5 ms·

I'm sure you didn't mean to imply this, but Grothendieck definitely used his new structures to prove some hard theorems.

• eigenvalue 2y ago
  This reminds me of the Grothendieck quote about his approach to solving problems (in contrast with Erdős, who I suppose in this analogy would look for a big hammer with which to smash the nut open quickly!): “I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise, you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marble, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.”
• vinnyvichy 2y ago
  With the caveat that Deligne (?) complained that his work was too moral, ie, a lot of crucial details had to be put in by others to prove anything nontrivial.