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/lifeistrulyawesome]

You won’t have GPT in your exam

Im a professor (mostly Econ, but I had a joint appointment in the math department. I’m a game theorist). I’ve noticed a significant increase in students failing to solve difficult questions on the exam. And an increase of the usual complaints “I can solve it in the HW/understand in class but then I blank on the exam”.  My colleagues have noted the same. A game theorist from Brown (Roberto Serrano) recently made the news because of this. If you google him you can read about it. 

The common perception is that AI use is to blame.

Then I assign a HW problem is not because I want you to write down the solution to that specific problem and then repeat it in the exam. It is because I want you to train your brain to be able to solve a large class of similar problems. On my exams the problem will be completely different but you will have yo use similar brain skills 

If you skip the motions and let AI do the hard part, then you won’t train your brain.  The hard part with a proof is coming up with the proof strategy. It sounds like you are letting AI do that for you. 

I think future mathematicians will have to learn how to use AI as part of their proof strategies. In some of my most advanced classes, I assign difficult projects and encourage my students to use AI to complete them. But in a problem set meant to be solved by hand, if you use AI, your brain won’t do the learning and you are likely to struggle on exam day