Understanding AI-generated mathematics in teams: an experiment

To encourage collaboration, learning, communication and understanding. Beyond this, there are also practical motivations for this experiment. It is likely that many people around the world are putting the same conjectures into LLMs, spending money, tokens, energy and resources, and then toiling away separately to understand and rewrite the outputs as quickly as possible so that they can be the first to submit the proof to arXiv. This is clearly wasteful and, if our goal is to enrich human understanding, then it is counterproductive. We can no longer get away with simply writing up proofs and "calling it a day," nor should we. Now that the task of finding proofs can be automated, we no longer need to compete to find them faster than others, and we should redirect our efforts to more important aspects of research.

I launched this project with 2 projects that I wanted to be a co-author of and 8 that I left to others to work on and write up without me. In a world where anyone with enough money for access to top AI models can prove the same theorems, there is no longer any value in being the "first" to claim a proof of a new theorem.

For the projects that I am remaining involved in, I am personally motivated to understand the underlying mathematics. However, this process takes time. Meanwhile, I am aware that other people may be working on the same projects. Given the current culture of mathematics, if they submit their paper first, then I will not receive much credit for continuing to work on these projects myself, and will most likely abandon them. Therefore, by keeping these projects secret, I would be pressured to write them up as quickly as possible and miss out on the opportunity to learn. For these reasons, I am sharing these projects openly and encouraging others to join me in the slower journey of understanding, rather than racing me to finish first.

Anyone could obtain the same proofs by prompting an LLM. What is the point in stealing them?

Technically, nothing. However, I would prefer to err on the side of trusting people to do the right thing. Some people may decide to "game the system," but I don't think that it will benefit them much in the long run. The biggest potential benefits of this experiment include learning mathematics from each other and building personal connections, not maximizing co-authorships. If someone decides to misbehave, then they will miss out on the best part; moreover, they will get a reputation.

I don't think so but, as the page title says, this is an experiment. So, it remains to be seen.

The way I see it, I am trying to encourage people to process the AI-generated math that they produce, and to do so at a reasonable pace, in collaboration with other people who are interested in similar math. There is very little clout that anyone will gain from generating dubious mathematics and submitting it here. The current system where we need to keep our proofs secret and race to be the first to post on arXiv seems to incentivize writing things up sloppily and more quickly than we can actually process the ideas. If we want to reduce slop, then we need to stop competing to be first.

As a personal anecdote, by posting these proofs here and inviting others to work with me, I feel less pressure to pay for the most powerful AI subscription myself. I'm now down to a $20/month ChatGPT Plus membership. There is a lot of work for me to do to try to understand the proofs and, while a little bit of AI can be helpful for that, a Pro subscription is over-powered. Moreover, talking to other human beings tends to be much better than an AI for learning mathematics. I hope to encourage more of that.

... that being said, if you do want to use some AI but don't want to pay the big AI companies, then I recommend trying out the open source models available on Open Math OS. It looks like a fun system for math collaboration.

Posting a proof to this site requires the consent of the people, or corporations, that were involved in using AI tools to generate the proof. It is mainly intended for people to submit proofs that they generated themselves.

While it would be very interesting to launch projects to understand the recent purported breakthroughs of OpenAI and Anthropic and share authorship credit among those involved in that work, it is ultimately up to the owners of these proofs to decide whether to allow this. For such high-profile results, there would be high demand for co-authorship credit which would clearly be difficult to manage. However, given the amount of work that it will take to work through these proofs, it is my personal opinion that the people who participate in that work should be listed as co-authors.