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 https://brilliant.org/veritasium 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.
▀▀▀ References: Some great videos about the cubic:
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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