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If you ask an AI if "P=NP", it will certainly give an answer. It has to, because the answer is either "yes" or "no". If you ask it to then prove its assertion,
by otabdeveloper4 12d ago
If you ask an AI if "P=NP", it will certainly give an answer. It has to, because the answer is either "yes" or "no".
If you ask it to then prove its assertion, it will then certainly output the tokens that look like a plausible proof. It has to, as it is programmed too.
This "proof" might even be thousands of pages of very technical looking and professional sounding jargon.
It's not a real proof though, and as an artifact it is 100% useless to both the field of mathematics and humanity.
- sigmoid10 12d agoThat's why this proof and all the other high profile AI proofs were written in lean, which allows you to verify them in a formal deterministic language. You still might not understand it as a human, but any computer with a simple processor can verify the proof's correctness. And from there you will undoubtedly see other people make sense of the proof's key steps using AI too. And the models might even pick up on further details useable for other proofs that humans didn't see. In the end I'm 100% convinced that abstract math will eventually be primarily done by computers, similar to how linear algebra and numerics have been done exclusively done by computers for a while. Noone would even consider multiplying a 100x100 matrix by hand anymore, if only because it is much more likely that you as a human will make a mistake.
- otabdeveloper4 11d agoThat's assuming that "formal deterministic language" is equivalent to mathematical reality, or that it even reflects it correctly. It's the accepted view nowadays but akshually quite the hot take.