A while ago, someone in a Discord server I’m in asked how much of the math behind a system you need to know to implement it. I thought it was an interesting question, and I felt qualified to answer it, so I ended up writing quite a lengthy response. It just occurred to me that it might also be useful to other people, so I thought I would clean it up a little bit and archive it here.

In the first part of this talk, I made the case that theory is useful because it allows us to find (or at the very least, have the correct toolkit and language to explore) solutions to real-world problems. In this part, we are going to look at some examples of such problems and develop mathematical language to be able to discuss them more abstractly. I’ve put the term “real-world” in quotes in the title, because I’m going to be talking about these problems in a lot of generality. However, I want to stress that specific instances of these problems are actually relevant in industry, and I think it’ll be easy to see why once I start talking about them.

The year 2024 was a really bizarre year for me, writing wise – while I had work come out in a relatively high-profile venue, and I finally started blogging again, I didn’t produce much in terms of “literary work”, and definitely did not write any creative works that I would consider to be publishable, which kinda sucks. I made some progress on some essays I hope to finish this year, wrote a few poems, and… I think that was it???? I was very academically focused in 2024 though, so it makes sense. I did do lots of academic writing, created some didactic/informational texts, and wrote some more informal stuff on this blog, so maybe in terms of pure wordcount I wrote more than I do most years. So I guess I still wrote, but the form and content of what I was writing shifted.