Wow, I swear I was just wondering last night if he was still alive or not, as I was reading about him in Serge Lang's Algebra. Personal coincidence for me.
May we never forget the Grothendieck prime, 57.
May we never forget the Grothendieck prime, 57.
One striking characteristic of Grothendieck’s
mode of thinking is that it seemed to rely so little
on examples. This can be seen in the legend of the
so-called “Grothendieck prime”. In a mathematical
conversation, someone suggested to Grothendieck
that they should consider a particular prime number.
“You mean an actual number?” Grothendieck asked.
The other person replied, yes, an actual prime number.
Grothendieck suggested, “All right, take 57."
But Grothendieck must have known that 57 is not
prime, right? Absolutely not, said David Mumford
of Brown University. “He doesn’t think concretely.”Grothendieck certainly knew what it means for p to be prime. I don't know, but maybe his thoughts went along the line of "primes are some substructure of the natural numbers and such and such changes happen in the functions that we can build on them".
So he was obviously able to speak about some collection of primes, yet whether an actual number is prime he probably doesn't think much about.