Accelerating Mathematics

Summary

Let’s say that someone had a big pot of money, and wanted to use it to accelerate mathematical discovery. How might they go about doing this? The traditional approach Historically it has been governments who have been driving this agenda, with taxpayer-funded institutions such as the NSF (in the US), the EPSRC (in the UK), the ERC (in Europe) and many other national institutions (NSERC, ARC, DFG, JSPS…) typically funding individuals and small teams to work on cutting-edge problems at the boundary of mathematical understanding. These institutions also fund centres and institutes where mathematicians gather for workshops and exchange ideas. The question I want to raise here is: can new advances in technology somehow accelerate the process of growing mathematical knowledge and understanding in different ways to the traditional ones? And I want to argue that right now this is not as easy as it sounds. “Duh just let AI do it” The immediate and unhelpful answer from the AI bros (who may have no understanding of the nature of mathematics) is “this question is not even relevant, AGI will happen within the next few years and then math will be solved”. But this is not what is happening on the ground. Right now there seem to be two relevant technologies poised to help disrupt mathematics: the language model (LLM) and the interactive theorem prover (ITP). There is progress, but there is certainly no “killer app” yet. How are experts using these tools in 2026? Uses of LLMs in mathematics Professional mathematicians seem to be using these tools to do a variety of things. For example: High-level brainstorming for ideas; Literature search; Solving intermediate undergraduate/PhD level questions which arise on the way to harder problems. Amateurs and cranks aim higher, and are currently producing large documents which purport to contain breakthrough results, but which do not survive 5 minutes of expert scrutiny. I continually find it surprising that a non-expert can genuinely believe that they might contribute to research mathematics using only the tools which the experts also have access to. The slop being produced by LLMs is getting better, and I find it extremely depressing ploughing through this kind of stuff, because the AI wants to please, so it wants to prove your theorem for you, even if your theorem is false or not accessible given the tools that humanity currently…