This Problem Broke Math (and led to Quantum Physics)

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.

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


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