5 ms·
One of my favourite Grothendieck stories from <https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/notices/200410/fea-grothendieck
by susam 4mo ago
One of my favourite Grothendieck stories from <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."
- cbolton 4mo agoI had to follow your link to get it: I hadn't realized that 57 is not prime. At least I'm in good company.
- Npovview 4mo agoTake 111 as an example.
- karmakurtisaani 4mo agoIt looks like a prime, but can be caught with the second-simplest test: sum of the digits is 12, which is divisible by 3. Hence it's divisible by 3. (The simplest test being of course if the number is even and bigger than 2) Edit: now that I think about it, probably should not have tried to impose ordering to the simplicity of tests. There's of course the divisibility by 5 test, which is even simpler.
- hiAndrewQuinn 4mo agoIn fact, most 2 digit numbers not divisible by 2, 3, or 5 are prime. [1] The only one that's likely to ruin your day is 7 * 13 == 91, but that's self-defeating because after you think about it long enough 91 falls victim to [2]. [1] https://til.andrew-quinn.me/posts/most-2-digit-numbers-not-divisible-by-2-3-or-5-are-prime/ https://til.andrew-quinn.me/posts/most-2-digit-numbers-not-d... [2]: https://en.wikipedia.org/wiki/Interesting_number_paradox https://en.wikipedia.org/wiki/Interesting_number_paradox
- deleted 4mo ago[deleted]
- seanhunter 4mo agoJohn H Conway proved that the smallest number which looks prime, but isn’t is 91. https://youtu.be/S75VTAGKQpk?si=fCGilXECmCOy7T7R https://youtu.be/S75VTAGKQpk?si=fCGilXECmCOy7T7R “This is an important theorem, and a result I’m very proud of.”
- alkyon 4mo agoI just noticed that it's 60-3 without any divisibility tests. Tao's 27 prime was much more embarassing but understandable as he's no a calculator. Savants are for things like remembering the first million primes. Someone like Tao or Grothendieck can't remeber them beyond 20, but it doesn't mean they can't actuly reason about them.
- karmakurtisaani 4mo agoWhat's Tao's 27 prime again?
- alkyon 4mo agoWas mentioned in a twin thread: "27 is a Tao prime. Terence Tao suggested 27 was a prime number on The Colbert Report in 2014. He was likely very nervous."
- deleted 4mo ago[deleted]
- tensegrist 4mo agothere was some interview where he illustrated the idea of a twin prime pair using 27 and 29
- analog31 4mo agoIt's referred to as the Grothendieck Prime for this reason.
- manfromchina1 4mo ago27 is a Tao prime. Terence Tao suggested 27 was a prime number on The Colbert Report in 2014. He was likely very nervous.
- assemblyman 4mo agoAs a curiosity, the contrast between Grothendieck and Ramanujan is very striking. One famous story about Ramanujan from Wikipedia (https://en.wikipedia.org/wiki/1729_(number) https://en.wikipedia.org/wiki/1729_(number)): "Hardy stated that the number 1729 from a taxicab he rode was a "dull" number and "hopefully it is not unfavourable omen", but Ramanujan remarked that "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways"." They, of course, were very different personalities, doing very different mathematics with very different impacts on the field. I always found it interesting that Ramanujan seemed to be very comfortable with numbers, their properties, patterns (continued fractions) and Grothendieck was very comfortable with structures and their rhythms without paying attention to concrete examples.