nostalgebraist:

I had some fun asking ChatGPT about cases from “Counterexamples in Analysis.” You get this kind of uncanny valley math, syntactically and stylistically correct but still wildly wrong.

This was a response to “Prove or disprove: there exists a nowhere continuous function whose absolute value is everywhere continuous.” It responded in TeX, which I coped into a TeX editor.

Another answer to the same question:

If I ask Bing the same question, it tells me about something called the “very not continuous function” (lol):

I can’t find the term “very not continuous function” anywhere on the web except this page, the one Bing cites.

The page looks kind of click-farm-like, and it’s not clear what function it means by “the very not continuous function.”  But it does discuss the question I asked, so at least there’s that.

Anyway, it’s not web search relevance that I care about here – it’s math ability.

I tried again with Bing, this time with a different “Counterexamples in Analysis” case, an injunction not to perform a web search, and a half-hearted nod to chain-of-thought prompting.

The resulting discussion was an adventure in Helpful™ overconfidence:

(I said “bing ai” in the last screenshot due to a bizarre UI decision by Microsoft that makes it very easy to say “bing ai” to Bing without wanting or intending to. Don’t ask me, I didn’t do it ¯\_(ツ)_/¯ )