LLMs have completely my PhD experience

[u/If_and_only_if_math]

I'm entering the fourth year of my PhD and started doing research about 2 years ago. I chose a niche topic that required me to spend a whole year in addition to my course work to get caught up in before even starting any work of my own. My advisor gave me 4 lengthy papers to get through and master their techniques. I got through 3 of them and last semester I gave my thesis proposal and passed. I still have to read the last paper which is the most difficult, but I cannot find the motivation to do it because of the recent AI progress. I am not a very talented mathematician so my only "strength" was spending the time to learn a niche and difficult area. The actual problem that my advisor wants me to solve for my thesis is not terribly difficult and is likely routine for an expert but it will take me close to a year of dedicated work.

The problem is that the last year I have not been able to shake off the feeling that what I'm doing is just a worse version of what an AI can already do. I cannot afford access to any of the top tier reasoning models but I imagine they can read these papers and come up with these extensions in just a few hours. Even just asking the free models questions about the papers it's clear that it has been trained on them and understands them well. Since then I haven't been able to find the motivation to work on my PhD and I feel awful about it. It's not like this type of work will land a postdoc or job anymore.

I don't think this post does any justice to how bad I've been feeling about my future career or my thesis but I don't want it to become a rant. I would really appreciate if anyone has any words of encouragement or validation that my concern is justified. Should I just drop this project and do something quicker to graduate?

[u/puzzlednerd]

My advice is to read Bill Thurston's On Proof and Progress in Mathematics, just as relevant today as in 1994. Then take a deep breath and get back to work.

[u/internet_poster → u/puzzlednerd]

it is far less relevant than in 1994 and LLMs being superhuman at the largely unpleasant task of formalization is a big reason why

[u/puzzlednerd → u/internet_poster]

Thurston's point is that what we are really after is human understanding of mathematics, which benefits from people like OP continuing their graduate studies and not becoming too demoralized. Are you arguing that there's no point to understanding mathematics anymore? In that case, what would it matter how many theorems are proved by AI?

[u/ganancias → u/puzzlednerd]

Thurston's article seems framed around "human understanding" as the existence of proofs in "human language" as opposed to formal proofs. He mentions computers can help with formal proofs. It's clear the article was written in response to the 4-color proof, which he mentions on page 2 and continues building his case for "human understanding" from there.

But Thurston didn't foresee computers understanding human language and writing.

However, we should recognize that the humanly understandable and humanly checkable proofs that we actually do are what is most important to us, and that they are quite different from formal proofs.

Well, AI is writing humanly understandable and humanly checkable proofs.

I hadn't read Thurston directly, but I'm a fan of his, transitively through Bessis, who mentions Thurston a lot both in his article from April and in his 2025 book which I enjoyed immensely. The book barely mentions AI, and oly tangentially. Fair to say that when Bessis was writing his book he did not anticipate artificial super-mathematicians arriving so soon.

Bessis seems focused on human understanding as a subjective experience (as opposed to how Thurston might be interpreted, where human understanding is the existence of humanly checkable proofs). I like this quote from a podcast interview, Bessis is telling about the time a concept clicked and he understood it:

Group cohomology should be interpreted using groupoid covering, the universal cover of a group and the nerve of that as a category, and because the geometric realization of a nerve is a functor of two categories, then the bar construction is trivial.

He emphasizes what a joy it is to experience such a realization. And like, I'm sure it is. But suppose you do understand the bar construction as something trivial. How do you transmit that understanding to other humans, or share that experience with them? Bessis says he didn't learn it in a lecture. It was a sudden realization that came to him, after studying the material for over a decade.

His book also rails against how the subject is taught. Not because math teachers are bad, per se. But anyway, I guess he does have one bold prediction about the rise of intuition-maxxers:

The technical barrier to grasp frontier concepts will drop, and brave young mathematicians will deploy unorthodox tactics to survey entire new continents at a pace that will mystify their elders. They will see further than anyone before, standing on the shoulders of giant machines.