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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 ChatG
by 0x5FC3 5mo 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.
- tonfa 5mo agoAfaik this is because there is a community and database around them.
- 0x5FC3 5mo agoInteresting. OpenAI could also be trying to solve other problems, but Erdos problems maybe falling first?
- CSMastermind 5mo agoNo, 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.
- ric2b 4mo agoI'm curious how the relative difficulty between the problems can be assessed when no one knows how to solve any of them.
- throw-the-towel 5mo agoThey're just famous because Erdos was a great mathematician, kinda like the Hilbert problems a century earlier.
- empath75 5mo agoIt'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.
- 1qaboutecs 5mo agoAlso fewer prerequisites to understand the statement than the average research problem.
- bananaflag 5mo agoErdos problems are easier to state, thus they make a great benchmark for the first year of AI mathematics.
- famouswaffles 5mo agoIt's not just Erdos problems - https://news.ycombinator.com/item?id=48213189 https://news.ycombinator.com/item?id=48213189
- jltsiren 5mo agoErdős 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.
- edanm 5mo ago> and [Erdős problems are] sufficiently uninteresting that people have not spent that much effort trying to solve them. Note that this is not really true of this problem in particular.
- dandaka 5mo agoDo we have a list of open problems? Would love to see a chart, where AI solves such problems one by one in the upcoming years.
- odie5533 5mo agoI was promised a cure for cancer, but all I got was this disproof of an Erdos problem.
- xyzsparetimexyz 5mo agoThe models can't actually so good work on practical problems so openai tasks them on stuff nobody cares about
- TrackerFF 5mo agoAs others have written, Erdős was a lifelong curator of mathematical problems, from high-school level problems to the types that will land you a Fields medal. Like the Collatz conjecture. Most new math problems appear in other papers, doctoral dissertations, etc. Usually you'll find them in the "future work" / "future research" section. So obviously in order to present and formalize these problems, you either need the author(s) to do it, or some reader. At this level of math, there are many extremely niche fields, where the papers might only be read by a small amount of people. In short, it is a visibility problem. But, I figure, there's some potential use in AI models to extract and present these problems, which would make them available to a larger audience. That is exactly what Erdős did. His life revolved around math, and seeking mathematical questions.
- cold_harbor 5mo agoErdos problems are well-posed for AI — elementary statements, exact counterexample targets, extensively catalogued. selection bias: these are exactly the problems AI can actually search