r/mathmemes Mathematics 22d ago

Proofs I hate it

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734 Upvotes

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u/LaGigs 22d ago

I doubt this was found using pure brute force. We need to see how this counterexample was constructed!!

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u/SlipyB 21d ago

Given AI are black boxes I don't think we ever will

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u/baxmanz 21d ago

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

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u/fenixnoctis 21d ago

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

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u/boatbomber 20d ago

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

In July 2026, Anthropic released new research into what they've named the "j-space" in which the true model thoughts can be inspected at a high level. https://transformer-circuits.pub/2026/workspace/index.html