It's good to see validated numerical proofs seeing a resurgence now that they are substantially easier to achieve.

Others might be able to chime in, but my experience is that AI is effectively taking proofs that were once iterative (pushing current ideas further, tightening arguments) but considered time-consuming, and turning it into very low-hanging fruit. So stuff like this, as well as the new lower bound on the asymptotic ratio of zeros on the critical line, really aren't that impressive anymore. But it is likely necessary to do nonetheless, just as low-hanging fruit has always been.

The real frontier remains (even if many were not operating there) the development of new definitions and ideas that push right past the walls that were previously there. AI still seems to be shockingly poor at doing this, and you can feel that when you use it for proper hard problems.

Anyone interested in the subject area has noticed the recent surge of AI-assisted or generated mathematics. From the outside, it is very hard to see, if AI indeed already speeds up progress in mathematics in general - apart from a number of spectacular results, (https://mathoverflow.net/questions/502120/examples-for-the-u...) - or if the quality of the large majority of these "proofs" is so poor that reviewing them is a waste of time.

I would be grateful, if someone familiar with the situation could say a word about this.

As for the proof in question - I'm not sure the author himself can firmly state he understands every detail of what he presented. In a way it's amusing that people who already enjoy a certain level of recognition outside the field are now using it to find (via shiny websites) reviewers for proofs they have worked out as a hobby using Chat GPT and the like.

What we definitely need is more recognition for those who possess the competence and energy to assess the correctness and relevance of such "results".

I'm not able to judge this for content, but it feels frustrating to read something so obviously Claude-authored as being written "by" Jude Gomila. It's interesting to see the (presumed correct) reduction in this bound and this presentation is pretty compelling. I learned a bit about the Polymath 15 project from this post and I enjoyed that a lot.

That said, I have no idea what contribution may have been done by Mr. Gomila or not. I don't know if I can ask him for more details. Even if he wrote the whole thing (and either has deeply internalized Claude's voice or had it edited and rewritten by an agent) it's difficult to believe that he's the sort of expert I'd expect of someone who had actually done all this work.

This is basically the same feeling I have about vibe code contributors.

Nice, is this the maths equivalent of AI slop?

It's really fun seeing Manim [1] used to illustrate a proof!

(See the video at the bottom)

[1]: https://github.com/3b1b/manim

Apparently the unfiltered Claude voice for mathematics is pretty similar to programming.

10.6% smaller. Not bad.

https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_const...

Λ ≤ 0 in the intro. Great site!

Wow, I have a hard time swallowing these Claude generated blogs. So many off-putting llmisms. I wonder if this is something I just need to accept and get used to, or whether it'll pass as models advance.