Investor Slater Stich interviews @polynoamial on applying AI to the Erdős unit distance conjecture and IMO benchmarks

@littmath Would love to hear what you disagree on. I'm not a mathematician (and I hope that came across in the interview) so I still have a lot to learn on where AI+Math is headed.

Last year, Slater talked to @DrYangSong, @jaschasd, and me about the history of diffusion. He's just started a new series on AI for math!

Very excited to share our interview with @polynoamial on AI for math — the Erdős unit distance problem, saturating the IMO, the future of math research, and more!

My sense is that @polynoamial's view of math research is that it's mostly about solving well-posed problems. That's certainly a big part of research (and a big part of how we ground other parts of research) but lots of mathematical activity isn't about solving well-posed problems. Not saying models can't or won't be able to perform other mathematical activities, just commenting on what I understand to be some underlying premises of the interview.

I don’t think I have particularly strong disagreements! In particular I really like what you said about this being another point on the curve, and more or less what you’d expect the first significant AI result to look like. Mostly just suggesting that there’s a lot of curiosity-driven math research that looks like “can I understand this phenomenon?” rather than “solve this open problem,” though it’s often benchmarked by solutions to open problems. And I think there’s arguably some skills relevant to this where AI progress has been comparatively slow, though maybe they can or will be substituted for by superhuman performance in other areas.

@littmath @polynoamial Would you be open to sharing your primary disagreements?

@polynoamial @littmath Ah! So you are a magician then?

@slaterstich @polynoamial Incredibly interesting @slaterstich @polynoamial

@polynoamial @littmath Self play as separate from ultimatum play (prisoners dilemma)(decisions on the face of a completely unknown variable) is very interesting. Also the ability to course correct versus a single play outcome is philosophically interesting.

@littmath @polynoamial I think however, that the impact of AI will be much greater there, since this really about enhancing the researchers ability to follow their interest (and them being able to guide towards possible solutions since they have intuition) rather than blindly shooting at everything.

@littmath @polynoamial Right, "can I understand a phen.." starts to make theories then open problems are implications*. But here with two headline erdos problem, the thing gave very elegant arguments 1) Golod shafarevich class field and 2)mangdolt+markov chain. Which litt up experts as it was obvious

@sedielem @DrYangSong @jaschasd That was a really good series!

@littmath @polynoamial 👀

@slaterstich @polynoamial On Thursdays we talk about the future of math. I'm glad you had a camera present this time @slaterstich.

@slaterstich @amandamhuang @polynoamial Beautiful

@slaterstich @polynoamial https://youtu.be/h4ZguzEMKAU?si=fQhKUVipliyDDABT

@slaterstich @polynoamial hawt.

@slaterstich @polynoamial Very cool!!!

@slaterstich @polynoamial thank you for making this, very interesting!!!

@littmath @polynoamial "Not saying models can't or won't be able to perform other mathematical activities"

We can dream though!