Today I learned...

I've decided to start a new series of writing down what I learn each day. Math has been a bit frustrating recently, with me feeling like I'm treading water but losing my energy. I don't want to feel helpless, so instead I'm going to write down every day what I learned. Most of you probably won't understand it, but you can make up your own fun definitions of what the words mean. It's probably more interesting that way ;).

Today, I learned that I can look at curves questions like number fields. I also learned my advisor doesn't know everything the moment I ask a question!
I learned where the roots of unity part of unit group comes from in the unit theorem.
I learned a few different proofs of the efg-theorem, and actually understand some of them.