A general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality.
References:
Some great videos about the cubic:
500 years of not teaching the cubic formula. -- https://youtu.be/N-KXStupwsc
Imaginary Numbers are Real -- https://youtu.be/T647CGsuOVU
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
What did you learn today?