notion, created inorder to explain an important theorem of Laurent Schwartz on functional operators (the“kernel theorem”), was subsequently used by the Russian school around Gelfand, andbecame one of the keys of the application of techniques from probability theory to problemsfrom Mathematical Physics (statistical mechanics, “constructive” quantum field theory).Grothendieck left this subject, after a deep and dense article on metric inequalities, whichfed the research of an entire school (G. Pisier and his collaborators) for 40 years.
