For a long time a general solution to the cubic equation was considered impossible, until we abandoned the requirement that the mathematics reflect reality. ???? SUBSCRIBE to watch all our videos: https://www.youtube.com/c/Veritasiume... Thanks to Dr. Amir Alexander, Dr. Alexander Kontorovich, Dr. Chris Ferrie, and Dr. Adam Becker for their helpful advice and comments on early versions of the script. ▀▀▀ References: Some great videos on the cubic equation: 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 (Journey through genius: The great theorems of mathematics) Toscano, F. (2020). The Secret Formula. Princeton University Press. -- https://ve42.co/Toscano2020 (The secret formula) Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. -- https://ve42.co/Bochner63 (The significance of some basic mathematical conceptions for physics) Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. -- https://ve42.co/Murio21 (Cubic equations of Babylonian mathematics) Branson, W. Solving the cubic with Cardano, -- https://ve42.co/Branson2014 (Solving the cubic with Cardano) Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. -- https://ve42.co/Rothman (Cardano vs. Tartaglia: The Great Feud Goes Supernatural) Vali Siadat, M., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. -- https://ve42.co/Siadat21 (Geometric algebra and cubic equations) 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 ▀▀▀ Written by Derek Muller, Alex Kontorovich, Stephen Welch, and Petr Lebedev Animation by Fabio Albertelli, Jakub Misiek, Iván Tello, and Jesús Rascón Mathematical animations made with Manim -- thanks to Grant Sanderson and the Manim community! SFX by Shaun Clifford Filmed by Derek Muller and Emily Zhang Edited by Derek Muller and Petr Lebedev Additional video provided by Getty Images Music by Epidemic Sound Additional music by Jonny Hyman Produced by Derek Muller, Petr Lebedev, and Emily Zhang How Imaginary Numbers Were Invented Video in English from the @veritasium Channel: • How Imaginary Numbers Were Invented How Imaginary Numbers Were Invented ------------------------------------------------------------------------ ???? This Youtube channel is administered by: https://www.unilingo.tv/ ❓Comments or translation suggestions: [email protected] ------------------------------------------------------------------------ #veritasiumenespañol