Why Was Euclid's Geometry Taught for 2,000 Years? - Science History #16

Around 300 BC in Alexandria, a man we know almost nothing about wrote the Elements: thirteen books that start from a handful of plain rules and prove 465 propositions, each from the ones before. For two thousand years it was how people learned geometry, and it became the model for how to argue anything. But a proof is only as sure as where it starts, and one of Euclid's starting rules, the fifth postulate, carried a question nobody could settle by proof. The answer finally came from a telescope. How We Know · Season 2, Episode 6: Proof CHAPTERS 0:00 Oxyrhynchus: a scrap that says "it is so" 0:58 465 propositions, every one proved 1:35 Rules that worked: Egypt and Babylon 2:09 Don't trust the picture 2:38 The first page: definitions, postulates, common notions 3:08 Proposition 1 3:47 Step by step to Pythagoras 4:10 No last prime 4:28 One chain, and no royal road 4:58 The Instrument: a compass and a straightedge 5:36 Three problems nobody could solve 6:04 The cost: a gap in Proposition 1 6:25 The fifth postulate 7:11 A whole new geometry 7:29 Which one is space? The 1919 eclipse 7:57 So what: Newton, Lincoln, encryption 9:03 Next time: Give Me a Place to Stand SOURCES Euclid, Elements, Book I (definitions, postulates, common notions; Propositions 1, 3 and 29), D. E. Joyce, Clark University: https://mathcs.clarku.edu/~djoyce/jav... https://mathcs.clarku.edu/~djoyce/jav... https://mathcs.clarku.edu/~djoyce/jav... https://mathcs.clarku.edu/~djoyce/jav... Abraham Lincoln, autobiography for John L. Scripps (June 1860) and letter to Henry L. Pierce and others (6 April 1859): https://www.abrahamlincolnonline.org/... https://www.abrahamlincolnonline.org/... Wikipedia: https://en.wikipedia.org/wiki/Papyrus... https://en.wikipedia.org/wiki/Oxyrhyn... https://en.wikipedia.org/wiki/Bernard... https://en.wikipedia.org/wiki/Euclid https://en.wikipedia.org/wiki/Euclid%... https://en.wikipedia.org/wiki/Rhind_M... https://en.wikipedia.org/wiki/Ancient... https://en.wikipedia.org/wiki/YBC_7289 https://en.wikipedia.org/wiki/Square_... https://en.wikipedia.org/wiki/Hippocr... https://en.wikipedia.org/wiki/Pythago... https://en.wikipedia.org/wiki/Euclid%... https://en.wikipedia.org/wiki/Royal_road https://en.wikipedia.org/wiki/Straigh... https://en.wikipedia.org/wiki/Hilbert... https://en.wikipedia.org/wiki/Paralle... https://en.wikipedia.org/wiki/Giovann... https://en.wikipedia.org/wiki/Non-Euc... https://en.wikipedia.org/wiki/Hyperbo... https://en.wikipedia.org/wiki/General... https://en.wikipedia.org/wiki/Eddingt... https://en.wikipedia.org/wiki/Philoso... https://en.wikipedia.org/wiki/Euclide... https://en.wikipedia.org/wiki/Archimedes https://en.wikipedia.org/wiki/On_the_... A NOTE ON THE EVIDENCE The Oxyrhynchus scrap carries the statement of Book II, Proposition 5 and a diagram, not the proof; it was first dated to about AD 300 and is now dated to about AD 75-125. The editions count is an estimate. Most of the Elements' content is thought to come from earlier mathematicians such as Eudoxus and Theaetetus. The royal road story is told by Proclus more than seven centuries later, and the same line is told of Menaechmus and Alexander. Hilbert's 1899 system had 20 axioms (21 in the first edition, one later shown redundant). Gauss never published his non-Euclidean work. The 1919 eclipse measurements carried large uncertainties and were confirmed by radio measurements in the 1960s; the star shifts on screen are exaggerated. "Give me a place to stand" is attributed to Archimedes by Pappus, five centuries later. CREDITS Narration: synthetic voice. Music, sound design and animation: original. Maps: Natural Earth (public domain). On-screen quotations follow T. L. Heath's translation as given by D. E. Joyce. Fonts: Fraunces, Inter, IBM Plex Mono (SIL Open Font License).