MoonMath
Interactive math visualization, algorithm demos, and Lean4 proof compilation.
Explore by Category
Number Theory
Properties of integers, primes, divisibility, and modular arithmetic
30 topicsGalois Theory
Field extensions, symmetry groups, and the solvability of polynomial equations
3 topicsGroup Theory
Symmetry, structure, and the building blocks of all algebra
21 topicsFractal Geometry
Self-similar structures, fractional dimensions, and iterated systems
6 topicsAnalysis
Limits, convergence, and the bridges between real, complex, and topological analysis
10 topicsCalculus
Fundamental calculus formulas — derivatives, integrals, and the theorems connecting them
13 topicsCombinatorics
Counting, partitions, and the algebra of finite structures
13 topicsAlgebra
Core algebraic formulas, equations, and identities
6 topicsLinear Algebra
Vector spaces, matrices, eigenstructure, and the bridges between geometry and algebra
21 topicsTopology
Compactness, connectedness, fixed points, and the language of continuous shape
21 topicsProbability
Concentration, conditioning, and the calculus of uncertainty
19 topicsComplex Analysis
Core theorems of complex function theory: contour integration, holomorphicity, analytic continuation, and the geometry of complex maps.
10 topicsFunctional Analysis
Core theorems of infinite-dimensional linear analysis: extension, mapping, fixed-point, and spectral theory in Banach and Hilbert spaces.
8 topicsRing Theory
Structural theorems about rings, ideals, and polynomial factorisation — from Euclidean domains to the Hilbert basis theorem.
8 topicsField Theory
Algebraic extensions, splitting fields, separability, and the structure of finite and infinite fields
8 topicsGraph Theory
Fundamental theorems on graphs, matchings, and combinatorial structures — from handshaking to matrix-tree.
8 topicsSet Theory and Logic
Foundations of mathematics: cardinal arithmetic, model theory, and computability.
10 topicsDifferential Equations
Existence, uniqueness, and solution methods for ODEs and PDEs — from Picard iteration to the heat and wave equations.
8 topicsDifferential Geometry
Integration on manifolds, curvature, and the interplay of forms, vector fields, and topology.
8 topicsInformation Theory
Shannon entropy, coding bounds, and channel capacity — the mathematics of optimal communication
8 topicsOptimization
Classical results in mathematical optimization: convexity, duality, equilibria, and convergence.
8 topicsCategory Theory
The abstract algebra of mathematical structure: functors, natural transformations, adjunctions, and universal properties unify mathematics.
8 topicsCryptography
Mathematical foundations of modern cryptography: number theory, group theory, and computational hardness assumptions.
8 topicsAlgorithms
Interactive visualizations of sorting, graph traversal, and cryptographic algorithms.
Coming soonLean4 Proofs
Write, compile, and render Lean4 proofs with LaTeX and Typst output.
View prime theorem proof