What's Behind It All

This is a running collection of short, hands-on walkthroughs connecting math most of us haven't touched since school to the systems we work with every day: optimization, rate limiters, autoscalers, search, all of it.

As software engineering matured, a lot of the math underneath it got abstracted away, and we're watching that happen all over again with AI. I think it matters to remember where these ideas come from, no matter how technical you are, so I want this to be for everybody. Anyone should be able to drop into the first topic and walk away able to solve a simple problem themselves.

The math on these pages is worked out by me, not Claude, which means it will occasionally be wrong. The worked examples sit behind a button so you can skip them, or click through and check my work. Please tell me if you find any discrepancies.

The idea came from two places. First, I need the Elixir practice. Second, I'm in the final stretch of my own education and need to review all of this anyway, so if I'm up past midnight cursing a math problem, I might as well write down what I learn and share it.

Lastly, I love math, or at least the idea of it. There's a suggestions button up at the top of this page. Please use it. If something gets a lot of requests, I'll research it. Promise. Kinda. I'm not doing it if it's too hard.