71–80 of 1001 posts
Is 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.
As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.
I guess if this stuff is going to make my employment more precarious, it’d be nice if it also makes some scientific breakthroughs. We’ll see
shame we won’t see any of these medical breakthroughs when we all lose our jobs and thus our healthcare
Can anyone find (or draw) a picture of the construction?
I’m very out of my depth, but the structure of the proof seems to follow a pattern similar to a proof by contradiction. Where you’d say for example “assume for the sake of contradiction that the previously known limit is the highest possible” then prove that if that statement is true you get some impossible result.
AI isn't going to supercharge science but I wouldn't be as dismissive as other posters here.
When I'm learning about a new subject, I'll ask Claude to give me five papers that are relevant to what I'm learning about. Often three of the papers are either irrelevant or kind of shit, but that leaves 2/5 of them that are actually useful. Then from those papers, I'll ask Claude to give me a "dependency graph" by recursing on the citations, and then I start bottom-up.
This was game-changing for me. Reading advanced papers can be really hard for a variety of reasons, but one big one can simply be because you don't know the terminology and vernacular that the paper writers are using. Sometimes you can reasonably infer it from context, but sometimes I infer incorrectly, or simply have to skip over a section because I don't understand it. By working from the "lowest common denominator" of papers first, it generally makes the entire process easier.
I was already doing this to some extent prior to LLMs, as in I would get to a spot I didn't really understand, jump to a relevant citation, and recurse until I got to an understanding, but that was kind of a pain in the ass, so having a nice pretty graph for me makes it considerably easier for me to read and understand more papers.
How central is it in the discrete geometry? Could anyone with the knowledge in the field reply?
While 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 aw…
Indeed, it's a pity. While many advanced math problems are highly abstract or convoluted to explain to a layman audience, this one in particular is about points in a 2D plane and distances. A drawing would have been nice.
I wonder how much this cost vs a Math Professor or a team of Math Professors.