ChatGPT finds an error in Terence Tao's math research
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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.
I'm a research mathematician working in Tao's field. I'm not claiming to be as prolific as he is, not by a long shot -- but other mathematicians do understand, critique, develop, and engage with his work. Indeed, many of his papers are collaborative with a variety of other mathematicians.
Picture him as the star player on a basketball team. He may be the strongest player on the court, but he's still playing the same game as everyone around him.
Picture him as the star player on a basketball team. He may be the strongest player on the court, but he's still playing the same game as everyone around him.
Yes I’m stretching this a bit, and certainly don’t mean this as a slight on Tao’s peers. That said I’m sure there’s someone out there who fits this description better. I was picturing a modern-day Ramanujan in my mind.
I certainly didn't take it as a slight against myself. Rather, I've met Tao and several other top mathematicians, and I don't imagine any of them would say they fit that description.
Indeed, Tao himself has written criticism of the "cult of genius":
https://terrytao.wordpress.com/career-advice/does-one-have-t...
Indeed, Tao himself has written criticism of the "cult of genius":
https://terrytao.wordpress.com/career-advice/does-one-have-t...
Normies* like me too. If only it wasn’t gonna eat us all soon it would be such a marvelous thing
* I delude myself
* I delude myself
No it’s going to eat all of us soon, right now for some careers and maybe 30-50 years for the rest. Or to put it in another way, we are never going to be replaced by AI, we simply don’t hire anymore.
> 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...
Fwiw, wiki Section 2(d): https://github.com/teorth/erdosproblems/wiki/AI-contribution...
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.
> 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