The author is a mathematician and I think to a certain extend the tweet reflects the current panic among (some) mathematicians. So ~~second sentence~~ third paragraph the claim that somehow ai could right now write a phd in physics or sociology is something we don't observe (at the moment). What we observe is, that ai can find counter examples to well established conjectures in mathematics quite well, but the thing is the other fields don't have the kind of well established riddles that currently produce the flashy results in mathematics.

To show my ignorance in mathematics a bit: do you feel that having such neatly defined riddles gives the AI an advantage in solving them?

A lot of Innovations or insights are obvious in hindsight, but no one thought to consider the problem, and put the pieces of the solution together. In this sense a well defined problem is a large portion of the solution as well.

I mention this because I feel AI software agents have a huge advantage due the body of prior work available to them and how provable solutions can be. This I feel gives the impression that the agents are more generally intelligent than they actually are.

Is this another example of that perhaps?

> something we don't observe

That's just lack of observation. Which PhD candidate is going to say "Chat wrote it for me?" We know a lot of academic articles are AI written. And a very, very large part of the student essays. Unless intercepted, they'll end up in the thesis. And in sociology, the texts are so vague, that it becomes even harder to pick out slop.

There are good reasons to assume PhD students see an advantage to using AI, so they will.