#360 — Oct 3, 2026 by Evan Chen

I'm glad that I finally see someone else in math talking about what I described 3.5 years ago in my blog post Everything I need is on the ground. Saw the following passage in Kevin Buzzard's recent post on grief:

As a PhD student of Richard Taylor in the early 1990s, I quickly understood that the statement of the theorem which I would attempt to prove in my thesis relied on a construction of Deligne attaching Galois representations to modular forms. I suggested to Taylor that I first read Deligne’s proof before continuing, and he was quick to shoot down this idea, pointing out that my funding was for 3 years only and I simply did not have enough time to get on top of all of the relevant literature at this point in my career. I never did find the time to read Deligne’s construction, or the proof of the Langlands–Tunnell theorem which was crucial in Wiles’ work, or many of the other things which I needed in my thesis and subsequent work. So do I “understand” my own work? What exactly do we even mean by “human understanding of mathematics”?

This is in contrast to undergraduate (and olympiad) level math:

Of course we all know it means to understand undergraduate-level results; we have taught the courses and checked everything carefully. I am able to explain all of the undergraduate algebra courses which I have ever lectured, right down to the axioms of set theory and also right down to the axioms of type theory. I understand the material in a visceral way.

… Though if I'm being totally honest, there are still some gaps for me there. For example, I never did learn the proof of the eyelid claim used in IMO 2014/6; all I know is that it is not too difficult and it's written in the shortlist packet, but 12 years later I never got around to reading it.