OpenAI posts hundreds of results on major maths problems, and mathematicians want proof

[Skibidi98]

OpenAI has published 722 manuscripts on GitHub containing solutions and partial progress on 372 major maths problems, produced by an unreleased ChatGPT model and checked by OpenAI's new advisory group, Engadget reports. Last month, the company said its models had resolved "more than 100 long-standing open problems across most areas of mathematics." The new release includes the model's reasoning, compute estimates and the number of problems attempted

OpenAI said the average result took about three hours of ChatGPT Pro use. It did not publish per problem compute times or the prompts used, which its own advisory group had suggested. Claimed results include a solution to the four dimensional Kakeya conjecture, improvements to computer algorithms and progress towards the Riemann hypothesis. OpenAI told Scientific American that nearly every paper came from a single prompt given to a single AI agent

Mathematicians are cautious. MIT's Andrew Sutherland urged treating the single agent claims as unverified "Until and unless they release the model and people can replicate their results". Engadget says the release may deepen the controversy over OpenAI's earlier claims about the Navier-Stokes problem, which already fuelled scepticism among scientists. Publishing manuscripts is not the same as having them peer reviewed

Even so, the scale is remarkable. Earlier this week, GPT-6 Astra cracked a 217 year old Napoleonic cipher, and AI tools are increasingly being used for scientific work. If even a fraction of these maths results hold up, it would be a significant moment. The difficulty is that checking hundreds of complex proofs takes human experts a very long time

Do you believe AI can now solve open maths problems? And how should the maths community deal with a flood of AI produced proofs?

OpenAI just posted hundreds more results on major math problems - Engadgetwww.engadget.com

[NeonPhantom]

A proof can be checked even if the method is secret. If the manuscripts contain rigorous proofs, mathematicians can verify them line by line

The problem is volume, not secrecy. A few hundred proofs could keep a lot of mathematicians busy for years though

[KeyboardWarrior47]

Formal verification tools like Lean could help. If AI proofs were written in a form a computer can check, the verification bottleneck would disappear. Some groups are already using AI with Lean for exactly this reason. It is the obvious way forward

[Nebula Diane]

Sutherland is right. Extraordinary claims need replication. Without the model or the prompts, other researchers cannot check how the results were produced. Peer review exists for a reason. Posting manuscripts on GitHub is not the same thing

[Rogue Sam]

If the four dimensional Kakeya result holds up, that alone is a big deal. Kakeya problems have frustrated mathematicians for decades. The three dimensional case was only settled recently, after decades of work, if I remember rightly

[Harbour17]

Progress towards the Riemann hypothesis is the kind of claim that makes mathematicians roll their eyes. Partial progress can mean almost anything. Proving it would be one of the biggest events in the history of mathematics