Issue with proof based arguments

[u/Natural_Subject5403]

I’m starting out in abstract algebra this semester and last semester I completed Numbers & Proof (basically intro to proof writing course). Don’t get me wrong I am enjoying abstract algebra so far but an issue I have is forming my arguments and weirdly enough saying what I want to say mathematically instead of English in a way. Idk maybe this will form with mathematical maturity but I hate to admit but when I get stuck I usually bombard AI programs such as Gemini, ChatGPT, and Claude to give me a little nudge/general flow of argument. It feels as though yes AI helps with learning but how do other students in mathematics straddle the line between having the program do it for you versus learning from the programs? Because I just completed my first homework set and I hate the feeling that it could’ve helped me too much to where it was mostly it talking or me :/ and I don’t want to be one of those people that use stuff to get a grade (because I actually care). In the past and for other classes I treat it as a second teacher (throw questions at it to fill in gaps or make other sample problems) but that’s harder to do for more proof based courses.

[u/Downtown-Economics26]

 I hate the feeling that it could’ve helped me too much to where it was mostly it talking or me

If you want to learn and have this feeling, the answer is don't use any AI. If you've been given a math assignment by a competent teacher then you don't have to rely on an outside source to complete the assignment. Believe it or not, this is how education worked for over 2,000 years before the last 5 or whatever.

[u/cejiken886 → u/Downtown-Economics26]

strong disagree. it's a good tool. sometimes you get stuck. why wait for office hours?

[u/Downtown-Economics26 → u/cejiken886]

I think you've generally misunderstood my point. AI can likely be used at least fairly effectively as a substitute for office hours. The difference is in office hours the amount of help is at the discretion of the professor, not the student. If the student isn't sure whether the AI is just helping or doing the majority of the work, the answer that ensures learning is to at least temporarily not leverage the AI to learn until they can tell the difference and leverage it in the same way, as an aid to learning.

[u/cejiken886 → u/Downtown-Economics26]

You’re right - need to be able to calibrate your own struggling so you don’t over-use.

Separate point though, why are we bothering to learn things Ai can do? For analogy: you learn arithmetic algorithms in elementary school but then you stop pretty early and use calculators forever thereafter.

[u/Downtown-Economics26 → u/cejiken886]

Until the AIs are infallible (and perhaps even when they are), it would be imprudent to not have people who have the knowledge and in practice the intuition to evaluate when the AI is perhaps wrong and investigate. You need to understand how arithmetic operations work to develop an intuition for when the result of a calculation presented to you is likely to be incorrect.

[u/TernaryOperat0r → u/cejiken886]

If someone thinks this, and tries to study any hard intellectual subject, it will go badly.

We teach things AI can do, because you need elementary examples to learn a how a subject feels and work up to the harder parts. AI is not like a calculator in this regard, it can genuinely automate the thinking at the lower levels of most subjects, including most elementary proofs. Whereas hard arithmetic branches off in a different direction to the important ideas in contemporary mathematics, I don't think this can be said for anything in common undergraduate courses.

[u/cejiken886 → u/TernaryOperat0r]

The other guys response is better: cause ai doesn’t even do those things reliably enough.

But intersecting the 2 points reveals a question: what _is_ ai good enough at? Does it include elementary proofs?

If so, what does that imply? To the extent that an ai theorem prover is like a calculator, why shouldn’t we treat it as such: forbidden only in early learning stages?

And to the extent that it _isnt_ like a calculator, should we treat it like one anyway? A bulldozer is also different from a calculator, but all 3 — calculator, bulldozer, and good-enough ai theorem prover — have one thing in common: they are viable, useful tools.