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By understanding does that mean you have to memorize all the proofs?
Can I give two different answers? Based on my experiences so far (so two years at Newcastle):
For pure maths: No, there's way too many to memorise! Sometimes the proofs have like common steps or start off the same way so you should try and remember those though. For applied maths: We don't get as many proofs in applied modules so yeah you should really try and memorise them.
But there is a difference between understanding something and memorising something.
Bonus answer: for stats I personally tried to memorise the proofs since I didn't even understand any of it. I am so glad I never have to learn statistics ever again in my life.