How Imaginary Numbers Were Invented

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=cUzklzVXJwo

A general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. • Thanks to Dr Amir Alexander, Dr Alexander Kontorovich, Dr Chris Ferrie, and Dr Adam Becker for the helpful advice and feedback on the earlier versions of the script. • ▀▀▀ • References: • Some great videos about the cubic: • 500 years of not teaching the cubic formula. -- • 500 years of NOT teaching THE CUBIC F... • Imaginary Numbers are Real -- • Imaginary Numbers Are Real [Part 1: I... • Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York. -- https://ve42.co/Dunham90 • Toscano, F. (2020). The Secret Formula. Princeton University Press. -- https://ve42.co/Toscano2020 • Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. -- https://ve42.co/Bochner63 • Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. -- https://ve42.co/Murio21 • Branson, W. Solving the cubic with Cardano, -- https://ve42.co/Branson2014 • Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. -- https://ve42.co/Rothman • Vali Siadat, M., Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. -- https://ve42.co/Siadat21 • Merino, O. (2006). A short history of complex numbers. University of Rhode Island. -- https://ve42.co/Merino2006 • Cardano, G (1545), Ars magna or The Rules of Algebra, Dover (published 1993), ISBN 0-486-67811-3 • Bombelli, R (1579) L’Algebra https://ve42.co/Bombelli • The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software]. https://www.manim.community/ • ▀▀▀ • Special thanks to Patreon supporters: Luis Felipe, Anton Ragin, Paul Peijzel, S S, Benedikt Heinen, Diffbot, Micah Mangione, Juan Benet, Ruslan Khroma, Richard Sundvall, Lee Redden, Sam Lutfi, MJP, Gnare, Nick DiCandilo, Dave Kircher, Edward Larsen, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Ruslan Khroma, Robert Blum, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson,Ron Neal • Executive Producer: Derek Muller • Writers: Derek Muller, Alex Kontorovich, Stephen Welch, Petr Lebedev • Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jesús Rascón • SFX: Shaun Clifford • Camerapeople: Derek Muller, Emily Zhang • Editors: Derek Muller, Petr Lebedev • Producers: Derek Muller, Petr Lebedev, Emily Zhang • Additional video supplied by Getty Images • Music from Epidemic Sound and Jonny Hyman

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