I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.
An OpenAI model has disproved a central conjecture in discrete geometry
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Re: An OpenAI model has disproved a central conjecture in discrete geometry
#22While the result is impressive, this blog post is extremely disappointing.
- It does not show an example of the new best solution, nor explain why they couldn't show an example (e.g. if the proof was not constructive)
- It does not even explain the previous best solution. The diagram of the rescaled unit grid doesn't indicate what the "points" are beyond the normal non-scaled unit grid. I have no idea what to take away from it.
- It's description of the new proof just cites some terms of art with no effort made to actually explain the result.
If this post were not on the OpenAI blog, I would assume it was slop. I understand advanced pure mathematics is complicated, but it is entirely possible to explain complicated topics to non-experts.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#23How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#24I would have thought a triangular grid works better than a grid of squares. You get ~3n links vs ~2n for the square grid. Curious what the AI came up with.
Yes, not providing visualization of the solution seems criminal.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#25I dunno, I'm skeptical without proof. I've had the MAX+ plan for a while and I'm sorry, the quality between GPT vs Claude is night and day difference. Claude understands. GPT stumbles over every request I give it.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#26How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?
There's pages of comments from like 8 mathematicians in the attached pdf
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#27Re: An OpenAI model has disproved a central conjecture in discrete geometry
#28AI isn't going to supercharge science but I wouldn't be as dismissive as other posters here.
It will notice things that humans may have missed. That said - it can only work off the body of work SOMEONE did in the past.
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#29"The proof came from a general-purpose reasoning model, not a system built specifically to solve math problems or this problem in particular, and represents an important milestone for the math and AI communities."
I trust openAI's marketing team 100%
Re: An OpenAI model has disproved a central conjecture in discrete geometry
#30Is there a reason why we only hear of Erdos problems being solved? I would imagine there are a myriad of other unsolved problems in math, but every single ChatGPT "breakthrough in math" I come across on r/singularity and r/accelerate are Erdos problems.