Comment Re:mostly mash-ups of existing techniques (Score 1) 114
Well, wait, I don't think that actually disproves the claim. I'm not saying it's not impressive, I just don't think it's as novel as you say.
When I ask an LLM to write me code that does something 'novel', it usually does quite a good job. I'm just using the freely available models, but they quite competently write code that is not truly derivative of any other code. If I give them some code of my own that has a bug in it, they'll find the bug and patch it, and that bug is, for all intents and purposes, unique.
You're still seeing a bunch of old patterns rehashed--I presume that other proofs introduce infinity families, and they can iterate through inside a clear logical structure to test whether or not something works. Again, this is impressive work, but I'm not personally convinced that this is 'novel' in terms of the broader corpus of mathematical knowledge. It didn't invent a new field of mathematics to solve your problem.
Even if you didn't prompt it, take a look sometimes at the contemplations of the models, if that's available to you. Before the model even arrives in your hands, it's got stacks of prompts giving it meta instructions, and it then generates prompts for itself to check your work. I think it would be interesting if you ran your experiment again on a new account that's fresh and see if you can watch the chain of reasoning. You might be right, it MAY be doing something TRULY novel, but as I've said, I've got my doubts.
Obviously, you're a mathematician and I'm not; I can't tell you that you're wrong about it if you insist that it is doing something new.