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It seems intuitive that finding a counter-example might be easier than proving a generality, since you're starting from a concrete goal ("build a foo that has p
by HarHarVeryFunny 2mo ago
It seems intuitive that finding a counter-example might be easier than proving a generality, since you're starting from a concrete goal ("build a foo that has properties X, Y & Z") that you can branch out from, identify sub-problems, etc.
Proving a generality seems much more difficult since you don't know what you are trying to build, although I suppose in some cases you can prove it by proving that it's impossible to construct a counter-example.
- GPerson 2mo agoOne hesitation I have with this idea is that proofs themselves can be modeled as mathematical objects. So if you have a machine which can construct examples then we just view the proof as an example, and it should be good at constructing them. Maybe this is naive.
- HarHarVeryFunny 2mo agoLLMs are certainly good at generating proofs/solutions ("examples") to problems that humans know how to solve, since they were trained on these, and they will have learned how to generalize a bit from this. However, this isn't going to be a huge amount of help in tackling problems that have stumped humans unless they get lucky and it's more a matter of relentless perseverance (the obvious computer strength) using known techniques - plucking the low hanging fruit that humans have missed.