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ChatGPT finds an error in Terence Tao's math research

42 points by codexon ↗ HN
https://www.erdosproblems.com/forum/thread/783

> Ah, GPT is right, there is a fatal sign error in the way I tried to handle small primes. There were no obvious fixes, so I ended up going back to Hildebrand's paper to see how he handled small primes, and it turned out that he could do it using a neat inequality ρ(u1)ρ(u2)≥ρ(u1u2) for the Dickman function (a consequence of the log-concavity of this function). Using this, and implementing the previous simplifications, I now have a repaired argument. TerenceTao

4 comments

[ 2.5 ms ] story [ 17.9 ms ] thread
mncharity
> On the wiki, I have decided to expand Section 2(d), "AI tools used to rewrite an existing argument" to also include cases such as the one here, in which the AI tool indirectly caused the argument to be rewritten in a substantive way (beyond mere typos etc.) by identifying a non-trivial mathematical issue in the previous version of the text, which was then fixed by a human author.

Fwiw, wiki Section 2(d): https://github.com/teorth/erdosproblems/wiki/AI-contribution...

squirrellous
It’s kind of interesting that AI opens up a new avenue for intellectual progress where even if you are the prevailing expert in your field and nobody else quite understands what you do, there is still an LLM that can mostly keep up with you and explain, critique, develop, and generally engage with your work. IOW people who are way ahead of their time now has a peer they can talk to.
7777777phil
Props to Tao for his response: he didn't just patch the sign error, he went back to Hildebrand's paper and found a better fix through log-concavity of the Dickman function.