Mathematics

From the derivative to the Fourier transform — the structures and patterns that underlie everything else.

19 articles

Logarithms: Taming Huge Numbers

Logarithms are the inverse of exponents: they answer what power produces a number, turn multiplication into addition, and — despite the name — grow astonishingly slowly.

10 min read·Sep 1, 2026

Mathematics

Matrices: Functions That Move Space

A matrix is a linear transformation of space in disguise. Its columns tell you where the basis vectors land, and multiplication is just composition.

10 min read·Aug 20, 2026

Mathematics

Infinity: Not All Infinities Are Equal

Infinity is not a number. Learn how bijections measure the size of infinite sets, why the naturals and the reals differ, and Cantor's diagonal proof.

10 min read·Aug 17, 2026

Mathematics

The Integral: Adding Up the Infinitely Small

The integral is not just a reversed derivative. It is the limit of a sum that measures accumulated area, and the Fundamental Theorem is what ties those two ideas together.

10 min read·Aug 4, 2026

Mathematics

Information Theory

Shannon entropy counts the yes/no questions you need to pin down an unknown. That count turns out to be the exact limit of lossless compression, and the reason error correction has a price.

10 min read·Jul 20, 2026

Mathematics

Markov Chains

How a process that remembers only where it is right now can settle into a stable long-run distribution — the idea behind PageRank, MCMC, and text generation.

10 min read·Jul 17, 2026

Mathematics

Eigenvectors and Eigenvalues

Almost every vector gets knocked off its line by a matrix. The rare few that don't reveal what the transformation is really doing.

10 min read·Jul 15, 2026

Mathematics

Game Theory and the Nash Equilibrium

How a single fixed-point idea — nobody can improve by changing their mind alone — explains cartels, auctions, arms races, and why cooperation still manages to survive.

10 min read·Jul 11, 2026

Mathematics

Chaos and Strange Attractors

How a rounding error in a weather simulation revealed that deterministic systems can be unpredictable in principle — and why that caps forecasting at about two weeks.

10 min read·Jul 10, 2026

Mathematics

Gradient Descent

How repeatedly stepping in the direction of steepest descent minimizes functions in millions of dimensions — and trains essentially every modern neural network.

10 min read·Jun 29, 2026

Mathematics

The Derivative

Speed is distance over time, yet a speedometer reads a speed right now. Resolving that paradox is the derivative — the foundation under optimization, physics, and machine learning.

10 min read·Jun 18, 2026

Mathematics

Complex Numbers

Nobody invented i to solve x² = −1 — the cubic formula forced it on them. How a bookkeeping trick became a geometric plane where multiplication is rotation.

10 min read·Jun 16, 2026

Mathematics

Bayes' Theorem

The rule for updating belief in the face of evidence, and why ignoring the base rate makes accurate tests wildly misleading.

9 min read·Jun 8, 2026

Mathematics

Euler's Formula

Why eˣ has anything to do with circles — and what rotating arrows have to do with waves.

9 min read·Jun 1, 2026

Mathematics

Taylor Series

Turn sine, cosine, and eˣ into polynomials — and discover why this works everywhere.

9 min read·May 12, 2026

Mathematics

The Central Limit Theorem

The theorem that explains why the bell curve appears everywhere from exam scores to measurement errors.

8 min read·Mar 28, 2026

Mathematics

Newton's Method

The algorithm that squares the number of correct decimal places with every iteration.

8 min read·Jan 18, 2026

Mathematics

Sieve of Eratosthenes

Start with every number, then cross out the non-primes. What's left is beautiful.

8 min read·Jun 18, 2025

Mathematics

The Fourier Transform

Decompose any wave into its frequency components — and see why this changes everything.

10 min read·May 10, 2025