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I wonder if we’ll end up in a weird situation a decade from now, where every conjecture will collapse into one of two states: counterexample found by AI, or as
by bee_rider 9d ago
I wonder if we’ll end up in a weird situation a decade from now, where every conjecture will collapse into one of two states: counterexample found by AI, or assumed to be true.
- AIiscoming 9d agoMight be a lot faster than you think. I'm wondering though when we as a society / all the normal money flowing into universicites and research start to recupe and invest AI resources more deliberate. Like are we working with ai on superconductors (easiest example i have, i don't know enough math). Whats the most 'math' we need to advance for human progress?
- kergonath 9d ago> Like are we working with ai on superconductors Yes, we are. Basically, for any scientific problem worth any funding, there is someone using AI on it. That said, for materials science it’s usually not LLMs, or even transformers (unless the AI used to write slop papers count). But there is a menagerie of AI or deep learning models that people are trying to use.
- vouaobrasil 9d agoNo way. Mathematicians don't assume things to be true even if there are no counterexamples.
- scrubs 9d agoAgree. I give up isn't the MO of many with graduate degrees.
- bmitc 9d agoGenerally, no, but sometimes, yes. It can be productive to assume something is true and see what happens.
- aleph_minus_one 8d ago> No way. Mathematicians don't assume things to be true even if there are no counterexamples. It depends: there do exist some conjectures for which there don't exist any proofs, but a huge amount of results assuming this conjecture (which is very near to assuming that the conjecture is true). Examples are: - Riemann hypothesis [1] - Generalized Riemann hypothesis (GRH) [2], and potentially also Extended Riemann hypothesis (ERH) [3] - Standard conjectures on algebraic cycles [4] - perhaps Schanuel’s conjecture [5] -- [1] https://en.wikipedia.org/w/index.php?title=Riemann_hypothesis&oldid=1375292396 https://en.wikipedia.org/w/index.php?title=Riemann_hypothesi... [2] https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Generalized_Riemann_hypothesis_(GRH) https://en.wikipedia.org/w/index.php?title=Generalized_Riema... [3] https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Extended_Riemann_hypothesis_(ERH) https://en.wikipedia.org/w/index.php?title=Generalized_Riema... [4] https://en.wikipedia.org/w/index.php?title=Standard_conjectures_on_algebraic_cycles&oldid=1374346010 https://en.wikipedia.org/w/index.php?title=Standard_conjectu... [5] https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conjecture&oldid=1375037872 https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conj...
- tha_hnrain 9d agoConjectures are always assumed to be true until a counter-example could be found/constructed. That's why they are an interesting conjecture in the first place.
- bee_rider 9d agoYour comment and this one: https://news.ycombinator.com/item?id=49748998 https://news.ycombinator.com/item?id=49748998 Make for a funny pairing.