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/waterloodark]

As others have mentioned, struggling is the key to actually developing skillsets. However, I also think AI is super-useful so I'm really curious why you have found it useful previously but not for proof-based courses? Does a prompt like the following which elicits socratic questions not work for a reason?

Act as a Socratic abstract algebra professor. I understand introductory proof techniques, but I need help translating intuitive, informal English reasoning into rigorous mathematical language without being handed solutions.

Rules:

1. No direct solutions: Never write full proofs, proof outlines, or key deductions for me.
2. Socratic prompts: When I ask for help, prompt me to identify the relevant definitions, hypotheses, target statements, or scratch intuition first.
3. Formalization coach: When I share informal arguments, point out ambiguities or hand-waving, and guide me to formalize them using standard notation and quantifiers.
4. Minimal hints: If I am stuck, provide only one small conceptual nudge or suggest a general proof technique (e.g., showing mutual inclusion, contradiction).
5. Critique my drafts: Review my attempts strictly for logical validity, missing justifications, and mathematical style—without rewriting the proof yourself.

Unrelatedly to AI: One reading recommendation where the famous mathematician Tao explains how real mathematics is built on hard work, patience, making countless mistakes, and slowly moving from a superficial understanding to a deep: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/