> 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."
"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.
(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.
“This is an important theorem, and a result I’m very proud of.”
[1] https://til.andrew-quinn.me/posts/most-2-digit-numbers-not-d...
[2]: https://en.wikipedia.org/wiki/Interesting_number_paradox
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.
https://mikepierce.github.io/grothendieck-kimchi/translation...
he mentions using whatever herbs he had in a european setting like juniper and rosemary but the canonical herb to add is korean chives and dropwort. never seen juniper or rosemary, frankly.
he does mention that the pepper is a specific variety in korea without exception. this is the korean chili, sun-dried and flaked. it's a very distinctive varietal, the taste will be very different without it
EGA: https://github.com/jcreinhold/ega (https://jcreinhold.github.io/ega/)
SGA: https://github.com/jcreinhold/sga (https://jcreinhold.github.io/sga/)
For more life and times stuff I also suggest Labatut's Cease to Understand the World book and https://theanarchistlibrary.org/library/konstantinos-foutzop...
I hated the movie Oppenheimer for the same reason.
Definitely, but do check the link.. I dug it up originally by trying to track down detail about the nonfiction background that the book is pulling from. Seems like the best short source, but I'd love to hear recs for a good biography. The autobiography that Groth is careful to say is not an autobiography is on my shelf and also in pdf form. Haven't read it yet, but I'm not sure it's the type of thing that's going to cover the descent into madness properly.
https://web.ma.utexas.edu/users/slaoui/notes/recoltes_et_sem...
But I think the biggest "sin" in terms of mixing fact/fiction was mostly implied and not actually stated. What's implied is that Groth saw inside mathematics some kind of terrible truth that motivated him to stop working and withdraw from the world. I don't think it's stated explicitly, but due to proximity with other topics in the book, reader is invited to conclude that there was a discovery of some kind inevitable doom, possibly a super weapon, etc.
We don't know that, but in a lot of ways it might be more surprising if he never thought along those lines. My understanding is that the other limited sources really do say he was talking to God in dreams, preoccupied with apocalyptic visions, became more interested in physics, politics, religion, the problem of evil, hostile entities ambiguously demonic, etc
