History of Mathematics

22 chapters spanning 4,000 years of mathematical discovery — from Mesopotamian clay tablets to modern computing

History of Mathematics

Four thousand years of human ingenuity — from counting tokens on Mesopotamian clay to the abstract frontiers of modern mathematics.

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A Journey Through Mathematical Civilization

This course traces the development of mathematical ideas across cultures and centuries. From the earliest number systems of Babylon and Egypt, through the logical revolution of ancient Greece, the algebraic innovations of the Islamic world, the invention of calculus, and into the age of rigorous proof and abstraction that defines modern mathematics.

44 Video Documentaries

Biographical documentaries on the greatest mathematicians in history, organized by era

Course Structure

Part I: Dawn of Mathematics

Mesopotamian arithmetic, Egyptian geometry, the Vedic tradition of India, and the mathematical legacy of ancient China.

Mesopotamia & EgyptEarly Indian MathematicsChinese Mathematics

Part II: The Greek Revolution

The birth of deductive proof — from Pythagoras and Euclid through Archimedes to the twilight of Hellenistic scholarship.

Pythagoras & EuclidArchimedes & ApolloniusDiophantus & Late Antiquity

Part III: The Medieval World

Al-Khwarizmi's algebra, Fibonacci's transmission of Hindu-Arabic numerals, and the remarkable Kerala school of calculus precursors.

Al-Khwarizmi & Islamic AlgebraFibonacci & Medieval EuropeBrahmagupta to Kerala School

Part IV: Early Modern Transformation

Renaissance algebra, Cartesian coordinates, and the invention of calculus by Newton and Leibniz.

Cardano & Renaissance AlgebraDescartes & FermatNewton & LeibnizPascal & Probability

Part V: Age of Rigor

The golden century of Euler, Gauss, Galois, Riemann, and Cantor — when mathematics became a precise, rigorous discipline.

Euler & LaplaceGaussGalois & AbelRiemann & FourierCantor & Dedekind

Part VI: Modern Mathematics

Hilbert's program, Gödel's incompleteness, Turing machines, Ramanujan's genius, and the dawn of the digital age.

Hilbert & PoincaréGödel & TuringRamanujan & HardyVon Neumann & the Digital Age

Timeline Highlights

c. 1800 BCEBabylonian clay tablets record quadratic equations and Pythagorean triples

c. 500 BCEPythagoras founds his school; proof-based mathematics begins in Greece

c. 300 BCEEuclid compiles the Elements — the most influential textbook ever written

c. 250 BCEArchimedes anticipates calculus with his method of exhaustion

c. 500 CEAryabhata in India introduces zero and decimal place-value notation

c. 820 CEAl-Khwarizmi writes Al-Jabr, founding algebra as a discipline

1202Fibonacci's Liber Abaci brings Hindu-Arabic numerals to Europe

1545Cardano publishes solutions to cubic and quartic equations

1637Descartes invents analytic geometry; Fermat states his Last Theorem

1687Newton publishes Principia — calculus transforms physics

1799Gauss proves the Fundamental Theorem of Algebra

1832Galois, age 20, writes down group theory the night before his fatal duel

1859Riemann formulates his hypothesis on the distribution of primes

1931Gödel proves mathematics cannot be both complete and consistent

1936Turing defines the universal computing machine

Recommended Reading

A History of Mathematics

Victor J. Katz

The standard comprehensive reference

Mathematics and Its History

John Stillwell

Elegant connections between topics

Journey Through Genius

William Dunham

Great theorems and the minds behind them

The Mathematical Experience

Davis & Hersh

Philosophy and culture of mathematics

Men of Mathematics

E.T. Bell

Classic biographical portraits

Mathematics in Ancient Iraq

Eleanor Robson

Mesopotamian mathematics in context

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