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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 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. --

Imaginary Numbers are Real --

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

Toscano, F. (2020). The Secret Formula. Princeton University Press. --

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

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

Branson, W. Solving the cubic with Cardano, --

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

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

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

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

Bombelli, R (1579) L’Algebra

The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software].

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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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