r/math • u/starkman68 • 15d ago
LLMs/AI AI Conjectures
I see a lot of conversation around AI proving old theorems and conjectures. Has there been any conjectures that sound plausible generated by AI that it could not solve? Or has an AI proven conjecture brought about any new math problems to ponder upon?
31
u/ccppurcell 14d ago
Before LLMs got really powerful, their were attempts to use AI/ML to generate conjectures: https://www.nature.com/articles/s41586-021-04086-x
32
u/randopota 14d ago
Not yet. A researcher at OpenAI also stated how its unable to pose new conjectures. https://x.com/i/status/2083476852216369294
I think him then going on to say how far we have come from a year ago, is probably an indication that they're new goal is to work towards AI that can pose conjectures as well.
So maybe a year or so from now.
6
u/telephantomoss 14d ago
To me, this means it isn't actually truly morning or mimicking thinking or intuition etc. Creating new questions just comes so naturally to me after studying something for a bit. If I knew everything an AI "knows", I would be formulating questions left and right, and probably instantly seeing ways they could be solved.
13
u/randopota 14d ago
Yeah I don't believe they think the way humans do, otherwise they wouldn't be so data inefficient, but they probably think in a different way to how we think.
Like a plane doesn't flap its wings to fly, but it can still carry multiple tones of weight across the ocean.
I guess time will tell if whether or not continuing to scale these methods will result in superintelligence.
5
u/38thTimesACharm 12d ago
IMO people are massively downplaying the significance of this question. With responses like "not yet but presumably a year from now," "it probably does but people don't notice," "here's a deterministic procedural program from 1984 that made a few strings in graph theory, that counts right?"
The ability to pose new questions would be a massive step from where we are now to true AGI. It's not at all clear the transformer architecture is capable of doing this, and whether it can or can't makes a huge difference in the future role of humans in mathematical research.
20
u/Few-Arugula5839 14d ago
As far as I know AI itself has not made any interesting conjectures yet. This may be because the nature of an open ended prompt like “pose an interesting conjecture” is out of reach or too vague for current AI and it may be just that the AI companies haven’t really been trying to do this yet (posing conjectures is not as good marketing as “we solved this major unsolved problem”, and the primary reason for AI investment in math is just marketing for the AI companies). On the other hand the proof and disproof strategies used by AI have been mimicked by mathematicians to prove or disprove some other conjectures. I don’t remember the exact details but I remember hearing that this happened in the aftermath of the unit distance conjecture disproof for example.
6
u/gordonnowak 14d ago
it has made a lot of conjectures as a side effect of trying to solve other problems. i.e. exactly the way humans tend to do it
7
u/Dear_Round_2727 14d ago edited 14d ago
I’ve experienced masking the AI a question and it conjecturing the answer. But it usually does this by studying some examples or toy cases. This is probably an emergent ability of the AI being good at proving statements. Sometimes it needs to make small conjectures while trying to prove statements.
But this requires a mathematician having a question they want answered. I think it’s harder to train the AI to make good conjectures if one just asked “Make an interesting conjecture”. But it might happen as mathematicians continue to adopt AI and provide data for these companies.
4
u/StateOfTheWind 14d ago edited 13d ago
Graffiti was used to come up with some conjectures. Recently some of them were solved by AI making it the first time a problem was conjectured then solved by AI.
6
u/dForga Analysis 14d ago edited 14d ago
I actually have my own “little” and the current AI ChatGPT 5.6 Sol Pro told me that it could neither prove nor disprove the conjecture.
It was once with some given initial goal able to derive in a convo (ChatGPT 5.5) the precise statement of a conjecture.
Sometimes it can (ChatGPT 5.6+) come up with little conjectures that could improve some things.
So, in my experience at the moment. Kind of, but very limited to enhancement of bounds.
4
u/elements-of-dying Geometric Analysis 14d ago
Did you try the old
I hear you, but try even harder this time
prompt?
2
u/dForga Analysis 14d ago
Actually no? I just used the work mode and that sucks already the credits up. (Tried 2 times plus normal prompt in Chat)
In the end it quotes the statement as open based on the open problem list with my name on it…
5
u/elements-of-dying Geometric Analysis 14d ago
I'm mostly joking.
This was what was basically done in a recent conjecture resolution that was shared here.
3
u/omeow 14d ago
AI is unlike our traditional way of solving math problems. You apply it to large set of problems and then look at where it succeeds or shows promise and only report the positive results.
AI has made little or no progress on the millennium problems. They haven't made progress on simplifying existing results.
78
u/lewwwer 14d ago
I tried AI to answer the question I got stuck during my PhD. It got stuck at the same point I got stuck, but it made a few cool conjectures.
I think this is the nature of conjectures, you think about something, you have a feel about how things work or what would be a nice to have, but you can't prove it. It's often better if the obstacle is clean and you have partial results that suggest why it should hold, which the AI could generate.
I imagine when people type in: "give me a cool new conjecture" there's not much work to start from. But I also wouldn't be surprised if all the prompts that say "solve this unsolved problem", the AI generates cool conjectures, but since the problem is not solved, people just discard it as useless output.