I wonder why the physicists are the only group to not want the full information released upfront? As a casual fan of physics[0] it seems like their completion of the standard model is possibly the biggest deal of all these breakthroughs, am I wrong?

[0]: PBS space time watcher

Not enough chatter about the QCD result here! I'm of the opinion that whatever the correct representation of the universe is, the GUT (Grand Unified Theory) will be authored not by humans but by LLMs.

These resolve 6 entries in my top 500 open problems list (LLM ranked, https://www.proofatlas.ai/open-problems/) and there is partial progress on #3 overall (Yang–Mills Existence and Mass Gap):

Kakeya conjecture — #38

Fourier restriction conjecture — #46

Local smoothing for wave equations — #187

Bochner–Riesz conjecture — #190

Exponential Time Hypothesis — #43

Strong Exponential Time Hypothesis — #63

> 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!

This is an exciting time, but also there are very real changes at hand. Game changing discoveries will likely not happen at universities but at private AI frontier labs. Moreover, the models that are used on this are not always open to the broader community today.

What will it be like in two years? Will such models that help enable paradigm shifts in science be only accessible to employees of those private companies? Still thinking about the ramifications ... amazing and discombobulating at the same time.

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

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.

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

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?

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