Lectures on Elementary Mathematics

Historical lectures on elementary mathematics by Lagrange.

Œuvres mathématiques d’Évariste Galois

Collected mathematical works of Galois, central to the development of group theory.

On Riemann's Theory of Algebraic Functions and their Integrals

Klein's treatment of algebraic functions, integrals, and Riemann surfaces.

Four Lectures on Mathematics

Lectures touching analysis, geometry, and mathematical methods.

The Meaning of Relativity

Einstein's Princeton lectures on the mathematical and physical structure of relativity.

Space—Time—Matter

Weyl's synthesis of geometry, relativity, space, time, and matter.

Introduction to Mathematical Philosophy

An accessible treatment of logic, number, order, classes, and mathematical foundations.

The Logic of Chance

A major historical work on probability, statistics, and inductive logic.

A History of Mathematics

A classic survey of mathematical development across cultures and centuries.

Life of Pythagoras, or Pythagoric Life

Includes substantial Pythagorean numerical material and Thomas Taylor's discussion of theoretic arithmetic.

The Algebra of Mohammed ben Musa

The Nine Chapters on the Mathematical Art (Jiǔzhāng Suànshù)

Use Mikami (1912) and Cajori (1919) public-domain selections; do not ingest modern copyrighted complete translations.

On Floating Bodies

Contained in T. L. Heath's The Works of Archimedes (1897).

Quadrature of the Parabola

Contained in T. L. Heath's The Works of Archimedes (1897).

The Sand-Reckoner (Psammites / Arenarius)

Contained in T. L. Heath's The Works of Archimedes (1897).

Posterior Analytics

Topics

Treatise on Light

Diophantus of Alexandria: A Study in the History of Greek Algebra

Historical study containing substantial translated Diophantine material.

The First Six Books of the Elements

An Investigation of the Laws of Thought

Newton's Principia: The Mathematical Principles of Natural Philosophy

The Game of Logic

Discourse on the Method

The Principles of Science: A Treatise on Logic and Scientific Method

The Character of Physical Law — Messenger Lectures

The complete seven-lecture Caltech viewer, with synchronized searchable transcripts.

Symmetry in Physical Law

Symmetry, invariance, transformations, and what remains unchanged when our description of a physical system changes.

Magnetism — Part Two

Oersted's link between current and magnetism, followed by visible experiments with iron in magnetic fields.

Young and the Wave Theory of Light

Young's pinhole experiment, diffraction, interference fringes, and experiments using Young's original wave trough.

National Committee for Fluid Mechanics Films

A 39-film visual archive of fluid mechanics: vorticity, boundary layers, turbulence, surface tension, low-Reynolds flow, cavitation, instabilities and more.

Visualization of Standing Waves

A focused physical demonstration making standing-wave structure visible.

Radio Wave Properties

Dipole antennas make voltage/current standing waves and electromagnetic radiation patterns physically visible.

But What Is the Fourier Transform?

Signals are wound around the complex plane so frequency decomposition becomes visible rather than merely symbolic.

The Essence of Calculus

A visual reconstruction of the core ideas behind derivatives, integrals, limits, and the fundamental theorem.

Group Theory, Abstraction, and the Monster

Symmetry becomes algebraic structure, leading from simple group actions to the monster group and monstrous moonshine.

Bayes' Theorem

Probability visualized as proportions and geometric restriction of possibilities, making Bayesian updating intuitive.

Bell's Theorem — A Glitch in Reality

A detailed mathematical treatment of Bell's 1964 theorem and the structure behind local hidden-variable constraints.

The Four Laws of Black Hole Mechanics

A book-length walkthrough of the Bardeen–Carter–Hawking black-hole-mechanics paper, including the differential mass relation and thermodynamic analogy.

Why You Can't Solve Quintic Equations — Galois Theory Approach

A visual explanation of quintic unsolvability through permutations, symmetry, field structure, and Galois theory.

Lie Theory — Visual Introduction and Series

A visual entry to continuous symmetry, Lie groups, Lie algebras, exponentiation, and matrix transformations.

Generalised Stokes' Theorem and Differential Forms

A geometric path through differential forms and the common structure behind several classical integral theorems.

The Most Useful Numbers You've Never Heard Of

An accessible introduction to p-adic numbers, alternative notions of distance, and their use in modern number theory.

You've (Likely) Been Playing the Game of Life Wrong

Power laws, outliers, fractals, self-organized criticality, sandpiles, the Ising model, and why averages can fail.

The Obviously True Theorem No One Can Prove

Goldbach's conjecture through Euler, prime distribution, Ramanujan, the circle method, and modern partial results.