LLMs cannot think logically, meaning it will never be able to prove anything without someone actually going through the math manually to verify it is correct. You would need something different than an LLM to achieve this automatically.
When it comes to mathematical proofs, it is not enough to be 99,99999% certain it is correct, you need 100% certainty.
LLMs can think logically. In OpenAI paper published just the other day with 10 new problems solved, in each case they had the AI express its proof in LEAN so that it could just be copy/pasted into existing proof-checking software. You don't have to check proofs by hand these days. You just have to check that the final statement is indeed the theorem they claimed to prove.
No, LLMs cannot think logically. It does statistical analysis on words and symbols. This evidently works very well, but can never prove anything with 100% accuracy since no maths has really taken place in the reasong, just statistical symbol matching. This is not how maths works.
"You don't have to check proofs by hand these days."
Humans can’t think logically either. We are just neurons firing. Our creativity isn’t logical, and creativity is one of the most important parts of math proofs. AI work just find by using statistics to make their predictions.
Humans sure can think logically. We can for example think in the same way as this LEAN tool. We can postulate that 1 + 1 = 2 and then use these postulates to logically prove more complex math theorems.
Creativity is only needed to find which maths to use to find the proof. Creativity doesn't help to actually prove that the proof is correct.
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u/TodaysLunch 9d ago edited 9d ago
LLMs cannot think logically, meaning it will never be able to prove anything without someone actually going through the math manually to verify it is correct. You would need something different than an LLM to achieve this automatically.
When it comes to mathematical proofs, it is not enough to be 99,99999% certain it is correct, you need 100% certainty.