FunSearch (so called because it searches for mathematical functions, not because it’s fun)

I’m probably not the only one who wondered.

Buried the fucking lede with misleading garbage. They came up with new, larger cap sets than were previously known. That’s cool, but it doesn’t actually prove anything related to open cap set conjectures. I’d contend this is similar to the early solutions of the four-color map theorem albeit built with a computer coming up with the models to brute force. Pretty fucking neat; not solving an unsolvable problem by any stretch of the imagination. I would expect that kind of hyperbole from the lay press not the fucking MIT Review.

Edit because this shit is really cool: I intentionally linked this to the four color map theorem because that was the first brute force proof (at least via computer). Lots of people got pissed at the authors and said it was invalid because they reduced their special cases to a finite set and had a computer chug through them. imo proof by computer is valid and one of the ways stuff like this can aid math. There are so many problems in combinatorics alone that could benefit from this treatment of just getting new, unknown special cases to get to a general case or handling previously too large finite sets of special cases.

We have solved the unsolvable problem.

Should probably rename it then.

“Gold among the garbage” sums up AI very nicely.

Does this mean computers can finally do floating point math!

This is the best summary I could come up with:

Google DeepMind has used a large language model to crack a famous unsolved problem in pure mathematics.

In a paper published in Nature today, the researchers say it is the first time a large language model has been used to discover a solution to a long-standing scientific puzzle—producing verifiable and valuable new information that did not previously exist.

FunSearch (so called because it searches for mathematical functions, not because it’s fun) continues a streak of discoveries in fundamental math and computer science that DeepMind has made using AI.

Built on top of DeepMind’s game-playing AI AlphaZero, both solved math problems by treating them as if they were puzzles in Go or chess.

It combines a large language model called Codey, a version of Google’s PaLM 2 that is fine-tuned on computer code, with other systems that reject incorrect or nonsensical answers and plug good ones back in.

Terence Tao at the University of California, Los Angeles, who has won many of the top awards in mathematics, including the Fields Medal, called the cap set problem “perhaps my favorite open question” in a 2007 blog post.

The original article contains 821 words, the summary contains 185 words. Saved 77%. I’m a bot and I’m open source!

Guarantee this comes out as untrue. Mark me.

Does it perform better in a significant way to genetic programming?

Can it divide by zero ?

I thought this was interesting bc it’s an instance where a LLM has done something undeniably novel and unique while expanding human understanding. It’s a chink in the armor of the idea that a LLM is a “stochastic parrot” that can only regurgitate and never create.

I’ve been toying with this idea that LLM are showing us that what we thought of as creativity, learning, and problem solving aren’t as rarefied as we thought. We know that AI isn’t conscious, maybe consciousness isn’t as prerequisite to behaviors and cognition as we thought.