I used to think of maths as the one thing LLMs couldn’t do well. While GPT 3.0 would excel in language-based tasks, it would struggle to solve elementary maths problems. But a lot has happened since then. Over the last year, I’ve come to take the idea of using AI as an aid for doing maths more seriously. In fact, I now believe LLMs might prove new theorems with no human guidance within just 3 years.

First, there was the silver medal at International Mathematics Olympiad (IMO). Although AlphaProof and AlphaGeometry 2 took well over 9h, the time given contestants are given, it’s quite a feat: IMO problems require an element of creativity. Not only that - it was able to formalise its solution in Lean. Lean is still a fairly new programming language, and there isn’t nearly as much training data as for other programming languages. The work of the DeepMind team shows two things: firstly, lots of clever people are trying to build AI systems for doing maths; secondly, apparently their current approach works pretty well. However, as of April 2025, you don’t need an AI specifically trained to do maths in order to solve tricky problems: the new o3 and o4 mini models achieve impressive performance in the American Invitational Mathematics Examination (AIME). What if we use RL to build AI systems specialised in more advanced topics? Perhaps these AIs might prove new theorems. Even if they don’t, they might provide researchers with insights.

Next, several top-gun mathematicians think AI might transform maths research in the next decade. Most notably, Terence Tao has highlighted ways in which machines can help human mathematicians. Here’s from a blog post of Tao:

“I could feed GPT-4 the first few PDF pages of a recent math preprint and get it to generate a half-dozen intelligent questions that an expert attending a talk on the preprint could ask. I plan to use variants of such prompts to prepare my future presentations or to begin reading a technically complex paper.”

In this report from Epoch AI, Richard Borcherds seems equally optimistic about the possibilities of using, predicting that AI might even surpass human mathematicians within 10 years. Overall, I think we’re starting to see a cultural shift in the maths community. People are recognising that AI is a huge deal.

Finally, I observed that 40% of students in the library seem to have a Chat-GPT tab open at all times. These are students doing STEM subjects, such as maths and physics. This seems like an important data point (and this isn’t just because I’m giving more weight to first-hand experience). LLMs are transforming the way students learn, and these are the people who will go on to do research in a couple of years. Chances are we won’t stop using LLMs just because the material becomes more niche. Even if you receive a hallucinatory answer, the LLM might reference a relevant concept, helping you get unstuck. I’m using Chat-GPT for my own studies, and I’m impressed by its explaining abilities. Basically, it can easily handle any concept you’ll come across in a master degree in mathematics. I’ve also prompted Chat-GPT to distill the key ideas from more recent papers and found its responses very helpful.

All in all, I’ve come to shorten my AI timelines quite a bit. But rather than thinking “Will I ever find a job?”, I find myself thinking “What a time to be alive!”