4 ms·
For those unfamiliar with the reference (from http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-p
by davmre 12y ago
For those unfamiliar with the reference
(from http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf):
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.”
- deleted 12y ago[deleted]
- Igglyboo 12y agoI'm not sure I understand what Mumford is alluding to, care to explain?
- deleted 12y ago[deleted]
- billforsternz 12y agoYou or I might try to understand some mathematics by mapping it onto some kind of real-world analog, for example a model or graph or specific example case. This guy was a genius who didn't need to do that.
- masklinn 12y agoHe was a very abstract mathematician, he built and worked with concepts and neither used nor needed numbers much.
- wires 12y agoHis style of thinking seems very categorical, where one does not focus on structure of the objects in question (say prime numbers), rather on the mappings between/from/to them. In fact, from the cat. perspective you need to put extra effort to point out particular objects in your collection (http://ncatlab.org/nlab/show/generalized+element http://ncatlab.org/nlab/show/generalized+element). 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.