LeoMath
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Understand mathematics. Don't just memorise it.

Start from definitions. Through derivation, proof, computation and visualisation, see why mathematics holds.

Start exploring →Leo software
① Drag the tip of the red arrow e₁.
A=(1001)A=\begin{pmatrix}\textcolor{#c2452d}{1}&\textcolor{#1f7a4d}{0}\\\textcolor{#c2452d}{0}&\textcolor{#1f7a4d}{1}\end{pmatrix}

A matrix is not just a table of numbers.

It describes how space itself is transformed.

Open “Linear maps” →

Mathematics is not a list of isolated formulas.

Hover over any node and its prerequisites light up. You will see where what you are learning sits in the whole of mathematics.

Tap a concept to see what it builds on.

Foundations of calculus

Foundations of linear algebra

Introduction to differential equations

Planned

This is how LeoMath teaches.

Why is the derivative of eˣ itself?

Don't read the definition yet. Drag the base a and watch when the difference-quotient curve coincides with the function.

f(x)=ax,f(x+h)−f(x)h=ax⋅ah−1hf(x)=a^{x},\qquad \frac{f(x+h)-f(x)}{h}=a^{x}\cdot\frac{a^{h}-1}{h}
Observe→Conjecture→Define→Derive→Prove→Apply
Intuition⟶Rigorous mathematics

Both. Intuition lets you see the result; derivation and proof let you know why it is true.

Open the full derivation of “The derivative” →
ax+h−axh=ax⋅ah−1h\frac{a^{x+h}-a^{x}}{h}=a^{x}\cdot\frac{a^{h}-1}{h}
difference quotient ÷ function 0.8284

Choose where to begin.

v0.1.1 has exactly three complete paths. Each starts from definitions, works through derivations, and comes with hands-on experiments and exercises.

Foundations of calculus

If you want to understand

change, limits, continuity and accumulation

  1. 1Limits
  2. 2The derivative
  3. 3The integral
  4. 4Taylor expansion

4 concepts · 1 experiments · 8 exercises

Start here →

Foundations of linear algebra

If you want to understand

space, transformation and structure

  1. 1Vectors
  2. 2Linear maps
  3. 3Matrices
  4. 4Eigenvalues

4 concepts · 1 experiments · 8 exercises

Start here →

Introduction to differential equations

If you want to understand

how a system evolves in time

  1. 1What is an ODE
  2. 2First-order equations
  3. 3Second-order linear equations
  4. 4Numerical solutions

4 concepts · 1 experiments · 8 exercises

Start here →

From learning to practice.

Mathematics does not stop at the classroom. This is where Leo's real experiments, computation and development live.

x˙=σ(y−x)\dot{x}=\sigma(y-x)

Math experiments

The Lorenz system, Fourier series, numerical integration and other hands-on experiments.

∥yn−y(tn)∥=O(h4)\|y_n-y(t_n)\|=O(h^4)

Scientific computing

ODE/PDE solvers, numerical error analysis, algorithm comparison.

v0.1.1\text{v}0.1.1

Dev log

Development notes for LeoMath itself and other public projects.

Coming soon

Turn mathematics into tools.

Mathematical and scientific-computing software by Leo. Binaries and release notes are hosted on GitHub Releases.

Leo AI

Coming soon · v2.1.2

A tool for scientific research and mathematical workflows.

Learn more →