A few weeks ago a friend told me I’m the type of person who probably keeps dozens of tabs open all the time, and I, naturally, was offended by how true it was. I think it’s a familiar feeling among mathematicians (and beyond): when learning something new it’s really tempting to go through all the references, chase down chains of citations, and get all the prerequisites, make sure you’re not missing any important details, just to be left with an overwhelming volume of resources that you’ll “get around to eventually”.

Unfortunately with how human knowledge works nowadays, learning all the details of a subject is too impractical, and we just have to accept some things as black boxes in order to go on with our lives. But. Every once in a while I encounter a result – maybe a small lemma, or an offhand remark from the authors – that makes me go “that shouldn’t be too hard”. So I make the mistake of looking into it, and yet as I start unpacking, I realize just how deep it actually goes.

This series of posts is supposed to be about my latest experience of this sort. Even though it took me so far from what I was originally doing, I’m kind of happy I looked into the details, just because it exposed me to some really deep beautiful ideas. And if I don’t wanna feel unproductive, I can even tell myself all of it will probably come in handy sooner or later anyways. Maybe once in a while it’s good to fall down a rabbit hole…

The cat asked, “Where do you want to go?”
“I don’t know,” Alice answered.
“Then,” said the cat, “it really doesn’t matter, does it?”