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Ryan Collison

I write about cool science and share it here.

Number Theory

The Queen of Mathematics

The integers look simple. They are not. Number theory is the study of their hidden structure — prime factorizations, modular patterns, and deep conjectures that have resisted proof for centuries. This series starts with divisibility and ends at the borders of what's known.

Multivariable Calculus

Multivariable Calculus Explained

Single-variable calculus is physics on a line. Multivariable calculus is physics in the actual world — where hills slope in every direction, fluids curl through space, and finding a maximum means climbing in dimensions you can't quite see.

Logic

Logic: The Architecture of Valid Reasoning

Logic is the skeleton beneath every argument. Master its rules and you can spot exactly where reasoning breaks — whether in a courtroom, a proof, or a tweet thread. Then come the limits: Gödel showed even logic has ceilings.

Logarithms

The Operation That Turns Multiplication Into Addition

Logarithms are the math world's great compressor. They're why a sound 10× louder adds just one decibel, why pH fits on a 14-point scale, and how slide rules calculated moon trajectories. One operation, hiding everywhere.

Linear Algebra

Linear Algebra Explained

Vectors, matrices, eigenvectors — linear algebra sounds dry until you realize it's the language of everything that transforms. This series builds the geometric intuition first and the formalism second.

Geometry

Geometry Explained

Geometry started with land surveyors and ended up describing the universe. The same intuitions behind parallel lines and similar triangles turn out to govern black holes, soap bubbles, and the shortest path between any two points on Earth.

Exponential Functions

Exponential Functions Explained

The exponential function is the only function that is its own derivative — a fixed point of calculus. That self-referential property is why it shows up in everything from population dynamics to the mathematics of entropy.