I Wrote the Maths Refresher I Needed

22 Jul 2026

Somewhere between an embedding model and a loss function, I noticed I was nodding along to mathematics I could no longer actually do.

I can talk about cosine similarity all day. Ask me to show why a dot product measures an angle and I would have needed a minute. Eigenvectors turn up in every explanation of PCA ever written, and mine had quietly become a word rather than a thing I understood.

That is an odd place to be after years of building this stuff. So I went back and rebuilt the foundations, and wrote down what I found.

What it is

A Mathematics Refresher runs from arithmetic to the mathematics underneath machine learning, in four parts: foundations, school level (10+2), the BSc core, and then maths for AI.

Seventy-seven pages. Forty-two figures. Three hundred and ten exercises in three tiers, from quick drills to one real challenge per chapter, with every answer verified by running it rather than by trusting anyone’s memory.

The thing I cared about most was not skipping steps. Textbooks written by people who still remember the material love the phrase “it follows that”. But the reader who has forgotten calculus has usually forgotten precisely those connecting moves, not the headline formula. So every worked example is narrated one step at a time, with the reason sitting next to the step.

The part I am most pleased with

There is a companion app, and it is where the book actually comes alive.

Twenty-five chapters, each taught as a flow: the concept, then a method worked step by step, then something to play with, a quick check, and practice that never runs out. Get a practice question wrong and it shows you the full working for that specific problem, not a hint.

Drag a tangent along a curve. Watch Riemann rectangles melt into an integral. Make gradient descent diverge by nudging the learning rate, which is a much better teacher than reading that it can happen. It is a single HTML file, it works on a phone, and it has a dark mode.

Written with AI, and I would rather say so

The book was co-authored with Anthropic’s Claude, Fable and Opus. They drafted, illustrated and checked a great deal of it under my direction, and every numerical claim was verified in code before it went in.

It went through several review passes, and errors will still have survived. They do in every first edition. If you find one, a wrong answer or a muddled explanation or a figure that misleads, tell me and I will fix it in the next edition.

Where to get it

• Work through it in your browser: abdulqabiz.com/book-app/
• PDF and EPUB: abdulqabiz.com/mathematics-refresher-book/

Both free.

If you work in this field and have quietly stopped being able to do the mathematics you talk about every day, that is exactly who I wrote it for. It was me, until fairly recently.