AI models are making mathematical progress at an unimaginable scale. There’s now a reasonable expectation that soon, we will be able to prove a theorem, or find a counterexample, at the touch of a button.
But the overall reaction of our mathematical community is closer to panic than it is to enthusiasm. AI is perceived as a threat, not just to humanity as a whole (which is a different story) but to mathematics specifically. We are collectively appalled by formally-verified but fully inexplicable proofs, and even more disgusted by companies that churn out one AI-generated (and equally verified) paper after the other without even having a single person on the team able to explain them.
We talk about the good old days when mathematics was about building a community of common understanding, facilitating personal growth, celebrating beauty.
What a feel-good fairy-tale that is!
In fact, our values have always been about who got there first. Collectively speaking, the one thing we, as a mathematical community, have always valued most has been a proof of a hitherto unproven theorem. It was not a nicer proof of a known result, and certainly not a beautiful exposition of a known proof.
You think I’m being cynical? Allow me to argue my point.
Follow the money.
Explaining a proof may have earned you an applause or a compliment. Completing a proof and doing so faster than anyone else is what has always had the potential of getting you a job. Also, when did you last write a grant proposal promising to deepen the communal understanding of an existing proof, or to find a more digestible proof to a proven theorem? How does the amount of funding you have acquired for promising new results compare to the funding you got for explaining existing ones?
Reflect on common behaviour.
What is more likely to keep you up at night? A fellow mathematician threatening to arrive at “your” result ahead of you, or a fellow mathematician having trouble understanding your arguments?
The other day, an eminent mathematician confessed to me over lunch that they worked through their summer holidays to get out a paper with a new construction that they got out of an AI model. Anyone asking the model the same question would get the same ingenious answer, so the logic went, hence they needed to publish this immediately.
On the flip side, I’ve sat through talks where the speaker afterwards, privately, declared “Today I have given a talk that was utterly incomprehensible. I’ve always wanted to give a talk like this.” To be fair, this was a singular, extreme case. But we would not tolerate this kind of behaviour if we really cared so much about a community of common understanding.
Acknowledge past grievances.
Personally, I vividly remember how, at a panel discussion on “Future Directions of Algebraic Topology” at Stanford in 2012, one of the younger members of the audience raised the question: What can we do to make mathematical culture more like music culture, where presenters are valued as much as composers? At that time, the idea of AI was still very much hypothetical. The question was about our very own, human culture.
Read the Leiden declaration.
The Leiden declaration, which has been widely endorsed by the mathematical community, lists the following as one of our five mathematical “values”:
Results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness. These principles ground the merit-based standards to which we aspire in mathematical research.
That is just another way of saying that the one thing that really matters for your standing within the community is that you arrive at a new result first.
So why am I saying this? Because I completely disagree with the notion that AI companies have hijacked our mathematical culture and turned it into something new and unrecognizable. They have not. Quite the opposite. They are playing to our rules. They are even solving our problems, problems that no one else cares about! They have just taken our existing culture to its extreme.
And now, we are disgusted!?
I would argue that what we’re really disgusted by is a key aspect of our own culture, now that we see it more clearly than ever before. We’re disgusted by the idea that getting there first is all that matters.
Let’s be honest about what was and what is. We defined our priorities. AI serves them better than we can. Perhaps, the priorities were off.
Received 25 September 2026.
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