31–36 of 36 posts
Earlier quoted context omitted.
I 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.
What's Tao's 27 prime again?
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
One of my favourite Grothendieck stories from 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…
"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.
For anyone interested in Grothendieck's opinions on kimchi … https://mikepierce.github.io/grothendieck-kimchi/translation...
all mention of aekjeot (fish sauce) and saeujeot (tiny shrimp) seems to be elided here. kimchi in coastal regions (and most commercialized korean kimchi) has a strong tendency to have that in, so if you take grothendieck's recipe as is, you won't have the exported korean taste. northern kimchis have diverged materially in addition, due to north korea being fucked up. aekjeot you can just add but the procedure to add…
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.