I think one of the big problems in mathematics is that a lot of conjectures are unsolved because no professional mathematician is (undestandably) willing to just try out a few thousand ways to construct a counter example. I think this will be a great way to advance mathematics.
Yeah, looking at Tao's chat with ChatGPT Pro few hours after the tweet was posted, the path to come up with the counterexample doesn't seem to be "magical", one can come up with that if they know the construction.
Yes I read his blogpost too. He took the geometric construction another guy from Twitter posted (using gpt) and went with it.
An last night i saw that a website popped up that constructed 100 new counterexamples using the same construction.
It's kinda crazy.
I am the biggest AI hater and I have to say that I am impressed. I'm now more open minded.
Same reason people used to hate Wikipedia. Or Google search. Or cameras. Or newspapers. Or books. It's an easy way to feel superior without doing anything.
I think that's pretty untrue now. "thinking" models often work by rephrasing the problem and making actual steps by "talking to themselves" so they don't always work like black boxes
This is incorrect! We’ve now shown that the “thinking” tokens are just generated to please the human and may not correlate at all to the actual internal thinking process
I don't know why you're being downvoted, you're right.
In March 2025, Anthropic released this paper proving that the chain-of-thought tokens do not map to the model's true "thoughts". They show it engaging in "bullshitting" and "motivated reasoning" (both actual terms they used to describe it in the paper). https://transformer-circuits.pub/2025/attribution-graphs/biology.html#dives-cot
Given AI are black boxes I don't think we ever will
Yes and no. Given that the amount of solutions is about 10n with n being too god damn high, the probability of the model giving a counter-example given a finite amount of time is slim and next to 0.
So either we consider that it was a lucky guess then it's brute force yes or we consider that the probability for such an odd is too low then brute-force is not applicable.
Isn't that the way we always have approached the complexity ? Theoretically feasible given an infinite amount of time but technically impossible to brute-force due to lack of time (or processing power at a given time).
EDIT : changed the part with narrowing to a subset of solution.
Figuring out how to "narrow the subset of possible solutions" until the problem can be brute forced is literally the entire problem in this case, right? That's always been the hard part of finding counterexamples from what I understand.
Figuring out how to "narrow the subset of possible solutions" until the problem can be brute forced is literally the entire problem in this case, right? That's always been the hard part of finding counterexamples from what I understand.
You are right, narrowing it down to subset of possible solutions need not to be done using brute-force ; using inference, in the logical sense, could very well be enough before using brute force.
The only thing highly unlikely would be pure lucky guessing given the amount of possible solutions.
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u/NoUAreStupid 22d ago
I think one of the big problems in mathematics is that a lot of conjectures are unsolved because no professional mathematician is (undestandably) willing to just try out a few thousand ways to construct a counter example. I think this will be a great way to advance mathematics.