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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 brilliant.org 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.

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References:
Some great videos about the cubic:

500 years of not teaching the cubic formula. — YouTube

Imaginary Numbers are Real — YouTube

Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York. — ve42.co

Toscano, F. (2020). The Secret Formula. Princeton University Press. — ve42.co

Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. — ve42.co

Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. — ve42.co

Branson, W. Solving the cubic with Cardano, — ve42.co

Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. — ve42.co

Vali Siadat, M., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. — ve42.co

Merino, O. (2006). A short history of complex numbers. University of Rhode Island. — ve42.co

Cardano, G (1545), Ars magna or The Rules of Algebra, Dover (published 1993), ISBN 0-486-67811-3

Bombelli, R (1579) L’Algebra ve42.co

Written by Derek Muller, Alex Kontorovich, Stephen Welch and Petr Lebedev
Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jesús Rascón
Mathematical animations done with Manim — thanks 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 supplied by Getty Images
Music from Epidemic Sound
Additional Music By Jonny Hyman
Produced by Derek Muller, Petr Lebedev and Emily Zhang