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How can you write such an article without mentioning the Grothendieck prime? https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/
by Someone 5y ago
How can you write such an article without mentioning the Grothendieck prime?
https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...:
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.
- danidiaz 5y agoMaybe Grothendieck, like Avicenna's conception of God, only knew particulars "in as much as they are universal". Grothendieck once flunked an exam due to—in his own words— "une erreur idiote de calcul numérique".
- davidivadavid 5y agoFor those who can read French, probably as good a place as any to mention Grothendieck's journal Récoltes et semailles recently got published by Gallimard: https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et-Semailles-I-II https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et...