The Evolving Relationship Between AI and Mathematicians
Benjamin Skuse
Last week, my broadband went down for a full five days and I had almost zero mobile data. I thought this situation would provoke an extreme reaction in me. Perhaps I would be tearing my hair out, constantly getting lost, crying out for Google Maps, or be driven mad by my inability to remember the actor who played the bad guy in Under Siege. Or maybe it would feel like heaven, cut off from the inanity of social media and the endless choices being pushed in front of my eyes by entertainment streaming providers. But instead, it was a muted response. I put a little more thought into my day and actions, dusted off my DVD player, and carried on more or less as normal.
Currently, this is exactly how many mathematicians would react if AI were to suddenly disappear from their working lives (at least, the ones who are not already regular Lean users). There would be annoyances in terms of slowing down tasks like literature searches and the dreaded pile of admin in their inbox, but there would be fewer distractions, more opportunity to just stop and think on puzzling mathematical problems. They would largely get on just fine.
But soon, perhaps very soon, AI could become so embedded in the discipline that the thought of conducting mathematics without it might be, well… unthinkable. And this is just the tip of the iceberg, with some predicting a future in which mathematics is conducted with no human in the loop whatsoever.
A Storm Begins to Brew
When this potential future scenario was posited by a host of different speakers at last year’s Heidelberg Laureate Forum, it provoked a strong and sometimes visceral reaction from the young mathematicians in attendance. While one young scientist told me they would be delighted if AI took over and solved the Langlands program or the Riemann hypothesis (joking that they looked forward to a future of leisurely pursuits all funded through universal basic income), others were questioning whether they should continue in mathematics at all, if mathematicians were likely to become surplus to requirements.
Around the exact same time this was happening in Heidelberg, Leiden University in the Netherlands was hosting a conference for around 60 mathematics stakeholders entitled Mechanization and Mathematical Research. There, the same hopes and fears induced by the introduction of AI into mathematical practice were being voiced by leaders in the field.
Some lecture titles from the conference expressed the genuine concern many professors had for their students: “What should students be learning when machines can do the proofs?”, “What do we tell our students about AI?” And others summed up the existential dread many mathematicians were beginning to feel for the entire field of study at the time: “Is Mathematics Obsolete?”, “Will mathematics exist in 2035?”
So moved was a select band of participants by the lectures and conversations at the conference that they formed a smaller working group afterwards to monitor the progress of AI in mathematics and come up with concrete actions to be taken in order for mathematics and mathematicians to continue to flourish in the age of AI.
Six Months That Changed the Game
But a lot happened in the months that followed. In December 2025, HarmonicMath’s Aristotle AI system independently and autonomously completed a simplified version of an Erdős problem that had lain unsolved for 30 years. (This would start a trend that continues to this day of using AI to attempt to solve some of the hundreds of problems posed and left open by legendary Hungarian mathematician Paul Erdős.) In late January 2026, Google DeepMind’s experimental AI system Aletheia autonomously produced, albeit somewhat unremarkable and obscure, publishable PhD-level research results.
February saw Axiom Math’s AI system achieve a similar feat, proving and verifying Fel’s conjecture, while a rival system from Math, Inc. formalized (i.e. formally verified) a 21st Century Fields Medal proof for the first time. Then, in May, a general-purpose AI system from OpenAI disproved an important conjecture in combinatorial geometry (one of the more challenging Erdős problems), a result that would have been deemed worthy of publication in a major mathematics journal had humans been the authors.
It was immediately following this flurry of activity that the Leiden working group finally published the Leiden Declaration on Artificial Intelligence and Mathematics on 2 June 2026. The Declaration is a call to action “to address the challenges posed by the use of artificial intelligence within mathematics research” and urges mathematicians, institutions, governments, and industry to preserve the core values of the discipline – such as scientific integrity, human accountability, open science, rigorous peer review, and research autonomy – as AI technologies become increasingly prevalent.
Within 24 hours of publication, the International Mathematical Union had endorsed the Declaration, more than 1000 people had signed it (at the time of writing, there are 3466 signatories) and major news outlets had covered its publication. It even sparked Nature to publish an editorial calling for other STEM subjects to follow suit.
Charting a Path Forward
Just two months after this landmark call to action, it seems to have had something of an effect. On 1 August, OpenAI cited the Declaration when the company shared a selection of 10 results that resolve or mark substantial progress on long-standing open problems spanning high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics.
Though OpenAI did not share details of its AI model, an internal model named Astra, nor what other problems Astra has been working on, it did openly share the Lean argument the model made for each of the 10 problems in formalized mathematics, and also offered the “model’s narration of its thinking process”: 62 pages detailing how the ideas came together, that they called a “reasoning walkthrough”.
The announcement concluded with the following statement: “We hope the mathematical community will engage deeply with these results, place them in context, and bring the ideas behind them to life through new research and discovery.” Though most likely stated in good faith, an obvious question is: If AI managed to get this far essentially on its own, why can’t AI conduct the new research and discovery that leads on from these results too?
Even more concerning is the level of human input required to produce these results within OpenAI. The announcement freely admits that human researchers “helped prepare the manuscripts and formalize the proofs in Lean,” but that “the mathematical arguments themselves were generated by our system.” AI is getting better and better at both manuscript preparation and formalizing proofs. If AI proves theorems, and then even takes over these relatively minor duties, what useful role can mathematicians play that funders would be willing to pay for? Or in other words, as AI takes on more of the work, can mathematicians justify the unique value they bring?
At this year’s Heidelberg Laureate Forum, mathematicians, computer scientists, and AI researchers will explore these and other questions surrounding the evolving roles of humans and AI in mathematics and computer science together on Tuesday, 15 September, during the panel session AI in Mathematical Research, which will also be streamed live on the HLF’s YouTube channel. How these roles should be shaped in mathematical discovery, even as AI surpasses humans on an expanding range of mathematical tasks, may prove to be one of the defining questions
The post The Evolving Relationship Between AI and Mathematicians originally appeared on the HLFF SciLogs blog.