By user 170039


2019-04-13 05:55:22 8 Comments

Disclaimer. This question was already asked in Mathematics Stack Exchange (see the link here). I wanted the question to be migrated here but I was told by a moderator that a question that old is impossible to migrate (something which I didn't know earlier).


Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found,

An anecdote survives about Grothendieck's arrival in Nancy: the story of his rude reception at the hands of Dieudonné when, on their very first contact, he showed him a dense handwritten manuscript on "generalized integrals". He had already mentioned this work in writing to Dieudonné, and had received a warm and friendly response in which Dieudonné praised his "ardor for mathematics". But Dieudonné's initial receptiveness did not outlast a first look at the actual text. Those who recall this incident (or rather, who recall Dieudonné's telling them about it) claim that Dieudonné gave Grothendieck a rather sharp dressing down, finding that the work displayed a reprehensible tendency to gratuitous generality.

Later it is also mentioned that (as Schwartz recounts in his autobiography),

He first gave Dieudonné an article of fifty or so pages, on "Integration with values in a topological group". It was correct, but absolutely uninteresting. Dieudonné, with the (always temporary) aggressiveness he was capable of, gave him a memorable scolding, claiming that one shouldn't work that way, generalizing just for the pleasure of generalizing. The problem one considered had to be difficult, and applicable to the rest of mathematics (or other sciences); his results would never be useful to anyone for anything.

Questions.

  1. Does anyone know how Grothendieck treated the problem of integration with values in a topological group which he submitted to Dieudonné (I can't seem to find anything on internet)?

  2. Why was Grothendieck's work on "Integration with values in a topological group" has been referred to as "would never be useful to anyone for anything" by Dieudonné?

  3. Has there been any future research on this topic?

  4. Where can I find (if possible at all) Grothendieck's original paper in the internet?

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