Mathematics
The study of quantity, structure, space, and change — the language underlying all sciences.
Mathematics is a web of interconnected ideas, not a linear path. The branches below are ordered so that each one builds on the ideas before it — you could follow them top to bottom and never need a concept you haven’t seen yet.
Explore
- 01
Logic & Foundations
The rules of mathematical reasoning itself — what constitutes a proof, what can be proven, and the limits of formal systems.
- 02
Set Theory
The language mathematics is written in — collections of objects, their relationships, and the axioms that make the rest possible.
- 03
Number Theory
The study of integers and their properties — primes, divisibility, and the deep patterns hidden in the simplest mathematical objects.
- 04
Algebra
The abstraction of arithmetic into structures — groups, rings, fields — that reveal the patterns behind equations and symmetry.
- 05
Geometry
The study of shape, size, and space — from Euclid's axioms through curved surfaces to the algebraic geometry of modern mathematics.
- 06
Topology
Geometry without measurement — the study of properties that survive stretching, bending, and continuous deformation.
- 07
Analysis
The rigorous study of change and continuity — limits, differentiation, integration, and the infinite made precise.
- 08
Combinatorics
The mathematics of counting, arrangement, and selection — how many ways can something happen, and what structures emerge?
- 09
Probability & Statistics
The mathematics of uncertainty — how to reason about randomness, measure likelihood, and draw conclusions from data.
- 10
Applied Mathematics
Mathematics in action — numerical methods, optimization, information theory, game theory, cryptography, and mathematical physics.