OpenAI Math: After 722 Papers

On October 6, OpenAI released 722 mathematics research manuscripts at once [1]. The results came from an internal model that has not been publicly released [2].

I waited a couple of days and looked at mathematicians’ reactions. They seemed to fall into four broad groups:

• Amazement and excitement. Scott Aaronson [3] said that some of the results, taken individually, could be a field’s result of the year.
• Excitement mixed with confusion. Dana Moshkovitz [3] began reading the proofs and found plenty of new things worth learning, while also saying frankly that the papers were hard to read.
• Careful scrutiny. Alex Townsend argued [1] that it should first be made clear which results had been verified and which still needed checking. Andrew Sutherland welcomed the prompt corrections but thought more was needed to regain the mathematics community’s trust.
• Strong opposition to the publication model. The mathematicians’ organization AHM [4] opposed releasing so many papers at once. It called on mathematicians to stop working with OpenAI and return mathematics research to a focus on human understanding.

I also saw that OpenAI had withdrawn three manuscripts because of errors and revised another 14 [5].

I don’t know whether I should feel relieved that AI still makes mistakes. If all these results had been correct, I would have struggled to take that in, too. But errors appeared, and OpenAI quickly made the problems public, corrected what could be corrected, and withdrew what could not.

What feels a little frightening to me is that they can already build such a powerful model and produce so many results, yet still accept their own mistakes so calmly. There seems to be little psychological burden: fix whatever is wrong and keep getting better.

I have two more questions on my mind.

First: how long will humanity need to fully digest these results?

For now, I can’t think of a better word than “digest.” But I also don’t know what fully digesting them would mean.

Does it mean someone has checked every result?

Or that people have understood the mathematical ideas behind them all?

Or that each result has found a practical application, or produced some actual value?

Second: what if there are a hundred times as many next month?

Last month, AI was still tackling a few major problems: the Euler equations [6], formal verification of a proof of Fermat’s Last Theorem [7], and the Navier–Stokes equations [6]. This month, OpenAI has already released more than 700 “results” in one batch.

Suppose this scaling hasn’t stopped, and the growth continues. Suppose what lands in front of us next month is a hundred times as many results as this time. Then…

Sources

[1] Retraction Watch: OpenAI’s withdrawals and revisions of mathematics manuscripts

[2] OpenAI: Sharing AI progress in mathematics

[3] Scott Aaronson: The Mathocalypse

[4] AHM: Public statements

[5] OpenAI: Official revision history of the mathematics results

[6] OpenAI: On the Navier–Stokes Millennium Prize Problem

[7] Anthropic: Formalizing Fermat’s Last Theorem

AI contribution

The author proposed the topic, the two central questions, and the growth hypothesis; decided the structure and emotional emphasis; and reviewed and adjusted the wording through successive rounds. AI helped check sources, organize ideas, draft and revise the text, and design and generate the cover. AI translated the Chinese article into English for the blog, with the author responsible for publication decisions.