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.
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?
> 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.
> 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]
Conjectures 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 · · focus · HN ↗
AIiscoming · · focus · HN ↗
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 · · focus · HN ↗
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 · · focus · HN ↗
scrubs · · focus · HN ↗
bmitc · · focus · HN ↗
It can be productive to assume something is true and see what happens.
aleph_minus_one · · focus · HN ↗
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] <a href="https://en.wikipedia.org/w/index.php?title=Riemann_hypothesis&oldid=1375292396" rel="nofollow">https://en.wikipedia.org/w/index.php?title=Riemann_hypothesi...
[2] <a href="https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Generalized_Riemann_hypothesis_(GRH)" rel="nofollow">https://en.wikipedia.org/w/index.php?title=Generalized_Riema...
[3] <a href="https://en.wikipedia.org/w/index.php?title=Generalized_Riemann_hypothesis&oldid=1370923804#Extended_Riemann_hypothesis_(ERH)" rel="nofollow">https://en.wikipedia.org/w/index.php?title=Generalized_Riema...
[4] <a href="https://en.wikipedia.org/w/index.php?title=Standard_conjectures_on_algebraic_cycles&oldid=1374346010" rel="nofollow">https://en.wikipedia.org/w/index.php?title=Standard_conjectu...
[5] <a href="https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conjecture&oldid=1375037872" rel="nofollow">https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conj...
tha_hnrain · · focus · HN ↗
bee_rider · · focus · HN ↗
<a href="https://news.ycombinator.com/item?id=49748998">https://news.ycombinator.com/item?id=49748998
Make for a funny pairing.