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I am thinking there’s a large category of problems that can be solved by resampling existing proofs. It’s the kind of brute force expedition machine can attempt

I am thinking there’s a large category of problems that can be solved by resampling existing proofs. It’s the kind of brute force expedition machine can attempt relentlessly where humans would go mad trying. It probably doesn’t really advance the field, but it can turn conjectures into theorems.

simianwords 6mo ago
How do you think you can design a benchmark to solve truly novel problems?
utopiah 6mo ago
Indeed, can't find my old comment on the topic but that's indeed the point, it's not how feasible it is to "find" new proof, but rather how meaningful those proofs are. Are they yet another iteration of the same kind, perfectly fitting the current paradigm and thus bringing very little to the table or are they radical and thus potentially (but not always) opening up the field? With brute force, or slightly better than brute force, it's most likely the first, thus not totally pointless but probably not very useful. In fact it might not even be worth the tokens spent.
PxldLtd 6mo ago
I'm of the opinion that everything we've discovered is via combinatorial synthesis. Standing on the shoulders of giants and all that. I'm not sure I've seen any convincing argument that we've discovered anything ex nihilo.
- mrtesthah 6mo ago
  How about this guy? https://en.wikipedia.org/wiki/Srinivasa_Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
t-writescode 6mo ago
I wonder if teaching an LLM how to write Prolog and then letting it write it could be a great way to explore spaces like this in the future. Other people in I wonder if teaching an LLM how to write Prolog and then letting it write it could be a great way to explore spaces like this in the future. I only ever learned it in school, but if memory serves, Prolog is a whole "given these rules, find the truth" sort of language, which aligns well with these sorts of problem spaces. Mix and match enough, especially across disparate domains, and you might get some really interesting things derived and discovered that are low-hanging fruit just waiting to be discovered.

simianwords 6mo ago

How do you think you can design a benchmark to solve truly novel problems?

utopiah 6mo ago

Indeed, can't find my old comment on the topic but that's indeed the point, it's not how feasible it is to "find" new proof, but rather how meaningful those proofs are. Are they yet another iteration of the same kind, perfectly fitting the current paradigm and thus bringing very little to the table or are they radical and thus potentially (but not always) opening up the field? With brute force, or slightly better than brute force, it's most likely the first, thus not totally pointless but probably not very useful. In fact it might not even be worth the tokens spent.

PxldLtd 6mo ago

I'm of the opinion that everything we've discovered is via combinatorial synthesis. Standing on the shoulders of giants and all that. I'm not sure I've seen any convincing argument that we've discovered anything ex nihilo.

mrtesthah 6mo ago
How about this guy? https://en.wikipedia.org/wiki/Srinivasa_Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

t-writescode 6mo ago

I wonder if teaching an LLM how to write Prolog and then letting it write it could be a great way to explore spaces like this in the future. Other people in I wonder if teaching an LLM how to write Prolog and then letting it write it could be a great way to explore spaces like this in the future. I only ever learned it in school, but if memory serves, Prolog is a whole "given these rules, find the truth" sort of language, which aligns well with these sorts of problem spaces. Mix and match enough, especially across disparate domains, and you might get some really interesting things derived and discovered that are low-hanging fruit just waiting to be discovered.