QuesnayJr

They didn't discover a missing sporadic group. The big gap in the proof (the quasithin case) happened because it was covered in a 600-page unpublished manuscript that under further investigation turned out to be incomplete.

I think people assume that it would end up not being usable by humans without a lot of hand-holding. Though maybe that's wrong, and somebody should try it.

I'm surprised they only found one gap. I would have expected multiple (fixable) gaps would have been uncovered, especially since the result was spread over many papers by many different people.

It is weird. We'll have to wait and see if they are the same algorithm or not.

This isn't getting any attention, but Anthropic claims Claude independently proved that the Exponential Time Hypothesis was false back on October 16th, and had been working on a cleaned-up draft.

Polynomial is something like exp(n log x), where x is the problem size. Exponential is something like exp(x). Superpolynomial but subexponential is roughly when the exponent is between n log x and x. An exponent of (log x)^2 would do the trick.

The actual exponent OpenAI found was x/sqrt(x).

The article reports it in an odd way, making it sound like it singles out students from Nigeria, Kenya, India and Pakistan. The fee applies to any student who pays international tuition rates.

Knowing the answer is valuable, but it's not everything. We also want to understand why. The four-color theorem has a computer proof, so we know it's true, but we learned much less from that than we do from a human-understandable proof.

Many of the OpenAI results can be made human-understandable, so it's better than the four-color theorem example.

I suspect 6.1 Astra is the model that kept showing up in the news stories about an internal unreleased model trying to hack the Pentagon or whatever.

But you are living in the world after the temporary shock, and you are asking the people who are still in the middle of the shock "Why aren't you over the shock yet"?

The chess example is not an inspiring one. It was true for a decade that humans and chess programs working in tandem were better than programs alone, but since then humans only hold chess programs back. Carlsen plus Stockfish is a worse chess player than Stockfish alone.

Anyone who thinks they can predict the future of this technology more than a few months out is foolish, but the models got so good at answering specific questions in math because the frontier labs could use RLVR to train them. There is no RLVR for mathematical taste.

There was more progress on open problems in mathematics in the last six months (because of AI) than in the previous decade.

You're asking this of the people who are actually in shock. What do you think "shock" is?

It doesn't make sense to compare CPI to real wages. Real wages are wages divided by CPI or another inflation index.