21–30 of 681 posts
The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709
What a world we live in.
Two, at some point AIs will be able to use other context like the fact that this is Terrence Tao and not your average Joe and change how it answers, either in tone or structure.
I'll have a blog post up tomorrow about it but the Jacobian Conjecture counterexample is a very funny cognitohazard for LLM assistants. It's a paradox for modern LLMs: they have enough math skills such that they can easily compute the Jacobian to formally verify the counterargument, but its own knowledge base is locked prior July 19th 2026 where all it knows is that the Jacobian Conjecture is unsolved and a random ch…
Maybe it's silly, but from someone who is ignorant on this topics, what are the consequences of this kind of "discoveries"? Is it something "revolutionary" or just another small brick that will pile up until something really "revolutionary" will happen?
By itself, no consequence. But over time, provided we keep pumping out talented and qualified mathematicians and keep subsidizing costs, we could maybe hit a breakthrough... somewhere... that has real impact.
Just awesome to see new knowledge hit an incredible mind like this. Having these "what if" discussions is what I miss most from JPL and academia.
Maybe it's silly, but from someone who is ignorant on this topics, what are the consequences of this kind of "discoveries"? Is it something "revolutionary" or just another small brick that will pile up until something really "revolutionary" will happen?
"Hey Fable, please generate me the next 1000 undiscovered bitcoin hashes"
Maybe they'll find a solution where P=NP.
That could really throw a wrench into the whole internet thing.
It seems they need an expert human driver for now.
Similar to how Cypher puts it: I know this is “just” next token inference, matrix mult and just software, ie there’s no “intelligence” there BUT, looking at this convo … damn! The fascinating this is that the LLM is not acting as a tool here AFAIk, but very much like a colleague. I have no knowledge of the domain and have only PhD EE level math knowledge, so maybe my bar is too low.
Expand the entire expression, then change the representation to find the core axis. You can't see the axis from just one perspective, so you change the representation. In programming terms, it's like applying multiple domain models. Then break it down into small contract units. Why is it a Jacobian monomial? Why does x satisfy a cubic equation? And so on.
Then swap out the modeling under a hypothesis, assemble it all back together, and verify it through the equation.
This feels similar to modeling in programming.
Observe the whole -> explore better modeling -> decompose local problem -> verify independently -> reason about the highre level structure -> integrate back into the original problem.
This feels similar to when I receive work from a client and write a programming proposal
Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same unfamiliar sense of total loss like when encountering hard mathematics.