A new ceiling for Λ: the de Bruijn–Newman constant
judegomila.com
judegomila.com
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.
As far as the exact breakdown we will never know. But questioning the authorship in a way that leads us to believe that the author did nothing is wrong.
It’s totally valid to question authorship when the author was an LLM.
I think we're used to the idea in math of generally every idea coming from a specific contributing human. In code, maybe less so, but still we generally we find it useful to attribute at least _lines_ to who touched them last. But maybe, if Claude were just less annoying in the prose it made, and could better imitate an actual human, we'd be able to get used to the idea of humans claiming credit for something that the human guided the software to create?
At the same time, when Koons or Chihuly or Cummins sign their work I do have that expectation that they guided the piece in a meaningful and material way or that the people who built it did it in such a way that owes lineage and authorization to the style Koons/Chihuly/Cummins developed. If I asked one of them about their work and it was clear that they had become so disconnected from it that they couldn't be seen as the authority on it, that they'd delegated that away, then I'd also feel them signing it had a mark of dishonesty about it.
To that end, I genuinely don't know Mr. Gomila's engagement here. Worse, it, to my ear, very clearly is written in a style that's extremely reminiscent of LLMs. In that way, it directly invokes that feeling of inauthenticity when he claims authorship.
This reminds me of academic writing there there's sometimes a convention in author lists that the first author(s) did more of the work and the last author(s) were the PIs and guides. This anchors the work amidst all the authors, at least loosely. I understand that if I want to ask a question about the details of the procedure I can reach out to the first author and if I'm trying to understand the larger research objectives of the lab I can investigate the last author.
Personally, I think I'd feel more comfortable with this piece if it were attributed in that style.
Or, again, if this is genuinely work done in the majority by Mr. Gomila and the writing feels LLM-derived for some other reason then it's merely an unfortunate side-effect of this writing register.
I get that and also find the style annoying. But, e.g. when I wear a garment that was clearly machine sewn, sit on furniture made with powertools, look at a photo (where a mechanical process determined what pigments appear where, with what intensity), if I eat a taco whose tortilla was industrially rolled ... none of those things seems like a reason to challenge someone taking credit and responsibility for creating a thing, even if 250 years ago they would have had to engage in a much more onerous manual process to create something similar.
So what is it about writing that feels so inauthentic when the human delegates the word choice and sentence structure to a machine? Is it just cultural expectations, and we'll get used to it as LLMs exist longer?
I wonder if partly there's a feeling of disrespect on the part of the reader -- if the author couldn't be bothered to write every word, it's presumptuous to think that other people's time is less valuable and they should read word by word.
Cummins doesn't expect anyone to examine the details of every poppy; we look at the overall effect and maybe admire the detail on one or two flowers. Koons doesn't leave enough evidence of the individual welds for audiences to inspect them; that would destroy the effect. But the default way to consume a language based work is at the word level, and you can't just take in the gestalt in a moment, so the implied demands on attention are greater?
But to take ownership over words and thought in this way reads as nearly fraudulent to me.
it starts with concentrated dose of ai-ness, combined with non-human website design
sure, it may become better the longer it goes, but it brings the worst to the front
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".
The author claims to have a proof in Lean. Checking the correctness of the result is now reduced to checking the definition of the constant.
But this doesn't mean the remaining task is small or doesn't ask much from the reviewer, does it?! Otherwise we'd see a considerable turn-out of new findings on https://palomar-registry.org/ or https://github.com/Vilin97/lean-pool , or not?! (A considerable number of the presented proofs claim new results, as far as I can tell.)
(See the video at the bottom)
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.
https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_const...
Every sentence delivered like this.
With overdramatic pacing.
Forever.