> 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.
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...
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/)
Money quote:
> In this paper I argue that the first assertion above is false, the second is dan- gerous, and the third is meaningless.
Articles on his life: https://www.math.columbia.edu/~woit/wordpress/?p=7335
Two Titans (Grothendieck and Witten) - https://www.math.columbia.edu/~woit/wordpress/?p=12868
AMS Math articles on Grothendieck - https://www.math.columbia.edu/~woit/wordpress/?p=78
It is also immediately clear why this plays a role in semantics for logics: although a ring is not that important in logic (I would think), the idea to study a theory through its syntactical consequences turned into semantics is very natural, and exactly what I do for abstraction logic as well, in particular via "valuation spaces". And it has the same property, once you set up everything the right way, things like completeness just automatically flow out of it.
