Today I Learned

Welcome

Here I've put some things that I learned. To be clear, sometimes I'll have skimmed a text in advance so that I already know the statement. So when I say "learn,'' I'll mean something roughly isomorphic to "learned a proof of.''

A few remarks on style might be helpful. First, my writing here is not good mathematical writing, per se. The goal in the presentation is not clarity but motivation, so I will often give arguments which appear more awkward than the standard argument in order to talk about why we are doing what we're doing. I find this personally helpful, given that this is my mathematical diary, but your mileage may vary.

Second, my writing contains significantly more details than healthy. Again, this is my mathematical diary, so I have no qualms adding in all of the details I want here, mostly to make sure that I can.