Comment by 0x5FC3
4 hours ago
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.
Erdős problems form a substantial fraction of all mathematical problems that have been explicitly stated but not solved; are sufficiently famous that people care about them; and are sufficiently uninteresting that people have not spent that much effort trying to solve them.
Solving problems people have already stated is a niche activity in mathematical research. More often, people study something they find interesting, try to frame it in a way that can be solved with the tools they have, and then try to come up with a solution. And in the ideal case, both the framing and the solution will be interesting on their own.
Erdos problems are easier to state, thus they make a great benchmark for the first year of AI mathematics.
Afaik this is because there is a community and database around them.
Interesting. OpenAI could also be trying to solve other problems, but Erdos problems maybe falling first?
No, Erdos problems were accepted as sort of a benchmark. There's a bunch of reasons they're favorable for this task:
1. They have a wide range of difficulties. 2. They were curated (Erdos didn't know at first glance how to solve them). 3. Humans already took the time to organize, formally state, add metadata to them. 4. There's a lot of them.
If you go around looking for a mathematics benchmark it's hard to do better than that.
It's not just Erdos problems - https://news.ycombinator.com/item?id=48213189
They're just famous because Erdos was a great mathematician, kinda like the Hilbert problems a century earlier.
I was promised a cure for cancer, but all I got was this disproof of an Erdos problem.
It's a large set of problems that are both interesting and difficult, but not seen as foundational enough or important enough that they have already had sustained attention on them by mathematicians for decades or centuries, and so they might actually be solvable by an LLM.
Also fewer prerequisites to understand the statement than the average research problem.
The models can't actually so good work on practical problems so openai tasks them on stuff nobody cares about