[gjm11]

One thing in the article that strikes me as very strange is this:

"I suppose that, on a practical level, a take-home for the practicing mathematician is that if you use ChatGPT, don’t trust it to generate valid proofs, and even when it finds a valid proof, don’t be so sure it’s a good proof. And whatever you do, don’t have ChatGPT create a bibliography for you."

In isolation, that's all very good advice. But however is a take-home from what goes before? You used ChatGPT, it did generate a valid proof, it was "a solid by-the-book argument that employed a method I’ve used myself" which may or may not imply "a good proof" but suggests it was at least OK, and nothing in the story you told involves ChatGPT generating bibliographies at all.

[jamespropp]

Thanks for catching this! What was in my mind when I wrote the first of those two sentences was the entirety of my past experience using ChatGPT as a research tool, and all the times it made mistakes. (For a funny example, see my January 17, 2023 essay “Denominators and Doppelgängers” in which I describe ChatGPT's proof that .999... is less than 1.) But you're 100% right that the version of my essay that I posted last week didn't make this clear; I'll update it appropriately. I'll also add a brief description of ChatGPT's bibliographic blunder.