Funny. I made a captcha challenge of calculus problems for a comment section on my personal blog page. But 5 years after college, I couldn't remember how to even do them myself so I changed it :-/
You don't actually need much, for a form I used to get spam in I just added a "write 42 here" so anyone who actually cares to read would be able to fill it. spam fell to 0.
(for a site with a slightly higher profile this wouldn't be enough, but for a minor corner of the internet with no ill intent actually aimed at it that turned out to be enough to block the fuzzing "fill all the forms" spam)
As contrasting experience, I did that (a simple math problem) on our contact form and it did NOT drop spam to zero; our spammers were too smart for that. Even an actual reCAPTCHA didn't completely eliminate it (although it mostly did, enough that it's fine for us).
Similarly an empty input field that is css'd to be outside the viewport is often filled by spambots but not humans. But I like the edge case UX of your idea more.
Just watch out that Chrome’s autofill doesn’t fill it in. Cost us a huge chunk of new signups until we found out. Chrome ignores autofill directives under some circumstances.
It's also visible for users with CSS overrides and/or other browser inpairments. The more I think about it the more strongly I prefer the "type 42" explicit input field.
The question I got was surprisingly simple: it asked to find "the least real root of the polynomial p(x) = (x+5)(x-4)(x+1)". A determined attacker can quickly hack together something with Tesseract and feed it into even GPT-3.5 to get the correct answer to questions like these.
I guess that means the captcha is doing its job, since running LLMs isn't very cheap or scalable. But any harder problem means you start filtering a significant chunk of human users. Based on the other replies to your comment, it seems that the questions at their current difficulty already stop a lot of human users, yet allow a determined attacker with the setup I described pass through easily.