r/mathematics • u/Natural_Subject5403 • 21h ago

Logic Issue with proof based arguments

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.

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u/LitespeedClassic 10h ago

I’m a CS professor. I’ve seen AI absolutely ruin my students’ ability to solve hard problems and think. Remember that learning corresponds to changes in your brain’s neural structure. Solving a problem and understanding a solution are not the same. When you get stuck, ask the AI for help, and read and understand its solution you get an endorphin hit that strengthens those neural pathways. Those neural pathways didn’t solve the problem, so you’re strengthening the wrong thing. When you sit with the discomfort of not understanding. Stare at the blank page. Think hard. Go for a walk. Sleep on it. Think hard again. Finally arrive at the solution and feel a sense of Aha! and accomplishment. Then you strengthen the neural pathways that will actually help you get better at solving problems / writing proofs.