4 ms·

A new ceiling for Λ: the de Bruijn–Newman constant

55 points by judegomila 1mo ago

tekacs 1mo ago
It's really fun seeing Manim [1] used to illustrate a proof! (See the video at the bottom) [1]: https://github.com/3b1b/manim https://github.com/3b1b/manim
unglaublich 1mo ago
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.
- deleted 1mo ago
  [deleted]
- Anthozoa 1mo ago
  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.
  - soulofmischief 1mo ago
    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.
StilesCrisis 1mo ago
Apparently the unfiltered Claude voice for mathematics is pretty similar to programming.
- nxobject 1mo ago
  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"!
arbirk 1mo ago
Λ ≤ 0 in the intro. Great site!
- rsstack 1mo ago
  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).
  - arbirk 1mo ago
    Yes, but Λ < 0 would make it negative
steinwinde 1mo ago
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-use-of-ai-and-especially-llms-in-major-mathematical-development 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".
- koliber 1mo ago
  In the new world of AI, capable QA will rule the world.
- zaik 1mo ago
  > 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.
  - steinwinde 1mo ago
    > 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/ https://palomar-registry.org/ or https://github.com/Vilin97/lean-pool https://github.com/Vilin97/lean-pool , or not?! (A considerable number of the presented proofs claim new results, as far as I can tell.)
tel 1mo ago
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.
- drx 1mo ago
  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?
  - NooneAtAll3 1mo ago
    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
  - nxobject 1mo ago
    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.
- koliber 1mo ago
  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.
1970-01-01 1mo ago
10.6% smaller. Not bad. https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_constant#Historical_bounds https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_const...
- lanstin 1mo ago
  There's a lot of 10% improvements between 0.1 and 0.
hodgehog11 1mo ago
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.
saberience 1mo ago
Nice, is this the maths equivalent of AI slop?

55 points by judegomila 1mo ago

It's really fun seeing Manim [1] used to illustrate a proof! (See the video at the bottom) [1]: https://github.com/3b1b/manim https://github.com/3b1b/manim

unglaublich 1mo ago

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.

deleted 1mo ago
[deleted]
Anthozoa 1mo ago
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.
- soulofmischief 1mo ago
  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.

StilesCrisis 1mo ago

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

nxobject 1mo ago
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"!

arbirk 1mo ago

Λ ≤ 0 in the intro. Great site!

rsstack 1mo ago
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).
- arbirk 1mo ago
  Yes, but Λ < 0 would make it negative

steinwinde 1mo ago

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-use-of-ai-and-especially-llms-in-major-mathematical-development 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".

koliber 1mo ago
In the new world of AI, capable QA will rule the world.
zaik 1mo ago
> 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.
- steinwinde 1mo ago
  > 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/ https://palomar-registry.org/ or https://github.com/Vilin97/lean-pool https://github.com/Vilin97/lean-pool , or not?! (A considerable number of the presented proofs claim new results, as far as I can tell.)

tel 1mo ago

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.

drx 1mo ago
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?
- NooneAtAll3 1mo ago
  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
- nxobject 1mo ago
  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.
koliber 1mo ago
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.

1970-01-01 1mo ago

10.6% smaller. Not bad. https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_constant#Historical_bounds https://en.wikipedia.org/wiki/De_Bruijn%E2%80%93Newman_const...

lanstin 1mo ago
There's a lot of 10% improvements between 0.1 and 0.

hodgehog11 1mo ago

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.

saberience 1mo ago

Nice, is this the maths equivalent of AI slop?