Woah, they got QCD! I didn't think they could do that. Three things jump to my mind: 1. Is it really true? Did they get the basic conditions right? 2. Would I ever be able to understand the proof 3. But the most important one. Can we compute hadronic masses now?

This is an incredible scientific achievement. One of our most fundamental theories is mathematically sound. Without the use of AI is very likely I would have never seen this in my lifetime

> In our view, these manuscripts are best understood as a form of raw research data.

Much better!

> For the computer science collaboration, the group has decided to make the natural language proof and Lean formalization public immediately, and we are publishing them directly to our GitHub repository. For the physics collaboration, the group has decided to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.

> All of these approaches involve tradeoffs. On the one hand, the collaborations empower experts to foster unpacking the results and contextualizing them in the broader academic community. On the other hand, choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information. We welcome feedback on how to broaden participation and make this process more useful.

Very good!

I was highly critical of their approach with the earlier mathematical publications, but this is much improved.

Most importantly, they aren't releasing slop papers that would never have been published in any self-respecting journal or made it past a deep round of peer review questioning.

> We are committed to ensuring funding for researchers to independently examine, explain, and build on the results above.

> We continue to invite feedback on the best way to disclose results and engage with scientists to accelerate discovery.

Well done!

Now you need to actually LISTEN to the community and the feedback, so you aren't done yet, but this is a much better start than last time. Keep it up!

I wonder how much compute they are throwing at problems in ML like continual learning and sample efficiency. Also how successful they are with these. Results like in the post make me hopeful we'll see some type of so singularity soon

It uses sparseness. I noticed a simple thing way back that for a n-boolean variables, the average size of a satisfiable boolean expression must be 2^n bits - basically every binary number that satisfies it listed out. So if a boolean expression of 4 variables is satisfied by 1111, 1110, and 0000, the number denoting it is 1100000000000001, and for every such number there is a boolean expression of 4 variables and for every expression one number of 16 digits. So it’s a fool’s errand to make a universal solver when average inputs scale at 2^n, if a solution exists it has to leverage the small size of the problems we actually care about, sparsity. Based on the AI description that’s what they did, something with polynomials, but it’s too soon. Looking forward to finding out.

The proof appears to be a sub-exponential algorithm for #3-SAT not just 3-SAT, I think this is considered a much stronger result?

this is the first time one of the big labs has published anything related to my field. and i'm actually pretty excited? im more on the applications side of QFD than the theory side of things, but gosh i actually cant wait for the results to be released to see if i can use it for anything! i kinda hope more results come out, in more ways relevant to what i do, its so cool to see any sort of progress! wow!

Kakeya conjecture is simple enough that anyone can understand it. The surprising part is its connections with other parts of mathematics.

https://youtu.be/5J3tYU_-IZI?si=t3B9d0Wtsvs26_i9

I'm a little surprised the article stresses Lean programs so much, without ever stating what that is or why it somehow proves something. Maybe that's expected knowledge for this sort of thing.

https://lean-lang.org/

The fact that ETH is false when many people expected it to be true is the amazing thing. This isn't AI finishing the last 10% of a proof and stealing the credit--this is AI exceeding human thinking. If nothing else, this buries the "stochastic parrot" position.

That said, AI is spiky, and I fully expect there to be a class of problems that AI is really good at solving and a (maybe larger) class where AI is worse than human mathematicians.