5 ms·
IMO problems aren't fundamentally different from chess or other games, in that the answer is already known.
by piombisallow 2y ago
IMO problems aren't fundamentally different from chess or other games, in that the answer is already known.
- Smaug123 2y agoI really don't understand what you mean by this. 1) it's not known whether chess is a win for White or not. 2) IMO problems, such as 2024 problem 1 which the system solved, are often phrased as "Determine all X such that…".
- diffeomorphism 2y agoYou are attacking a straw man and the point made is pretty good. Competition problems are designed to be actually solvable by contestants. In particular, the problems should be solvable using a reasonable collection of techniques and many "prep courses" will teach you many techniques, tools and algorithms and a good starting point is to throw that stuff at any given problem. So just like chess openings putting in lots of leg work will give you some good results for that part. You might very well lose in mid and late game, just like this AI might struggle with "actual problems" It is of course still very impressive, but that is an important point.
- Smaug123 2y agoI'm attacking nobody! I literally couldn't understand the point, so I said so: as stated, its premises are simply clearly false! Your point, however, is certainly a good one: IMO problems are an extremely narrow subset of the space of mathematical problems, which is itself not necessarily even 50% of the space of the work of a mathematician.
- wufufufu 2y agoKinda? Chess isn't solved. Complex problems can have better solutions discovered in the future.
- jeremyjh 2y agoIt isn't solved but the evaluation (which side is better, by how much, and which moves are best) of a strong engine is - for all practical purposes - an answer to every chess position you can pose to it. This makes it easy to gauge improvement and benchmark against other systems compared to some other problems.
- Davidzheng 2y agolol
- osti 2y agoBut the answer is probably not known by you, in particular.
- piombisallow 2y agoYes, sure, but this doesn't mean that this generalizes to open math research problems, which would be the useful real-world application of this. Otherwise this is just playing known games with known rules, granted better/faster than humans.
- energy123 2y agoIMO and Chess are the same in the most important respect, you can use Lean or a simulated chess game to create unlimited quality training labels. Any problem of this category should be solved with enough compute and clever architecture/metacognition design. The more intractable problems are where data is hard to find or synthesize.
- almostgotcaught 2y ago> in that the answer is already known. you realize this holds true for all of math right? outside of godel incompleteness potholes every proof/theorem is a permutation of ZFC. And you can fix the potholes by just filling them in with more Cs.
- diffeomorphism 2y agoThat seems shallow and not really useful. Like sorting is easy, just take all permutations and look at each one to see whether is sorted.... it just might you take longer than the heat death of the universe to actually do that.
- lanstin 2y agoThere are elementary Diophantine equations that are independent of ZFC. What is your approach for those?