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.
So, maybe this is not quite a fair analogy but a lot of famous modern artists don't do a lot of the actual execution of their work. If Jeff Koons relies on a team of artisans and technicians to make a balloon dog, and if Dale Chihuly depends on a workshop of glass blowers to make a chandelier, and if Paul Cummins used a team of ceramicists to make poppies, what did the headlining artist contribute? Not everything, certainly, but also not nothing. Ideas, vision, feedback, guidance?
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?
I appreciate the connection to artists guiding their teams. I think that's a good analogy.
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.
> 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.
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?
He posted it. That’s some of the work you question. Presumably he queried the AI and led it in some way. That’s also work.
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.
For one, the whole text would show up in Safari's Reader mode, so I can skip past the hilariously low UI density that AI-generated websites have these days. Before AI you'd have to go out of your way put that much CSS padding into Wordpress! If everyone's going to play Terence Tao, at least copy his stylesheet.
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".
> 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.)
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.
It's not wrong, is it? I didn't want to trust myself, Wikipedia agrees that the Riemann hypothesis is equivalent to Λ = 0 (because the lower bound is now 0). This proof lowers the upper bound, but we still don't know if it's 0 or between 0 and that upper bound (inclusive).
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.
Historically, the creative process has been a revolving door of people who are fed up with the status quo, and who later become the status quo, so I wouldn't worry too much about that.
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.
So, maybe this is not quite a fair analogy but a lot of famous modern artists don't do a lot of the actual execution of their work. If Jeff Koons relies on a team of artisans and technicians to make a balloon dog, and if Dale Chihuly depends on a workshop of glass blowers to make a chandelier, and if Paul Cummins used a team of ceramicists to make poppies, what did the headlining artist contribute? Not everything, certainly, but also not nothing. Ideas, vision, feedback, guidance?
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?
The issue is AI text is annoying to read, not that the human didn't work alongside the AI to get the result in the first place.
I appreciate the connection to artists guiding their teams. I think that's a good analogy.
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.
> 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.
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?
He posted it. That’s some of the work you question. Presumably he queried the AI and led it in some way. That’s also work.
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.
Are you sure both of these things aren’t also done by AI?
It’s totally valid to question authorship when the author was an LLM.
Personally I found it pleasant to read. Why does it matter if/how much AI was used to write it if the end result is great?
For one, the whole text would show up in Safari's Reader mode, so I can skip past the hilariously low UI density that AI-generated websites have these days. Before AI you'd have to go out of your way put that much CSS padding into Wordpress! If everyone's going to play Terence Tao, at least copy his stylesheet.
I personally didn't
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
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".
> 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.
> 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.)
In the new world of AI, capable QA will rule the world.
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.
OpenAI's been building bridges with quite a few math departments these days – I'm sure they first thing they said is "please, god, no analogies"!
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.
10.6% smaller. Not bad.
https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_const...
There's a lot of 10% improvements between 0.1 and 0.
Λ ≤ 0 in the intro. Great site!
It's not wrong, is it? I didn't want to trust myself, Wikipedia agrees that the Riemann hypothesis is equivalent to Λ = 0 (because the lower bound is now 0). This proof lowers the upper bound, but we still don't know if it's 0 or between 0 and that upper bound (inclusive).
Yes, but Λ < 0 would make it negative
Nice, is this the maths equivalent of AI slop?
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.
The worst part is how in a decade, newer generations will write like this having been exposed to it their whole life.
Every sentence delivered like this.
With overdramatic pacing.
Forever.
Historically, the creative process has been a revolving door of people who are fed up with the status quo, and who later become the status quo, so I wouldn't worry too much about that.