101–110 of 562 posts
Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...
Earlier quoted context omitted.
The reason this was "easy" is because the conjecture turned out to be false. If the collatz conjecture holds true (and most mathematicians seem to think it will), it will be much harder to prove than your average Erdos problem.
True but Noam brown (openai researcher) said that in 2 years AI will start creating new math.
For the people saying goalposts have moved etc, whats your endgame?
Earlier quoted context omitted.
The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?
Reading the chain of thought for Fable, it is incredulous as well. It keeps thinking that it must be missing something or that this is a trick, because it can't have just found a counterexample to a famous conjecture. It's just like us! https://cdn.xcancel.com/pic/orig/EA1E99C3DAE99/media%2FHNpQX... https://cdn.xcancel.com/pic/orig/3B5C0B867A7C3/media%2FHNpQU...
Earlier quoted context omitted.
Maybe, maybe not. The "proofs" may not have helped at all with finding a counterexample. Either way, it doesn't matter. A counterexample was found, no one found one before even though clearly a lot of people have tried who also had access to the prior "proofs".
This makes me wonder, what if anyone uses Fable-class LLM and passes of its novel results as their own work? There's no shortage of folks doing that in software, right now.
Earlier quoted context omitted.
I'd rather wait for independent seasoned mathematicians to verify such claims first before someone at said AI lab posting a claim about solving a proof online. Let this be a lesson to those who fell for such AI psychosis and to not believe everything you see on the internet as real.
Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.
Earlier quoted context omitted.
The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?
Reading the chain of thought for Fable, it is incredulous as well. It keeps thinking that it must be missing something or that this is a trick, because it can't have just found a counterexample to a famous conjecture. It's just like us! https://cdn.xcancel.com/pic/orig/EA1E99C3DAE99/media%2FHNpQX... https://cdn.xcancel.com/pic/orig/3B5C0B867A7C3/media%2FHNpQU...