The Problem: Math Is Hard Because of Intuition, Not Calculation
The author argues that the difficulty of mathematics lies not in computation or proof, but in intuition. You may know that eigendecomposition of a covariance matrix is rotation + stretching, or that PCA finds directions of maximum variance—but can you *see* it? If you cannot "see" mathematics, you are only memorizing formulas—and formula-memorizers never truly understand machine learning.
The Iris Book Series (full name: Iris Mathematics Series: From Arithmetic to Machine Learning) exists to turn counterintuitive mathematical properties into things you can see, touch, and rotate, using graphics and code.
What Is the Iris Book Series?
A 7-volume series on math + programming + visualization + machine learning, authored by Jiang Lubin (online name "Shengjiang") under the team name Visualize-ML. All code and Jupyter Notebooks are free and open source on GitHub.
The seven books:
1. Easy Programming — zero-to-basics Python: variables, functions, OOP 2. The Beauty of Visualization — plotting math with matplotlib, plotly, etc. 3. Essential Mathematics — calculus, linear algebra, probability/statistics, fully visualized 4. Linear Algebra Made Easy, Vol. 1 — geometric intuition for vectors, matrices, linear transformations 5. Linear Algebra Made Easy, Vol. 2 — visualization of eigenvalues, SVD, matrix decompositions 6. Data Made Easy — statistics, data analysis, probability distributions 7. Machine Learning — classic ML algorithms from linear regression to neural networks
> The name "Iris" honors Fisher's 1936 iris dataset—the classic entry dataset in machine learning history—a tribute to the origins of statistical learning.
Why Visualization Beats Formulas
Traditional textbooks follow: definition → theorem → proof → exercises. This suits people who already have mathematical intuition, but demands beginners "prove" concepts before they've ever "seen" them. The Iris series reverses this: see the picture first, write code next, read the formula last.
Example—matrix multiplication: rather than starting from (AB)ᵢⱼ = Σ Aᵢₖ Bₖⱼ, the series shows an animation of a matrix transforming a vector (stretching + rotating), then matrix products as compositions of transformations, then has you code the effect of different matrices on the unit circle. Finally: matrix multiplication is composition of linear transformations, the determinant is an area-scaling factor, eigenvectors are directions that don't rotate.
> One picture beats a thousand words. One animation beats a thousand pictures. One interactive notebook beats a thousand animations.
3Blue1Brown pioneered this approach, but its videos are passive. Notebooks demand active participation—running code, changing parameters, observing results—which retains knowledge an order of magnitude better.
The Power of Graphics: Three Counterintuitive Cases
Case 1: The volume of a high-dimensional ball approaches zero. With V_n = π^(n/2) / Γ(n/2 + 1) · r^n, as n→∞, V_n→0. A radius-1 ball in 100-dimensional space has almost no volume. Plotting V_n against n makes the brain accept what the formula states. This matters for ML: in high dimensions, data points concentrate in "corners"—the geometric root of the curse of dimensionality.
Case 2: Sample means are not always normal. The CLT requires finite variance. For heavy-tailed distributions like the Cauchy, the sample mean never converges to normal—it stays Cauchy. Sampling from a Cauchy and histogramming the means proves this more convincingly than any proof.
Case 3: Zero correlation does not imply independence. If X ~ N(0,1) and Y = X², then corr(X, Y) = 0, yet Y is fully determined by X. A scatter plot shows a perfect parabola with correlation zero—an "aha" moment that motivates why causal inference is necessary.
A Complete Path: From Arithmetic to Machine Learning
The series' most ambitious feature is its scope: Programming (Book 1) → Visualization (Book 2) → Mathematics (Books 3–6) → Machine Learning (Book 7). Each layer builds on the previous one—a bottom-up path, unlike top-down curricula that teach algorithms first and patch in math later, leaving learners stuck at the "library caller" level.
> If you truly understand the math, ML algorithms follow naturally: linear regression is matrix multiplication + gradient descent, PCA is eigendecomposition, SVM is Lagrangian duality, neural networks are the chain rule.
Open Source: More Than Free Books
All code is open-sourced on GitHub (Visualize-ML organization), and every notebook runs in Google Colab—no installation required. The code is treated as core content, with the book as commentary on the code, not the reverse. Knowledge itself is free; revenue comes from print sales.
Who Should Read It?
Target readers:
- People with high-school math wanting to enter data science/ML
- People who took university math but "forgot it after the exam"
- Practitioners who use sklearn/PyTorch without understanding the principles
- Teachers who want to explain mathematical intuition
A Paradigm Shift in Math Education
The series embodies a shift from "symbol-first" to "visual-first" education. Most people need intuition before symbols; graphics and code are the bridge. In the AI era, LLMs make writing code nearly free—but interpreting what you see remains a uniquely human skill. Future math education teaches not "how to compute" but "how to see." When you can plot eigenvector directions, watch data deform under PCA projection, and observe gradient descent rolling across a loss surface, math stops being a symbol game and becomes a way of seeing the world.
---
Series: Iris Mathematics Series: From Arithmetic to Machine Learning (7 volumes) Author: Jiang Lubin / Visualize-ML Open-source code: https://github.com/Visualize-ML
All books mentioned are available here: https://b23.tv/4vCEQYn