A Whole Bunch Of Math: Jaw-Dropping AI Model Gains This Week

News just dropped that researchers at OpenAI have had a surprising amount of progress over the past couple of days, with an internal frontier reasoning model that does not yet have a name.

Apparently, this nascent form of an LLM worked on hundreds of previously unsolved math problems, like the Mahler conjectures from the 1930s, the irrationality exponent of pi, Unique Games approximation and a whole laundry list of thorny math, some of it named after the human pioneers who first explored it, and some significant quantum applications, too.

In announcing all of this, OpenAI spokespersons shared that they have been consulting the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study⁠, for the sake of trying to move forward on this research in a safe and ethical way, using the Lean programming language as a vehicle. Here’s a statement on method:

“For this release, we’re publishing the results in a GitHub repository, with protocols for paper revisions and citations. We’re continuing to explore other community-hosted alternatives for this release which meet the committee’s guidelines. For future releases, we are committed to further improving the quality of the papers via the citations, mathematical exposition, and presentation of the results for better understanding.”

What is the New Math?

Have you heard of the Riemann hypothesis?

I hadn’t, until last year when I wrote a piece about it, and got some flack from some quarters. It turns out there’s a million-dollar reward for solving this problem. That’s not what the OpenAI model did, exactly, it solved for a “Riemann zeta function” establishing a new zero-free region, which doesn’t, on its own, solve the hypothesis.

Then there’s the model’s Quantum Heisenberg ferromagnet research – looking at quantum spins, small ones, in a particular way that’s apparently novel.

A Bunch More Math

Is that enough, or do you want more?

The Weight of this Week

Here’s another way to explain this: