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A comment on GPT-4. Parent comment

Re:GPT-4 by resource0x on Tuesday March 14, 2023 @04:06PM (#35157603)
It 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.
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Re:GPT-4 by bob1029 on Tuesday March 14, 2023 @04:51PM (#35158347)
Just tried your query on GPT-4 preview: 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".

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Re:GPT-4 by resource0x on Tuesday March 14, 2023 @07:44PM (#35161246)
This 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).

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Re:GPT-4 by bob1029 on Tuesday March 14, 2023 @08:21PM (#35161762)
Thank you for clarifying.

I put your remarks into the same prompt and it essentially devolved into recursive garbage after agreeing with you.

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