I have been working on a French translation for the math book and in the process I stumbled upon some really powerful “authoring hacks” that I would like to describe here in case they might be useful for other bilingual authors and educators.

**Let’s see les maths!**

Before we begin with the “How it’s made” episode, let me show you some examples of the final product. I have selected the best four “backports” — explanations that now exist in the English version thanks to the additions in the French version.

- Reader feedback was consistent at pointing out the
**algebra sections as boring and TL;DR.**Readers are willing to learn algebra (the rules for manipulating math expressions), but then when it comes to algebra “techniques” they are not sold on the concept. One solution to this problem would be to drop the “boring stuff” (lower the expectations of the reader), but I was having none of this. Instead I decided to just**improve the explanations and add pictures**: Completing the square en Français et in English. - Functions (modelling superpowers) are the best thing ever, and probably the most powerful tool readers will develop in the book. This is why proper definitions and examples of functions are essential.
- Polar coordinates are super important—for both practical reasons and for the “aha” moment (knowledge buzz) that occur when readers understand $(x,y)$ is just
*one**example*of the many possible representations of the points in the Cartesian plane and $r\angle \theta$ is an equivalent representation (instructions that specify the position of a particular point int he Cartesian plane based on the distance $r$ and direction $\theta$). - Speaking of knowledge buzz through representation theory, the book now finally has a proper motivation why readers need to think about the concept of a basis (a set of direction vectors that is used as the coordinate system for a vector space). On this one I go back to the basics—explain through an example.

Contuinuez à lire si ça a l’air intéressant. Read on if you’re interested.