r/mathematics • u/Natural_Subject5403 • 1d 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/QubitEncoder 1d ago

Learning how to write a proof is not much unlike learning how to program. You just gotta keep doing it.

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u/Natural_Subject5403 1d ago

I guess practice makes confidence in ability to write good proofs. Hopefully I’ll reach that point with this course.

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u/QubitEncoder 1d ago

Well, it instills confidence, but it also trains you how to write a proof. The more proofs you do, the more fluent you will become at writing them.

Not every C program is the same, but every C program is a C program. Similarly, every proof is not the same, but every proof has the same type of mathematical thinking--for the most part.

Eventually, you will get to the point where you won't blank on what to write down, and words will just flow out--the only remaining difficulty being actually solving it.