Just read a recommendation letter from the main advisor of a very promising job market candidate that was 100 percent AI generated according to Pangram. Don’t do this!!

they’re going to automate you. AI will do your job. it’ll be better than you at everything. when you want to smell a flower it’ll smell for you, better than you ever could. it’ll be the flower too.

In 1974 Deligne proved the last of the four Weil conjectures—an analogue of the Riemann hypothesis in a world where some prime number has been set to zero. While Deligne’s work was celebrated, his doctoral advisor, Grothendieck, was unhappy. Can solving a problem be bad? I think not, but I want to explain my understanding of the story, which in my view sheds some light on the present moment. In his memoir, “Récoltes et Semailles” (Reaping and Sowing), Grothendieck explains his approach to problem solving and mathematics more generally: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, 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 it finally surrounds the resistant substance." He compared a precise mathematical question to a nut, which, rather than being cracked open by a chisel, yields at the perfect time to simple hand pressure once it has been soaked in the ocean of mathematical understanding. According to this account of mathematical progress, solutions, though important, are ancillary to the advance of the rising sea of mathematical understanding. At best they measure it to some extent, but the goal is to raise the water level. Grothendieck had laid out a program to resolve the Weil conjectures: the standard conjectures, which are part of the philosophy of motives. The proof circumvented this program. Deligne characterized Grothendieck's reaction as "he did not care...the proof was a trick" but in fact Grothendieck excoriated Deligne in his memoir, claiming Deligne and others tried to "bury" the theory of motives, and Grothendieck himself. The standard conjectures remain open today. Deligne's result relied on a lot of work that was not yet well-exposited in the literature, around the theory of étale cohomology. Deligne himself wrote an exposition of this in SGA 4.5, and Illusie contributed additional necessary material in SGA 5. Some have referred to this additional work as "thankless," but it was completed. While Grothendieck is one of my heroes, and I find his view of mathematics very appealing, I think he was wrong here. Though the standard conjectures are still open, there is an immense amount of work on the theory of motives. People worked very hard to clarify the issues left unclear by Deligne's argument. And crucially, Deligne followed up on his work with a different proof, in "La conjecture de Weil II," that completely revolutionized arithmetic geometry, in many ways going beyond the philosophy of motives as it existed at that time. I think Grothendieck's view that the first proof Deligne provided was insufficient was, in some sense, correct. But he was wrong about the fact that the theory he so desired, and the attendant quest for understanding, would be abandoned, and that his ideas would be buried. I don't think anything can stop us from trying to understand.