Contact with Grothendieck

Contact with Grothendieck

[John Duskin]

My first contact with Grothendieck was in the late sixties through a letter to him from a naive grad student (me) asking him if I could come to France and study with his group in Paris as I expected a Canadian post doc which would take me there. In reply, I received a very nice letter from him telling me that I should go to Strasbourg and study with a new student of his, J.-L.Verdier. That the same sort of thing had sent him to Nancy rather than Paris when he was young and he had never regretted it. This I did and learned a hell of a lot.

I  got to know him personally quite well after that in Buffalo when he came here  for two summers in 1970-71 thanks to NSF and the department and (his view) that the IHES was funded by the french military. It was a way that he could fund Survivre. 

Among others, he gave a beautiful series of advanced lectures on the Grothendieck-Teichmuller group  as well as elementary lectures on sheaf theory. Some of these were recorded and were redone more recently by Bill Lawvere . Perhaps now these should become available….

John Duskin
     

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Re: Contact with Grothendieck

[Michael Barr]

I met Grothendieck only once, in the summer of 1971.  There was a NATO-sponsored logic conference in, I think, England and some people decided to sponsor a counter conference that would have no connection with anything military.  It was held in a private boarding school in a town called Uldum, Denmark which is something like 50 km south of Aarhus.  G. had given up mathematics at that time and agreed to come presumably because it was anti-military. I was spending half of that summer in Aarhus and I had a car, so on the day G. was scheduled to speak, I got in my car and drove down.  His talk was  interesting.  As I recall, he stated the Giraud axioms for a topos and then said that to him, they looked an awful lot like set theory and logicians should study them from that point of view.  Maybe he said intuitionistic set theory; I don't recall.  Well the Giraud axioms didn't--and don't--look much like set theory to me.  So at the end of his talk I asked him if he was  familiar with the Lawvere-Tierney axioms for a topos, which looked a lot more like set theory than the Giraud axioms.  He said that he didn't know what they were and asked me to come to the board and explain them.  Which I did (I added complete and cocomplete to recover the original definition that  G. had used).  He agreed that looked a lot more like set theory.  A few logicians did study toposes, but whether they were motivated by G.'s lecture,  I can't tell you.  After that we had an hour-long discussion of Survivre, which didn't convince me.

Bill can correct me if I am wrong, but I recall that at the Nice meeting a year earlier, Bill had tried to tell him about elementary toposes, but G. wasn't interested in anything mathematical.

Michael



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