Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem (twitter.com)

Super interesting but what does this mean for us mere mortals?

out of curiosity, i wonder if people are taking stabs at p!=np

I've always said this but AI will win a fields medal before being able to manage a McDonald's.

Math seems difficult to us because it's like using a hammer (the brain) to twist in a screw (math).

LLMs are discovering a lot of new math because they are great at low depth high breadth situations.

I predict that in the future people will ditch LLMs in favor of AlphaGo style RL done on Lean syntax trees. These should be able to think on much larger timescales.

Any professional mathematician will tell you that their arsenal is ~ 10 tricks. If we can codify those tricks as latent vectors it's GG

Interesting but not surprising to me. Once a field expert guides the models, they most likely will reach a solution. The models are good at lazy work for experts. For hard or complicated questions, many a time the models have blind spots.

When I was younger I remember a point of demarcation for me was learning the 4chan adage “trolls trolling trolls”, and approaching all internet interactions with skepticism. While I have been sure that Reddit for a while has succumbed to being “dead internet”. This thread is another moment for me- I can no longer recognize who is a bot, and who has honest intentions.

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Like so many things -- the evolution of AI math will I think follow trajectories hinted at in the 90s by the all time great sci-fi author Greg Egan. The nature of math won't change -- but the why of it definitely will. Egan imagined a future ai civilization in Diaspora where "math discovery" -- by nature in the future perhaps accurately described as "mechanistic math discovery" is modeled by society as a kind of salt mine environment in which you can dig for arbitrarily long amounts of time and find new nuggets. The nuggets themselves have a kind of "pure value" as mathematical objects even if they might not have any knowable value outside the mines. Some personalities were interested in and valued the nuggets for their own sake while others didn't but recognized that there were occasionally nuggets found in the mind that had broader appeal.

Research institutes like those founded by Terence Tao in our current present feel like they will align to this future almost perfectly on a long enough timeline -- tho I think on a shorter timeline this area of research is almost certain to provide a ton of useful ways to advance our current ai systems as our current systems are still in a state where literally anything that can generate new information that is "accurate" in some way -- like our current theorem prover engines are enormously valuable parts of our still manually curated training loops.

Ramanujan is a good analogy for this situation. Theories could be right/wrong, until there's a proof. Same with anything AI produces. There's always a "told you so" baked in with it's response.

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In the paper, they give part of their system prompt:

> * After EVERY exploreXX.py run, IMMEDIATELY update this file [plan.md] before doing anything else. * No exceptions. Do not start the next exploration until the previous one is documented here.

Is this known to improve performance for advanced problem solving? If so, why this specific prompt?

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Seems like we are ready heading to what the OpenAI CEO wanted "intelligence just available thru a subscription"

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If you give 100 monkeys 100 guns and room full of building materials, how long will it take before they build a house?

How long will it take before they rob a bank?

If they do either of those things will the results have been intentional from the simian’s POV?

There are people who think knowledge discovery is just a matter of parroting past behavior and trying things at random until something sticks. I don’t.

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