Mathematics is hard not in calculation or proof, but in intuition.
You may know that eigendecomposition of a covariance matrix is rotation + stretching — but what do you actually *see* in your head? A blob of symbols. You may know the level sets of a normal distribution are ellipses — but can you picture it in 3D? You may know PCA finds directions of maximum variance — but can you imagine how the data deforms during projection?
If you can't "see" math, you're just memorizing formulas. And people who memorize formulas can never truly understand machine learning.
That's why the "Iris Book Series" (鸢尾花书) exists: it uses graphics and code to turn counterintuitive mathematical properties into things you can see, touch, and rotate.
What is the Iris Book Series?
It is a 7-book series combining math, programming, visualization, and machine learning, titled "Iris Math Series: From Arithmetic to Machine Learning." The author is Jiang Lubin (online name "Shengjiang"), with the team Visualize-ML. All code and Jupyter notebooks are open-source and free on GitHub:
https://github.com/Visualize-ML
The seven books:
1. Easy Programming — zero-to-one Python: variables, functions, OOP 2. The Beauty of Visualization — plotting math with matplotlib, plotly, etc. 3. Essential Math — core calculus, linear algebra, probability & statistics, all visualized 4. Easy Linear Algebra, Vol. 1 — geometric intuition for vectors, matrices, linear transformations 5. Easy Linear Algebra, Vol. 2 — visualization of eigenvalues, SVD, matrix decompositions 6. Easy Data — statistics, data analysis, probability distributions 7. Machine Learning — classic algorithms from linear regression to neural networks
> The name "Iris" comes from the Iris dataset Fisher used in 1936 — the most classic entry dataset in machine learning history. It's a tribute to the origins of statistical learning.
Why visualization beats formulas
Traditional math textbooks go: definition → theorem → proof → exercises. That works for people who already have intuition, but it demands you "prove" a concept before you've ever "seen" it.
The Iris series does the reverse: see the picture first, write the code, then read the formula.
Example — understanding matrix multiplication. Traditional teaching gives you (AB)ᵢⱼ = Σ Aᵢₖ Bₖⱼ and drills. The Iris approach: first an animation of a matrix transforming a vector (stretching + rotating), then two matrices as composition of transformations, then you write Python to plot how different matrices deform 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.
This idea wasn't invented here — 3Blue1Brown pioneered it. But 3Blue1Brown is video: you watch passively. The Iris series is notebooks: you must run code, change parameters, observe results. Active participation retains far better than passive viewing.
Counterintuitive math, made visible
Case 1: The volume of a high-dimensional ball approaches zero. V_n = π^(n/2) / Γ(n/2 + 1) · r^n, and as n→∞, V_n→0. A radius-1 ball in 100 dimensions has nearly zero volume. Plot V_n against n and your brain finally concedes. This is the geometric root of the curse of dimensionality: in high dimensions, data lives in the "corners," not the center.
Case 2: Sample means aren't always normal. The CLT says sample means are asymptotically normal — but for heavy-tailed distributions like Cauchy (infinite variance), the sample mean never converges to normal. Sample, average, histogram: no matter the sample size, the shape stays Cauchy.
Case 3: Zero correlation ≠ independence. Let X ~ N(0,1), Y = X². Then corr(X, Y) = 0, yet Y is fully determined by X. Plot the scatter: a perfect parabola. The "aha" moment here is the starting point for understanding why causal inference matters.
A complete path from arithmetic to machine learning
Programming (Book 1) → Visualization (Book 2) → Math (Books 3–6) → Machine Learning (Book 7)
Each layer builds on the previous one. Unlike top-down curricula that teach algorithms first and backfill math — leaving you stuck at "library caller" level — the Iris philosophy is: 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: free means the code too
All notebooks run directly in Google Colab — nothing to install, just open a browser. In Chinese tech publishing this is rare: code here is core content, not an appendix. The books are annotations of the code, not the other way around. Knowledge is free; revenue comes from print sales.
Who should read it?
Target readers:
- People with high-school math wanting to enter data science / ML
- Students who took university math but "forgot it after the exam"
- Practitioners who use sklearn/PyTorch without understanding principles
- Teachers wanting to explain mathematical intuition to students
- Those seeking frontier deep learning paper walkthroughs (this is classic ML, not Transformers)
- Math majors (not deep enough, though the visualizations may inspire teaching)
- People unwilling to run code (just read 3Blue1Brown instead)
Not for:
A paradigm shift in math education
The series represents a shift from "symbol-first" to "visual-first" education. Traditional teaching assumes you can extract intuition from symbols — few can. Most people need the reverse: intuition first, symbols after.
This matters even more in the AI era. LLMs make writing visualization code nearly free, but "understanding what you see" remains a human skill. Future math education won't teach you to compute — it will teach you to see. When you can plot eigenvector directions, watch data reshape under PCA projection, and observe gradient descent rolling on a loss surface, math stops being a symbol game and becomes a way of seeing the world.
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Series: Iris Math Series: From Arithmetic to Machine Learning (7 volumes) Author: Jiang Lubin / Visualize-ML Open-source code: https://github.com/Visualize-ML
(Original post also links to a video channel for the books: https://b23.tv/4vCEQYn)