How Imaginary Numbers Were Invented

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

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

Special thanks to Patreon supporters: Luis Felipe, Anton Ragin, Paul Peijzel, S S, Benedikt Heinen, Diffbot, Micah Mangione, Juan Benet, Ruslan Khroma, Richard Sundvall, Lee Redden, Sam Lutfi, MJP, Gnare, Nick DiCandilo, Dave Kircher, Edward Larsen, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Ruslan Khroma, Robert Blum, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy ‘kkm’ K’Nelson,Ron Neal

Executive Producer: Derek Muller
Writers: Derek Muller, Alex Kontorovich, Stephen Welch, Petr Lebedev
Animators: Fabio Albertelli, Jakub Misiek, Iván 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

30 gedachten over “How Imaginary Numbers Were Invented”

  1. A beautiful work: the best depiction of that epic struggle among mathematicians.
    Yet, to me the sentence at 18:03 appears quite bold: "the cubic equation led to the invention of there new numbers and liberated algebra from geometry". Also, the sentence at 22:11 "only by giving up math's connection to reality could it guide us to a deeper truth about the way the universe works".
    This is quite the opposite attitude of Geometric Algebra: the core idea within is to show that everything is geometry and even more abstract algebraic structures can have a direct (thus real) geometric interpretation. Imaginary numbers are perhaps the most tantalizing evidence of this approach.

  2. 5:17 “You can have my hotfix when you pry it from my cold, fully-vested hands.”

  3. 0:12 Has this guy been smoking weed?? You can see the smoke and his eyes are red lol

  4. Agree with use of negative numbers in quadratic equation to transform mathematics qualitatively; progressing from visual methods, Euclidean Geometry & General mechanical methods.
    However negative numbers had been used previously; e.g., Astronomy and more practically Accounting in Vedic/Indian Maths, Brahma Gupta in his Brahmadphutassiddanta (Around 7th Century A.D)

  5. Most adults forgot about useless formula for the type of drone work we do.

  6. Del Farro wouldn't have been able to keep his cubic equation secret if he had been required to show his work ..

  7. I have never been so blown away by mathematics in my life. 😲 Wow

  8. One thing I love about the history of math is its a global phenomenon. Like in this video, a problem was worked on and evntually solved over a period of 400+ years in entirely different parts of the planet by people with almost nothing in common.

  9. Before, I thought imaginary numbers were just a conspiracy made by the mathematician cult. Now I realize that they are a lifestyle. They are in everything. I am assimilated

  10. Did I watch this again and suggested a modification that i^2= -1?
    (and sqrt (-1) is a paradox and no sqrt(-1)?)

  11. I watch these vidoes not understanding anything but im always amazed that there are people out there that love this

  12. You need to dig up on indian mathematics and vedic mathematics

  13. If this was taught alongside the actual math during school, it would stick better, imo.

  14. As a grade 12 just finishing the last few of my finals this week… this video has blown my mind

    I NEVER understood why the method was called 'completing the square' until just now when you literally complete the square in front of me.
    If only all teachers and textbook writers were as dedicated as you.

  15. Their is internet puzzle by pink Floyd called publius enigma. I think the prize is numbers that is physical objects. Numbers are tones so it should be possible to make sculptures of them. Otherwise numbers will be fantasy language.

  16. So can complex numbers be called real? Since they do exist in waves.

  17. I hated math in high school, this is all like someone speaking a foreign language to me. Could never wrap my head around it. =)

  18. if they were averse to negative numbers, what they did if someone was in debt?

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