Аполлоний, Диофант, Гипатия

Three people, almost nothing known about any of them, and two books that changed mathematics. Apollonius of Perga wrote the Conics; Diophantus of Alexandria wrote the Arithmetica; and Hypatia of Alexandria, the best-known woman mathematician of the ancient world, taught and commented on both before a Christian crowd killed her in March 415. This is the story of the books, the people who carried them, and the legends that grew up around her. Also in Profiles in Mathematics: • Pythagoras of Samos:    • Pythagoras   • Euclid: The Elements of Proof:    • Euclid: The Elements of Proof | Profiles i...   • Archimedes & Eratosthenes: The Sand-Reckoner and the Sieve:    • Profiles in Mathematics - Archimedes & Era...   Watch the full series:    • Profiles in Mathematics   Told as a painted graphic novel with worked mathematics: Fermat's note in the margin, Halley's Arabic Conics, Apollonius's one cone and one plane, the names parabola, ellipse and hyperbola, the foci and Pappus's directrix, the problem of Apollonius and Descartes's circles, Diophantus's notation and the riddle of his age, Problem II.8 as a line through a circle, Theon and Hypatia's school, Synesius's letters and the silver astrolabe, stereographic projection, Ptolemy's Sun in base sixty, Orestes and Cyril, the three accounts of her death, the myths of the Library and the "last scientist", the road of the Conics through Byzantium, Baghdad and Oxford to Kepler and Newton, Halley's comet, the Mashhad manuscript, and Book IV, Problem 24 as a tangent to an elliptic curve. Where the story comes from: • Apollonius: the prefaces to his own Conics; Eutocius (6th century) and Pappus (4th century). • Diophantus: the Arithmetica's own preface and problems; the riddle in the Greek Anthology (date unknown). • Theon and Hypatia: Theon's commentary titles; Synesius's letters and On the Gift (394–413); Socrates Scholasticus, Church History VII.13–15 (about 440); Philostorgius; Damascius's Life of Isidore (about 520, through the Suda); John of Nikiu (about 690); the Theodosian Code 16.2.42–43 (416, 418). • The books afterwards: Eutocius's edition and Vat. gr. 206; the Banū Mūsā's Arabic Conics; Halley (Oxford, 1710); de Moivre's memorandum of Halley's visit to Newton (1727); Kepler's Astronomia nova (1609); Bachet's Arithmetica (1621) and Fermat's notes (1670); the Mashhad manuscript (copied 1198; Sesiano 1982, Rashed 1984). • The legend: Toland (1720), Gibbon (1788), Kingsley (1853), Hubbard (1908), Sagan's Cosmos (1980), Agora (2009). The mathematics on screen: • Computed in Tungsten (4,140 checks): the symptoma with p = 4 and d = 8, the foci and focal distances, all eight circles of the problem of Apollonius, the Apollonian gasket's integer bends, the riddle (84 years), II.8 and every slope's triple, the astrolabe's tropics (0.6512 × 1.5356 = 1), 360 ÷ 365;14,48 in base sixty, Mars's ellipse, and IV.24's tangent. • Checked in Satori, our proof checker (77 theorems). Chapters: 00:00 Fermat's margin 00:33 Halley and the lost eighth book 00:52 "My daughter, Hypatia" 01:21 The carriage 01:46 Apollonius of Perga 02:23 "Too hurriedly": the Conics 03:07 The Great Geometer 03:33 One cone, every conic 04:31 Parabolē, elleipsis, hyperbolē 06:03 The foci, and Pappus's directrix 07:53 The lost books 08:15 The problem of Apollonius and Descartes's circles 09:51 Diophantus of Alexandria 10:43 The riddle of his age 11:03 The first algebraic signs, and the riddle solved 13:04 Arithmetica II.8 13:20 Sixteen as two squares: a line through a circle 15:03 Theon of Alexandria 15:41 Hypatia 16:50 Synesius's letters 17:31 The silver astrolabe 18:18 Stereographic projection 20:15 The hydroscope 20:54 Almagest III in base sixty 22:28 The Serapeum, and Cyril 22:58 Orestes against Cyril 24:17 The rumour 24:59 Hypatia's death, March 415 25:24 Three accounts of her death 26:29 After 415 27:14 The legend: Toland and Gibbon 27:57 Kingsley, Hubbard, Sagan and Agora 28:54 What happened to the Library 30:38 The Conics survive 31:00 Baghdad 31:30 Halley's Conics, 1710 31:59 "An ellipse" 32:41 Kepler 33:07 Orbits are conics 34:16 "May your soul be with Satan" 34:44 Fermat's Last Theorem 35:08 Mashhad, 1968 35:48 Book IV, Problem 24, and elliptic curves 38:08 A teacher's work The channel:    / @unstablemaths   Tungsten, the language the animations and computations are written in: https://tungsten-lang.org Satori, our proof checker: https://github.com/tungsten-lang/tung... Painted panels generated with Nano Banana 2 and Seedream 4, two motion clips with Seedance 1.5 Pro; voices, music and sound by ElevenLabs; mathematical animation in Tungsten. The panels are illustrations, not evidence: no likeness of Apollonius, Diophantus or Hypatia survives, and the killing of Hypatia is not shown. #math #history #Hypatia