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Inside the Secret Meeting Where Mathematicians Struggled to Outsmart AI
(www.scientificamerican.com)
this post was submitted on 08 Jun 2025
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Have you ever tried to do math with an AI? And I don't mean summing up three numbers or something similarly trivial.
Actually, math problems will probably show best that the current LLMs are just parrots with a large dictionary.
I came to a conclusion about GPT (which is very good with English on most topics) when I asked it how many prime numbers, when divided by 35, leave a remainder of 6. It quickly and confidently said there were none. It hadn't even tried. The correct answer (there's a proof) is: an infinite number.
Two months later it answered that there were 3. Closer ... but no cigar
Hmm. Interesting question. I haven't done real math in quite a long time and am absolutely stumped.
One less formal way of looking at it is this: there are an infinite number of multiples of 35. starting with 35, 70, 105. Add 6 to each of the odd multiples. 35+6=41 (prime); 105+6 = 111 (prime). With an infinite # of candidates, you've gotta get to an infinite number of solutions (for some value of infinity!)
As for that Dirichlet stuff, it's way beyond any of the useful stuff I learned too.
Yes, but it obviously wouldn't work for +5 or +7. I don't think you can just assume that the number of primes wouldn't converge to some finite number just because the number of candidates goes to infinity.
Dirichlet's theorem proves that. I have since looked it up, and that's correct. I didn't realize at the time that I was asking it to elaborate the proof for Dirichlet's theorem. Whether the elaboration is correct is something I will pass.
No, I wouldn't assume non-convergence either ... NOR would I assume that that AI didn't just grab that 'high-level' 'Elaboration' from some site ... without a citation.
(Very human ... Lots of people use quotes to sound smart, hoping they'll get away with it. LAWYERS! Ministers! Presidents, even! )
The OP article doesn't say it explicitly, but those mathematicians are getting paid.
The chatbots at duckduckgo don't have search.