Three hours on how people learned to count, measure and prove, from the notched bones of Africa to the computers that now check proofs.
It covers the Ishango bone and the tally sticks older than writing; the clay tokens of the Near East and the scribes of Uruk; Babylonian numbers in sixties, the square root of two on a tablet the size of a biscuit, and Plimpton 322; the Rhind papyrus and the Great Pyramid; Thales, Pythagoras and the discovery of lengths that no ratio of whole numbers can express; Zeno, Plato’s Academy and Aristotle’s logic; Euclid’s Elements, Archimedes, Eratosthenes measuring the Earth, the Antikythera mechanism and Hypatia; the Indian mathematicians who gave the world zero and the numbers we write, and the Kerala school; counting rods and the Chinese remainder problem; the Maya; the House of Wisdom, al-Khwarizmi, Omar Khayyam and the long road of the parallel postulate; Fibonacci and the merchants of Italy; the cubic equation and the quarrel between Tartaglia and Cardano; logarithms, Descartes and Fermat, Pascal and the birth of probability; Newton, Leibniz and the calculus; the Bernoullis and Euler; Gauss, Galois, Abel, the new geometries of Bolyai and Lobachevsky, and Riemann; Cantor’s infinities, Hilbert’s program, Gödel and Turing; Noether, Ramanujan, Shannon, von Neumann and the Monte Carlo method; chaos, fractals and the four colour theorem; Fermat’s Last Theorem and the Poincaré conjecture, both proved, and the Riemann hypothesis, still open; and the proof assistants and machines that have begun to take part.
Chapters
0:00 The argument that has not changed
1:53 Marks that stood for things
8:31 Sixty
17:05 The gift of the river
24:28 The Greeks ask why
37:05 Alexandria
51:45 Nothing, and the infinite
1:01:41 Rods, cords and the long count
1:11:53 The House of Wisdom
1:25:10 Merchants, painters and a secret
1:37:33 A grid, a margin and a game of dice
1:47:29 The mathematics of change
2:02:58 The prince, the rebel and the strange new worlds
2:20:52 Infinity, and the limits of proof
2:33:22 The century of structures
2:48:10 The old problems fall
3:00:23 The machines, and the list that never ends
Made with AI. The narration is a synthesised voice, and the research, script and assembly were done with AI assistance. The pictures are reconstructions made with AI, except the photographs credited below, which are real, from Wikimedia Commons under free licences, and the maps, which are drawn from real elevation data and Natural Earth. The reconstructions are not records of events.
Photographs from Wikimedia Commons, by licence. CC BY-SA 4.0: Abigail Harris, Ad Meskens, Ahmed Khalil, Alexey Kljatov, Alexxx1979, Angkun-ane, Badhan.kv, Benjamin Smith, Brigade Piron, Celette, Charles J. Sharp, ChasingMeToo, Daniel Schwen, Deiadameian, Didier Descouens, Diego Delso, Dietmar Rabich, EPFL innovation park, Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tet, George Bergman, Gerard Dukker, Gts-tg, Hadrianus1959, Héliotype : E. Le Deley, Paris., Ingo Dierking, Ingo Mehling, Jakub Hałun, Johannes Poets, Joyofmuseums, Karl Gruber, LBM1948, Lacambalam, Lewis Hulbert, Mariordo (Mario Roberto Durán Ortiz), Martinvl, Mary Harrsch, Matt Fitt, Michielverbeek, MusikAnimal, Osama Shukir Muhammed Amin FRCP(Glasg), Palickap, Partonez, PattayaPatrol, PaulT, René Hourdry, RishadImtinan, Royal Society uploader, Science Museum Group, Serra Massuda, Smb1001, Son of Ugly, Soraie8288, Sumitsurai, Tomisti, Txllxt TxllxT, University of Pennsylvania Museum of Archaeology and Anthrop, Vaija, Vcarceler, Vchebolu, W. Bulach, Yair Haklai, Zairon, Zeete, Zunkir, user:shakko. Public domain: Aert Anthoniszoon, After Godfrey Kneller, After Lysippos, Agence Rol, Alfred Bogen (1885-1944), Alfred Edward Chalon, Andreas Cellarius, AnonymousUnknown author, Benedikt Listing, Benjamin West, Berthe Chégaray née Becher, Charles F. Wilson, Charles-Philippe Larivière, Christian Albrecht Jensen, Claude Duflos, Didier Descouens, Edmund J. Sullivan, Elliott & Fry, Euclid, Euclid, Boethius, Eugène Delacroix, Eugène Pirou, Florence Nightingale, Frans Hals, François de Poilly, Georges de La Tour, Godfrey Kneller, Gottlieb Biermann / After Christian Albrecht Jensen, Graham’s Art Studios, Gumerov Ildar, Guo Xi, Irakischer Maler des Kräuterbuchs des Dioskurides, J. M. W. Turner, Jacopo de’ Barbari, Jakob Emanuel Handmann, Johan Gørbitz, Johannes Vermeer, Justus Sustermans, Justus van Gent, Laplace, Pierre-Simon Marquis de, Leonardo da Vinci, Lieve Verschuier, Maurice Quentin de La Tour, Nuclear Regulatory Commission from US, Original author unknown. Translation help provided by Manuel, Otto Zeth, People from Warring States Period (476-221 BC), Photos taken for William Winfield; uploaded by Kimberlyblake, Piero della Francesca, Pierre-Antoine Demachy, and others; full credits at the end of the film.
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