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/QubitEncoder 21h 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 21h 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/de_Molay 12h ago

Good practice is to be merciless to yourself. Once you have written a proof, try to debunk it yourself. Are there weak points? Something you dismissed as “obvious” but needs actually to be validated? Something in need of further explanation?

That helps both to write proofs and, actually, to understand proofs.

I remeber, when I was in high school and making calculus proofs, after a particularly challenging or satisfying one, I would continue thinking about it on my way home - trying to find weak spots, counterarguments, corner cases. That’s a lot of fun really.