3 ms·
LLMs are much better at answering math when told to take the character of a drunk mathematician
by FormerBandmate 4y ago
LLMs are much better at answering math when told to take the character of a drunk mathematician
- resource0x 4y agoIt assumes this character by default. I asked several AI engines (via poe.com, which includes ChatGPT) to compute Galois groups of polynomials like x^5+x+1 and a couple of others, and in each case got not only a wrong answer, but a total non sequitur reasoning.
- bob1029 4y agoJust tried your query on GPT-4 preview: https://pastebin.com/6wPPCdBW https://pastebin.com/6wPPCdBW I have no expertise with this area, but it looks plausible to me - i.e. "You didn't give me enough info" vs "lol heres some fan fic about math".
- resource0x 4y agoThis is exactly the problem. It looks plausible. Every sentence makes sense. But they don't add up. Quote: > The polynomial given is f(x) = x^5 + x + 1. Since the polynomial has no rational roots (by the Rational Root Theorem) and it is a polynomial with integer coefficients, it is irreducible over the rationals The polynomial has no rational roots - true. But it's not irreducible. Irreducibility doesn't follow from the absence of rational roots. Here's the factorization: x^5 + x + 1 = (x^2 + x + 1)*(x^3 - x^2 + 1).
- bob1029 4y agoThank you for clarifying. I put your remarks into the same prompt and it essentially devolved into recursive garbage after agreeing with you.