In early August, I was at TIFR Mumbai for an “AI for Math” conference [1]. This is one of many such events happening in mathematics departments all over the world in recent times. Among the speakers was Dinesh Thakur. In his talk, he described how he had received an email from an auto mechanic in France about a conjecture attributed to him [2]. The email came with a disproof of this conjecture about primes over function fields that he had written about in 2015. What was surreal about this incident was that the person sending this counterexample did not even know what finite fields are! He had just asked Claude (Opus 4.8) to find a “precisely stated conjecture about polynomials with some examples worked out and something that can be checked by computations”, quoting Dinesh. Dinesh told us that eventually the author did learn more about the problem via more prompting. The preprint is currently on arXiv [3].
The reaction from the audience was quite dramatic. There was laughter in the room, but also shock and disbelief. Two reactions that I recall were “what does it mean to have any expertise anymore?” and “it’s a great time to be an amateur mathematician”. By mid-October, these stories are becoming more common, and I expect that trend to continue. I would like to present my thoughts about this.
Mathematics is full of delightful stories of outsiders making an impact. The most famous is that of Ramanujan, whose letters to Hardy still bring pleasure to the mathematics community even after repeated readings. It seems to me that every professional mathematician at one point in their career must have gotten an email from a Ramanujan-wannabe. Most of these are bogus emails and we don’t bother replying to them. But now these emails are getting smarter and more intricate because of AI. Firstly, a crackpot with a crazy claim can now instead run his ideas through a language model and spare a mathematician a few bytes of mailbox space. Secondly, a mathematician can receive an interesting piece of mathematics tailor-made to appeal to their taste.
I recently had my Ramanujan-Hardy moment myself when Michael Simkin, who lives in Georgia (the country), sent me a new lower bound on sphere packings in high dimensions. The model’s write-up was an astonishing mess that would be difficult to read for any poor soul having to go through it, perhaps more so for Michael, who is mostly an outsider to research mathematics. He asked AI to recommend a mathematician who could verify the result, and it gave him my name.
When Michael reached out to me, I did get interested. At first, I thought he was Michael Simkin, the lecturer at MIT. But after a few emails I realized this was someone else. The output from the model had nice tricks to make progress on some of the ideas that I had long abandoned. So I asked Michael if he would like to coauthor this with me. I also (with his permission) added a PhD student to this project—Matthias Gröbner (because who owns AI-generated results?). The preprint is now out on arXiv [4].
I wanted to understand what had drawn Michael to this problem, so we talked about it. Michael told me that he had been interested in mathematics since high school. He grew up in Tel Aviv and had even won an IMO bronze medal in his teenage years [5]. Mathematics has kept him going in life, even though his parents could not afford university education for him. Michael is now known for interesting life form constructions in Conway’s Game of Life [6]. For the past few years, he had been living as a digital nomad all over the world before settling in Georgia. These days he works part-time for a brain imaging center. He is proud of his AI-prompting skills and wants to keep helping mathematicians.
I asked Michael what he thought about expertise in mathematics and whether he felt that he could replace mathematicians with his AI chats. He had an answer that I found pretty nice. Coming from a software engineering background, he knows the feeling of AI being able to do the job better than humans. But he adds “as a programmer, I still have skills that are important but I cannot pinpoint what they are”. I guess this is quite close to what mathematicians feel.
The post-AI age could be a good time for mathematicians to reach out to people like Michael. It could be of mutual benefit. Not only do people outside want to understand what the mathematics produced by the models is saying, but we might also need them to understand how the public sees and interacts with mathematics. Human mathematicians should exist to talk about mathematics to humans, and the humans are finally reaching out to us. They are speaking our language and learning about our work at their own pace. I think we should engage with at least some of them as a kind of individual outreach. AI might be taking away some of the fun parts of our jobs, but there might be new opportunities in our mailboxes.
The following are my thoughts as of now, and I expect to keep updating them as interactions between professional and hobbyist mathematicians become more common in the AI era.
It might look as though mathematicians spend most of their time going through the gory details of individual lemmas and propositions in papers. In practice, however, mathematicians often focus on the few parts of a paper that are genuinely novel or interesting, without checking every detail once they are convinced that the result should be true. Much of the communication of mathematical ideas also happens through conversations between mathematicians, who have developed a shared language for talking about what matters in a proof. My advice to hobbyist mathematicians is to be patient with and respectful of this process. Try to understand how mathematicians communicate with each other, and learn to talk about your own ideas in that language. Being imperfect is okay, but trying will earn you a lot of respect.
The goals of hobbyist mathematicians might sometimes seem outrageous or too far removed from those of a professional researcher. They might be especially keen to be the first to prove a theorem, improve a bound, or put a result into the world just to have their name on it. But these could be respectable ambitions and, pre-AI, were (often tacitly) shared by many professional mathematicians. Even when we do not share precisely the post-AI goals of human understanding, there is still an opportunity for collaboration between hobbyists and professionals. Professional mathematicians should be mindful of their own priorities while respecting hobbyists’ expectations.
PS: I used AI for speech-to-text, proofreading, and locating references. I thank Dinesh Thakur for comments on an earlier draft.
Addendum: Michael’s new homepage is [7]
This page was updated on October 19, 2026.
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