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The Fine Details and How To Deal With Them

I know a lot of posts on here are about people struggling in grad school so I hate to make another, but there's been an issue I have been having that I am yet to see a good thread about. It's sort of a big problem too: I suck at the fine details of a proof. Now, to put this in some perspective I got into graduate school to do my Master's with the option to do a PhD after with a rather substantial amount of funding. I did my undergraduate in mathematics and got a job as a machine learning researcher right out of my undergrad. After about a year and a half my employer offered to send me to graduate school through a certain funding program and as I had plans to go already, I accepted.

Now, nearing the end of my first semester, a glaring problem has come up with my mathematical ability. I do not have an eye for detail. When I do proofs, I tend to leave little things out, assume certain things are obviously true, and just leave out important details that make the proof sub-par. It's not usually totally wrong and it's not a struggle for me to understand things (at least no more than most graduate students) but for the life of me I cannot seem to write a good proof. My supervisor says he's not too worried, but that I really need to work on that, as it seems to be not on par with my ability to "see the big picture". My question is basically how do you get good at that? Is it normal to struggle with it?

submitted by /u/MaxMachineLearning
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