I don’t use LLMS. I’m not going to say that you shouldn’t; it’s a choice.
I don’t see the advent of LLMs as an existential challenge to mathematicians. Why would we lose our fascination with deep truths, patterns and connections just because computers can help? That, too, is a choice.
I am continually surprised and disappointed to hear eminent mathematicians speculating on the end of mathematics and on the idea that there would be nothing left for us to do. No matter how powerful the technology becomes, how could that be true? If a theorem gets proved in a forest when nobody is there to hear it, what difference would it make to human understanding? These new things are tools, which humans can choose to use to help them do maths. If a senior mathematician is openly speculating that maths is a dead subject, all they are doing is driving away the young proto-mathematicians who would otherwise be pushing and developing the subject in 20-30 years’ time.
The reason it looks to some as if the end is nigh is that a lot of energy and capital is currently being expended by big companies to produce impressive theorems, independently of the mathematical professoriate, and they are succeeding: I was genuinely interested by the existence of a complex structure on the 6-sphere. Of course, they are doing this to prove to their investors that they have achieved something and that more investment would be welcomed. But if there were no human mathematicians to gawp and tell them how significant are their results, the investors wouldn’t be much impressed. This is the reason for my firm conviction that attempts by mathematicians to provide said companies with benchmarks or open problems to test out their machines are misguided, though I understand they come from well-intentioned efforts to hold these companies accountable to science. The truth is that these companies are accountable only to their investors, and science is a secondary concern.
The biggest existential risk to mathematics is what it has always been: a widespread public belief that mathematics is all solved and what’s the point of it anyway? Whilst the advent of LLMs re-unearths both of these questions, they are much older than LLMs. Of course, we know that maths will never be “all solved” by any finite state automaton (like a human or a computer). Any progress is just pushing back against the infinite cloud of unknowing. The question “what’s the point?” is much more apposite, and should be at the forefront of our minds more often than it is.
If we think maths is a race to prove theorems, the harder the better, then what is the point? Take a paragon of a result like Fermat’s Last Theorem: does it help anyone to know that there are no solutions to ? No, and that’s not the point. Indeed, if an LLM found a counterexample tomorrow, nothing would really change except the stress levels of the global population of number theorists. The problem inspired centuries of mathematical development before it was finally resolved. Whole swathes of algebraic number theory were developed by people frustrated by the fact they couldn’t answer this one, highly specific and ultimately pointless question about triples of integers. The result was a thriving discipline, having deep and surprising connections and interactions with other areas like cryptography. By the time the result was proved, it had served its purpose: mathematics was a richer field which touched the world in more ways. The fact that we now know the answer to the original problem is not the point.
Mathematics, like astronomy, literature, or history, is about helping human understanding to flourish. Of course, LLMs, used well, could help with that. However, these companies are pushing the narrative that maths is a race to prove big-name conjectures, because they believe their technology can excel at that. This is precisely the kind of activity which, seen from the outside, looks wholly pointless. They’re helped in this by the fact that many mathematicians have pushed the same narrative, because that’s how they have motivated themselves to make progress and measured the progress we have made. The whole system of rewards: top journals, top prizes, is dominated by this worldview. No wonder that at the top of mathematics, we find those who are now wondering loudly about the demise of mathematics, or even abandoning the subject themselves.
Whether or not we use the tools they produce, we cannot let these companies, whose interests are orthogonal to our own, dictate how we practice our subject. Letting them do so is a choice. It’s the choice to make promotional videos for AI companies. It’s the choice to hand over your favourite problems to them in exchange for temporary free access to a “frontier model” and then blog breathlessly about the results. It’s the choice to push for institutional subscriptions, when the time comes. It’s the choice to give a sense of inevitabilism and defeat, or pressure and anxiety when you talk to the early career researchers in your department. It’s the choice to say, when they knock down your favourite Clay Problem or Named Hypothesis, that you are now redundant.
Whether or not you use their tools, you can choose not to do any of these things. You can choose to promote a healthy vision for what mathematics will be and should always have been. You can choose how you contribute to the flourishing of human understanding. You can choose to be a mathematician.
Received 1 September 2026.
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