Math Process

A number of posts I make illustrate the process of mathematics rather than the results, while still trying to appeal to those primarily interested in the results. This post serves to explain how those are written, and how to read them.

Hidden Text

The whole point in showing the math process is to record most of my mistakes and reasonings behind steps that normally just get thrown in the trash when writing a final draft. The upside is that readers get to see how I stumbled along the way, and how I dealt with it, and how far I got not knowing where it would take me. The downside is that the most primary information (the results, and their relationships) usually get lost in the noise.

I decided to solve this by having all my extra information about my mistakes and reasonings in side comments that the reader has to click to see. That way, a cursory glance over the document gives the backbone results, while any steps the reader is curious about how they came about can be investigated right there.

Different Kinds of Readers

There are many ways to approach math process posts, depending on what your objective is:

  • If you just want to understand the results or the process primarily, always collapse or always expand the extra text, respectively, and simply read.

  • If you want to derive the results yourself, then leave the "proof" statements collapsed and try to prove each claim as it comes by. Expand each to check yourself when you finish the proof.

  • If you want to derive the process yourself, then only read anything when you have a good guess as to what it will say. When you have no idea what's coming, put it down and try to investigate things and make some guesses.

These three ways of approaching my math process posts actually apply to all formal math reading. It's just normally, everything is written together, and it takes practice to identify which bits are what you want to avoid reading. In general, the more time you try to predict text before reading it the better, but you have to balance that with the time you have to spend.