Proofs and Prompts

Notes from the common room

Joint Statement about Mathathon

A coalition of Caltech Mathematicians1. Also cross-posted at Terry Tao’s blog.

Mathathon is centered around one question: how can we use AI to augment human understanding of mathematics?

This past week, the original organizers of Mathathon2, two coauthors of Open Letter about the Mathathon3, and other members of the Caltech community4 engaged in a conversation to redesign this event. We quickly reached a consensus: problem solving is but one component of mathematics; mathematical understanding and exposition are similarly meaningful. But these components have often been overlooked by grantmakers and hiring committees. We want to celebrate human mathematicians who undertake this work.

Thus the new theme of Mathathon is Old Problems, New Proofs.

Consider the four color theorem, the ABC conjecture, or the Navier-Stokes problem. Many mathematicians find their proofs—or claimed proofs—difficult to understand or unsatisfying. We invite our participants to pick a problem with an unintuitive solution, learn as much as possible in 40 hours, and present their findings to their peers. Then, they will take two months to develop an alternative proof or exposition. Afterward, they’ll submit an explainer and a GitHub repository. The explainer can take any form: a paper, a blog post, a video, an interactive game, et cetera. The repository will store whatever was used to produce the explainer—LLM chat histories, code used to produce visualizations, and more—so the mathematics community can examine the ideas behind the finished product.

By shifting the focus from open problems, we want to encourage Mathathon participants to explore everything else we do to make sense of mathematics: generalizations, new notations and techniques, connections to other problems. These innovations can be more exciting than solving individual problems.

Mathathon treats AI as one of many tools available to mathematicians. We no longer receive sponsorships from developers of proprietary AI models. Participants are given a cash grant to purchase any tool they need, whether that be LLM credits, HPC access, or pen and paper. Proprietary models are allowed, but we encourage the use of open-source tools. Our goal is to empower each participant to make their own decision about the tools used at Mathathon and in their own work. 

The new event will take place on November 13–15. It is co-organized with the Foundation for Science and AI Research (SAIR), which will provide compute, host workshops, and offer prizes to teams that use open-source models. SAIR is also administering travel grants for participants. Our lead donor is XTX Markets, an algorithmic trading firm and a major supporter of academic research, open-source infrastructure, and community-led initiatives in AI-for-math.

The organizers and advisors of Mathathon range from AI proponents to critics, from undergraduates to well-established mathematicians. Working with this group has been a learning experience for everyone involved. We hope that it will bring together a similarly diverse set of judges and participants. 

If you want to deepen your understanding of math, we hope to see you at Mathathon. Our mission is for you to learn from and teach your peers. 

If you want to have fun, we hope to see you at Mathathon. It’s still a student-led event, run with the same playfulness that first inspired it. 

If you are curious about AI capabilities, we hope to see you at Mathathon. Finding alternative proofs to solved problems and presenting them in human-oriented ways is a novel challenge for LLMs. 

If you are concerned about AI’s impact on mathematics, we hope to see you at Mathathon. It celebrates human-oriented expositions. Mathathon requires participants to fully disclose and justify LLM usage and asks them to consider whether smaller-scale open-source tools would suffice. 

Finally, Mathathon isn’t a conclusive guide to AI in mathematics. The organizers hold different opinions about AI-assisted problem solving, open-source versus proprietary models, and more. But we all believe that mathematicians can use AI to advance human understanding. Mathathon is a first experiment. We want to pave the way for future initiatives that explore AI’s roles in learning, teaching, review, and research, while placing human understanding and community building at the forefront. Mathematics is undergoing its biggest change in decades, and we must work together to adapt.

Acknowledgements. We are grateful to Terence Tao and Andrew Wu for reviewing this statement and leaving comments, as well as to countless others who offered feedback about Mathathon. All of the views above are solely our own and do not reflect those of Caltech or any other organizations we belong to.

  1. This is a joint statement by everyone named in footnotes 2-4. ↩︎
  2. Alvan Arulandu, Andrea Li, Avni Garg, Brian Zhao, Caiman Moreno-Earle, Sathvik Redrouthu. ↩︎
  3. Dylan King, Tasmin Chu. ↩︎
  4. Mayla Ward, Merrick Hua, Robert Joseph George, Sergei Gukov, Shaowu Zhang, Tony Yue Yu, Vihaan Dheer. ↩︎

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11 responses to “Joint Statement about Mathathon”

  1. just different Avatar
    just different

    This seems much less problematic to me—in fact, I’m interested in how this goes. I’m also wondering how these changes have affected who wants to participate, because my impression was that the earlier Mathathon proposal was mostly attracting people who were much less interested in pure mathematics research than in resume-polishing for industry jobs.

    Reply
  2. Wolfgang Avatar
    Wolfgang

    I doubt that the current theme of “understanding” will change much. XTX markets and SAIR want AI, bow to the current pressure but won’t change their agenda.

    Reply
  3. Joint Statement about Mathathon | What's new

    […] was initially written in a different file format and converted using AI. It is also crossposted at Proofs and Prompts— […]

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  4. Anonymous Avatar
    Anonymous

    The goal of exposition of existing problems is interesting from an intellectual service standpoint. But much like Gartner or 3blue this is a niche that is simply not going to get anyone tenure in any Math department anywhere.

    It is misguided career advice to imply to young people that this is a winning strategy to become a professional mathematician— there is in fact no serious incentive to that effect.

    I wonder if the new framing, as well meaning as it is, is simply the wrong message at the wrong time to focus toward young people.

    Reply
    1. just different Avatar
      just different

      Same is true for any math contest. So?

      Reply
      1. Wolfgang Avatar
        Wolfgang

        The “understanding” framing is not limited to math contests but put forward as the general coping mechanism for the future of mathematics.

        That is a very dangerous path, especially since the Silicon Valley antagonists co-opt any new narrative that buys them time and prevents harsher opposition in the form of IP lawsuits.

        Reply
  5. Novum Organum Avatar
    Novum Organum

    I’ll grant the statement everything it asks for: the consensus process, the cash-grant-instead-of-tokens design, the tool-agnostic framing, the “mathematics is undergoing its biggest change in decades” line — all good, all necessary. And I agree that exposition and understanding are under-valued in the profession, and that a dedicated venue for them has real value.

    But I’ll be direct: the shift completely away from open problems is the disappointing part, and it’s a retreat, not a redesign. The one thing this event was going to show the community — what a stretch of AI-augmented work on a problem nobody has solved actually produces — has been replaced with a digestion workshop on problems already solved. Important? Yes. Primary? No.

    Here’s the sequence the statement gets backwards. Across the sciences, the order is discovery → manipulation → understanding, not the reverse. Physics ran on this for a century: quantum mechanics was built as a computational machine before anyone agreed on what the machine meant; the renormalization group turned a “subtract the infinities” trick into a theory of scale and universality. GR is the clean case: the field equations produced working predictions — light bending in 1919, gravitational waves in 2015 — before the geometric picture was fully understood, and the Schwarzschild solution sat around for decades before we had the words for a black hole. You can hold a formalism and its predictions before the understanding lands, and that lag is not a defect to be repaired with better exposition. Ramanujan is the pure-math version: identities he could “see,” and decades of structure to find underneath them. Fourier’s “sloppy” series didn’t get cleaned up — they generated Lebesgue integration, functional analysis, Hilbert spaces. Understanding is often the consequence of discovery, not its prerequisite.

    That’s also why the field has a lag phase. A conjecture exists precisely because identifying a true statement precedes, and must precede, full understanding of why. And the AI output is not just conjectures — it’s proofs too, often in forms nobody has yet digested. The discovery phase is now being produced at a scale the community has never seen, and most of it arrives before anyone understands it. The community’s job — the part that actually needs a venue and a culture — is to absorb that output, which is a phase that comes after, by design. By switching the theme to “Old Problems, New Proofs,” the event has removed the incoming discovery phase and is left digesting only the old stock.

    Which brings me to the real cost. Mathematics no longer has the luxury of being understanding-first, and I don’t think the profession wants to cede the discovery phase permanently. The conjecture and problem-solving parts are not going to accept a permanent back seat; that’s where the value now accrues, precisely because AI has absorbed the proof-millwork. If the profession retreats to explaining solved problems, it’s downstream — it becomes the interpreter of a discovery process happening elsewhere, at the labs. The Navier–Stokes construction is already in the literature, a two-scale mechanism a specialist who’d worked the problem for decades says he’d never personally thought of. The question was never whether the discovery phase is happening. It is. The question is whether the community will be in the room when it does — and right now, the profession has to catch up to a discovery engine it’s been defining itself against.

    I don’t think this statement is wrong. I think it’s safe. And for the first experiment in the biggest change the field has seen in decades, safe is the wrong shape. The next version should run both tracks: an open-problem track, where the discovery engine runs and the community has to learn to work with its output in real time, and an exposition track, where the digestion culture gets built. Doing only the second one is deciding, the morning the printing press arrives, to hold a very well-organized symposium on how to hand-copy manuscripts more elegantly.

    The math is undergoing its biggest change in decades. This event made the conservative choice about what that change should look like. The more interesting choice is still on the table.

    Reply
    1. Yemon Choi Avatar
      Yemon Choi

      Since you are so enamoured of what your chatbot writes when prompted, the two of you should get a room and leave us out of it. (You have previously dismissed criticism of your penchant for doing this as merely criticising style rather than substance, but in fact when one strips out the verbiage and rhetoric that are emulations of something knowledgeable, there is no substance. If there were, you could write these posts in 50-60% of the length without all the fools’ gold.)

      Reply
  6. Andrew Ng Avatar
    Andrew Ng

    I’d like to commend all of those involved in the redesign on what seems to have been a productive dialogue that thoughtfully took into account the community’s protests and has led to a better version of the same event. I think the current iteration has good claim to being a much better use of LLMs: it is really quite difficult for me to ‘unsee’ a proof that I know and try to come up with a new/better one. I suspect many other people struggle similarly, and I do hope that LLMs don’t suffer from this defect in the same way so that they might see what we have missed.

    Furthermore, the community does not credit this as much as it should, and while it will take time to change the community norms around this, I believe that the work carried out in this version of the Mathathon is extremely valuable, and it is sending *exactly* the right message to the community: this is what we should value. A new proof of an old result is just as likely to result in better understanding/new directions of research as a new result, but the community doesn’t recognise this yet, so it makes sense to have this sort of event directed as producing new proofs.

    Reply
    1. Nilima Nigam Avatar
      Nilima Nigam

      Agree entirely! I commend the original organizers and the co-authors of the open letter for fruitfully discussing a fraught matter, and arriving at a reasonable solution. This current incarnation seems a much better one!

      The original organizers of the event (I understand most were undergraduate students?) have displayed a great deal of initiative, intellectual integrity and openness to constructive criticism. [In strong contrast, we continue to read reports of major AI firms being unwilling to disclose safety/containment episodes, and unwilling to change corporate behaviours.] Being publicly confronted with strongly differing views on something one’s created, and then refining it in response – this is to be admired. Also to be admired are the co-authors of the open letter and other colleagues who worked with the organizers. Thanks to all.

      Reply
  7. The Navier-Stokes Announcement: A case study in mathematical values – Proofs and Prompts

    […] we are not powerless. The wave of signatories to the opposition to the Mathathon led to its revision into a more productive form. The Leiden declaration, and the Mathematics and AI Statement, have changed the local behavior of […]

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