Proofs and Prompts

Notes from the common room

I’m giving my theorems away

Jonathan Noel, Associate Professor at University of Victoria

Over the past couple of months, the same open problem may have been solved by prompting AI by 10 different people on 10 different days. Each of them knows that posting AI-generated text that they don’t understand is heavily frowned upon,1 and so they keep their proof secret. They also know that anyone else with a subscription to the same AI might have access to this proof, and so they need to work fast. They send 50 more prompts to the AI to help understand the proof, most of which are unhelpful, and toil away independently to write it up. Eventually, one of them finishes and puts the paper on arXiv, and the rest abandon their work for zero credit, and vow to be faster—and more sloppy—with the next one.

This is incredibly wasteful, not only of mathematicians’ time and effort, but of money and computational and natural resources.2 It is also very lonely. Moreover, it is counterproductive if, as many have suggested, we are hoping to transition to a system that credits contributions to human understanding over generating proofs.3

I believe that the dystopian scenario described above, that many of us are living through now, is forced by three assumptions of the existing systems of mathematics: (1) if you prove something, then you should not make it public until you have a polished arXiv-worthy draft, (2) co-authorship is sacred and shouldn’t just be given away and, relatedly, (3) the person who generates a proof should always be a co-author. However, as many have observed, this system no longer makes sense in a world where everyone with a subscription to a top AI model has access to almost the same set of proofs as anyone else.4

At first, it may seem difficult and painful to come up with a new system that does not feature these assumptions but, for the time being, I am hopeful that it may turn out to be much easier than we thought. Of course, the devil is always in the details. But, for now, I am holding onto this naive optimism because, without it, I may be paralyzed with indecision, and that has no chance of being valuable. As the 10th greatest Canadian of all time (as of 2004) said, “you miss 100% of the shots you don’t take.”5

So, here’s my shot; I’m calling it proofsandpeople.org/, inspired by the name of this blog. The concept is as follows. Anyone can submit a “project” to the webpage which consists of an AI-generated proof that has not yet been understood by humans. Each project will have a “leader” and a “team” of other researchers who are interested in working together to understand the proof, extract valuable human insights from it, teach them to each other and, eventually, write up the proof and submit it to arXiv for shared credit as co-authors. The leader has the option of allowing new team members to join openly, to close the project to new members, or even to remove it from the webpage. The person who submits a project may decide to lead it, join the team, or completely leave it to other people to carry forward. In the latter case, they should normally not retain any rights to co-authorship; however, the decision of how to assign credit for a project is left up to the leader, submitter and team members for an individual project.

I launched this site with 10 projects that I generated with AI myself, 2 of which I plan to lead and 8 that I am giving away for others to take forward. I recognize that my time, energy and attention are limited and it is unrealistic for me to bring all of these projects to fruition. So, I’m going to focus on working on the projects that I’m most deeply interested in, doing so at a pace that is appropriate for truly digesting the ideas, and sharing the journey with other people. I invite you all to join me in this.

While I believe that the main benefits of this initiative are to encourage collaboration, community and human understanding, I also have a financial motivation. I don’t want to pay hundreds of dollars every month to OpenAI anymore. In a system where we all work in secret and 99.9% of the credit is given to the person who posts to arXiv first, I feel that I would have no choice but to use all of the tools at my disposal to speed up my workflow. Meanwhile, all of my competitors are also pouring money and resources duplicating the same work that I’m doing in an attempt to beat me to arXiv. Surely, we would learn more, enjoy the process more, and save a lot of money and resources if we just share the ideas and co-authorship credit openly. Personally, partly because of this new initiative, I’ve recently gone from the US$200/month ChatGPT Pro account to a US$20/month Plus account, which is more than enough to support my productivity when I’m not trying to generate new proofs and working feverishly to write them up. Moreover, in this system, members of the community who are abstaining from using LLMs themselves may have an opportunity to get involved and share their insights and expertise, depending on their level of openness to doing this type of work.

I do not claim that this is a foolproof or long-term solution. You can probably already see some potential headaches that will emerge with this model; so can I. Moreover, the value of this system may decrease if/when AI figures out how to write a beautiful math paper. But, as Patrick Morris suggested in his recent essay, now is a time for us to innovate.6 I don’t believe that we will find the perfect solution by sitting in an armchair and theorizing about it without testing it in the real world.7 This is my experiment; I hope some of you will join me and the other guinea pigs.

I apologize in advance if you find the system clunky. I hope that someone with better web development skills will take over one day. As with my AI-generated proofs, I would be happy to hand over ownership of the domain to anyone who is interested in taking this idea and making it bigger and better than I am able to.

AI Disclosure

ChatGPT 6.1 Sol Max was used to help me consolidate my ideas and suggest most of the references below.

Received 4 November 2026.

  1. The Association for Human Mathematics’ second membership commitment asks members not to publish mathematical texts generated by AI models. Its FAQ clarifies that this includes writing produced mainly by prompting a model. For explicit opposition to public release by AI companies, see Lorenzo Riva’s comments published by AHM, urging companies not to release their results and to cease work on open mathematical problems. ↩︎
  2. Alexandra Sasha Luccioni, Yacine Jernite and Emma Strubell, “Power Hungry Processing: Watts Driving the Cost of AI Deployment?,” ACM FAccT, 2024, measures energy consumption and emissions during inference. Cooper Elsworth et al., “Measuring the environmental impact of delivering AI at Google Scale,” 2025, reports energy, carbon and water measurements for Gemini Apps text prompts. ↩︎
  3. William P. Thurston, “On proof and progress in mathematics,” Bulletin of the American Mathematical Society 30 (1994), 161–177, especially p. 162. For recent proposals responding specifically to AI, see Daniel Litt, “A beginning for mathematics,” Proofs and Prompts, 14 September 2026, especially “Producing high-quality mathematicians”; and Bryna Kra’s guest essay on Terence Tao’s blog, 13 September 2026. Litt proposes evaluating demonstrated understanding and mathematical discussion more directly; Kra calls for incentives that recognize verification, explanation and collective understanding. ↩︎
  4. For a related discussion of duplicated AI effort, shared verification and the distinction between generating an argument and understanding it, see Marco Trombetti, “ProofForum: Keeping AI-Generated Mathematics Human,” Proofs and Prompts, 22 September 2026. ↩︎
  5. Wayne Gretzky finished tenth in CBC’s 2004 The Greatest Canadian competition; see the results. For Gretzky discussing the saying himself, see his MasterClass lesson. ↩︎
  6. Patrick Morris, “Let’s stop writing papers…,” Proofs and Prompts, 30 October 2026, especially “Big Mathematics” and “Ok but what should we actually do now?” ↩︎
  7. The armchair imagery is inspired by W. T. Gowers’s “The Two Cultures of Mathematics” (2000): “One will not get anywhere in graph theory by sitting in an armchair and trying to understand graphs better.” ↩︎
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7 responses to “I’m giving my theorems away”

  1. Alt Avatar
    Alt

    Wonderful idea! Most constructive proposals ever.
    ps. PhD projects should also be allowed to register there, so that AI mecha can avoid running into them by mistake.

    Reply
    1. gleamingspeedilybb59fcc54d Avatar
      gleamingspeedilybb59fcc54d

      Interestingly, there has already been one project that I posted which turned out to be part of someone’s thesis. It has been taken down at the request of the PhD supervisor. While it might have caused a bit of stress for the student or supervisor, I think this is a better outcome than if I had worked on the project in secret and ended up inadvertently submitting it before them, unaware of their work.

      I actually wonder now whether it might have been better to leave it up on the site as a “cancelled” project with a note saying that we have learned that someone else has proven the same thing. This way, maybe others would see the note and leave it alone. I don’t know… There is one such project (a different one) at the bottom of the page.

      My current thoughts about PhD projects is that, if they don’t want to get scooped by AI, then the topic of the project should be something totally novel that the student and/or supervisor has come up with. That is, don’t work on a problem that has been stated in a paper somewhere, or you know that people have thought about before, because you may as well assume that all such problems are already solved…

      If a PhD student does want to work on a problem that has appeared publicly, then maybe they need to do it “out in the open” somehow, like you’re suggesting. But that also has risks. I have no solution to this…

      Reply
  2. Galyna Livshyts Avatar
    Galyna Livshyts

    Yeah I feel the same way, whenever I sit down to think about math for an hour I get like 3 good drafts with interesting directions which I have absolutely no time to pursue. I was trying to work out a similar system in which we may work in labs: say, a 100 people interested in the same topic get a common AI account where they can all prompt and share together, distribute roles, and aim for much greater advances together. My hope is that once such a community is formed, AI companies may be willing to provide the resources.

    Reply
    1. gleamingspeedilybb59fcc54d Avatar
      gleamingspeedilybb59fcc54d

      Regarding the idea of having a team of people with the same account: you should check out Open Math OS. It is basically what you’re describing. It is also free, for now! However, it only uses open source models, but some of them seem pretty good. Not sure if you can solve many open math problems with them, but for helping you work on understanding or writing a paper or something, they should be more than enough.

      Reply
  3. markfhagen Avatar
    markfhagen

    depending on their level of openness to doing this type of work.

    It sounds pretty boring, is one problem.

    What was — in fact, still is! — interesting is: talking to a few people for years and years about stuff that’s hazy and inchoate and hard to pin down (which is not the same as “badly-written but laid out on the page in some sort of order”), and sometimes succeeding together (or alone) in getting something to be clear, and repeating until you have (1) a deep and hard-won familiarity with a small piece of the mathematical landscape and (2) a deep experiential understanding of how those other people think about stuff, and hence a type of connection to those people that’s a bit different from many other types of human relationship.

    Having to give that up and resigning oneself to parsing terribly-written slop maths text (even with one’s friends), as a way to make the best of an annoying situation foisted on us by (mostly) the silent compulsion of economic forces and (slightly) by specific pyschopathic tech-bros, does not sound terribly appealing. It is understandable that people are angry about this prospect, even though it is true that there are much more serious consequences in the world, AI-wise.

    You will, I imagine, get takers, because there are few other constructive suggestions (I think “carry on as you were, for now, but with a finger more firmly on the pulse of things” is also a constructive suggestion, though), and of course the profession will attempt survival even in the event of some of the primary activities of the profession becoming unavailable or unrealistic for most people.

    (Also: why was AI needed to “consolidate” this particular idea? It’s not a bad idea, but it’s seemingly not that complicated, nor is the reasoning behind it.)

    Reply
    1. anonymous Avatar
      anonymous

      I thought about your last parenthetical as well. Why not digest (new or old) human papers that are not well understood? Surely there are such papers out there? Why do ai results have priority here? One reason I thought of is social dynamics: the fact that there’s no name attached to an ai generated result reduces some kind of social friction. I don’t want to paint a cynical landscape, but it’s kind of obvious that it’s socially easier to gather around a result with a (more or less) nameless author no?

      Reply
    2. gleamingspeedilybb59fcc54d Avatar
      gleamingspeedilybb59fcc54d

      Thanks for the comment! AI was used to help me organize the arguments in the post, not the basic idea of the webpage. But, to be honest, when I say that it “helped” I mean that I rambled to it about a bunch of reasons why I was doing this, asked it to suggest a plan for the essay, disliked its suggestion, and did it myself anyway. But maybe something it did was inadvertently helpful, so I should acknowledge it!

      I think you’re probably right that this sort of work isn’t as rewarding in the long term. As you also seem to recognize, this type of work will probably become common whether we like it or not.

      On one hand, it is often satisfying to be able to answer questions so quickly by prompting. I often have a feeling of “ah, I knew that would be true and I was right!” or “oh wow, that’s a surprise!” But this is a bit like a sugar rush and doesn’t last long and, when it fades, there isn’t much of a feeling of accomplishment left over. And then the work of reading AI proofs isn’t fun. On the bright side, it’s technically easier and faster work than proving things from scratch, but, again, less feeling of having “done something.”

      Regarding the reply: it is definitely an interesting and worthwhile endeavor to work on understanding old mathematics, too. There are tons of great ideas that we’ve forgotten. Unfortunately there seems to be zero reward for this in one’s career, currently, and so I am not sure if many people will jump on board. Maybe when systems are rebuilt in the future there’ll be a way of incentivizing this, but right now there isn’t.

      Reply

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