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1Jesse_wiedinmyer
I've probably been up way too long, but I can't remember this to save my life. Composite number, in the 30's iirc, that's known as xxxxxxx's Prime, because the mathematician whose name takes the place of the x's once mentioned it as a prime when listing examples. What's the number and who's the mathematician?
3Jesse_wiedinmyer
THANK YOUUUUUUUUUUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
That was driving me batshit.
That was driving me batshit.
5Jesse_wiedinmyer
I think it's actually pointed to as kind of paradigmatic of his thinking. And in some sense, I really don't think anyone's knocking Grothendieck. He's generally considered visionary.
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.” Consider by contrast the Indian mathematician
Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them
more abstract. I don’t think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It’s just very strange. That’s the way his mind worked.” Norbert A’Campo of the University of Basel once asked Grothendieck
about something related to the Platonic solids. Grothendieck advised caution. The Platonic solids are so beautiful and so exceptional, he said, that one cannot assume such exceptional beauty will hold in
more general situations.
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.” Consider by contrast the Indian mathematician
Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them
more abstract. I don’t think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It’s just very strange. That’s the way his mind worked.” Norbert A’Campo of the University of Basel once asked Grothendieck
about something related to the Platonic solids. Grothendieck advised caution. The Platonic solids are so beautiful and so exceptional, he said, that one cannot assume such exceptional beauty will hold in
more general situations.
http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf
6elenchus
Ohhh, I'm loving that.
Is there a good bio that you know of, or another book for a non-mathematician interested in such stuff? I'm happy to plow through equations as long as there's more to the book, but if the book relies on mathematical theory, I won't be able to follow.
Is there a good bio that you know of, or another book for a non-mathematician interested in such stuff? I'm happy to plow through equations as long as there's more to the book, but if the book relies on mathematical theory, I won't be able to follow.
7Jesse_wiedinmyer
Not that I know of off the top of my head. The only one I've read (I think) The Artist and the Mathematician-, which focusses on Bourbaki as a whole, and I found pretty weak. I could be wrong.
