How Imaginary Numbers Were Invented

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01.11.2021
Veritasium

Veritasium

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343
21.07.2010
US
Описание видео:

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 🤍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: 500 years of not teaching the cubic formula. 🤍youtu.be/N-KXStupwsc Imaginary Numbers are Real 🤍youtu.be/T647CGsuOVU Dunham, W. (1990). Journey through genius: The great theorems of mathematics. New York. 🤍ve42.co/Dunham90 Toscano, F. (2020). The Secret Formula. Princeton University Press. 🤍ve42.co/Toscano2020 Bochner, S. (1963). The significance of some basic mathematical conceptions for physics. Isis, 54(2), 179-205. 🤍ve42.co/Bochner63 Muroi, K. (2019). Cubic equations of Babylonian mathematics. arXiv preprint arXiv:1905.08034. 🤍ve42.co/Murio21 Branson, W. Solving the cubic with Cardano, 🤍ve42.co/Branson2014 Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural. arXiv preprint arXiv:1308.2181. 🤍ve42.co/Rothman Vali Siadat, M., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations. Math Horizons, 28(1), 12-15. 🤍ve42.co/Siadat21 Merino, O. (2006). A short history of complex numbers. University of Rhode Island. 🤍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 🤍ve42.co/Bombelli The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.13.1) [Computer software]. 🤍🤍manim.community/ ▀▀▀ 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, 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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How Imaginary Numbers Were Invented
How Imaginary Numbers Were Invented
How Imaginary Numbers Were Invented
How Imaginary Numbers Were Invented
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Комментарии пользователей:
Danny Martial
2022-11-30 16:14:26

I could take a modern math textbook back 1000 years and rule the world 😂

drumphil00
2022-11-30 13:46:08

Gawd damn.

CaribSurfKing1
2022-11-29 00:30:04

There were a few jumps in the math that even the smart viewer has to accept without understanding. My math teachers did the same in school. Take more time with the math, in steps

David Reid
2022-11-28 07:55:47

I studied [relatively] quite a lot of maths and physics and was mesmorised by mathematic elegance and it's description of the real. Watching Veritasium videos is like a trip down memory lane except that the clarity and insight provided is like having a cherished memory filmed in black and white and finally watching it in colour. The part where the spiral geometry of e^ix on the imaginary place is easily viewed as the combination of the real element (cosine) and imaginary element (sine) is both simplistic and elegant. I wish that my professors and teachers had shown me this many decades ago, and I hope that future students will benefit from this type of approach. Most of us probably grasp ideas easier when it is clearly (and elegantly!) explained.

JEFFIN K DEVASIA
2022-11-28 04:23:45

Giving the context of these principles helps to understand the concepts better... Just awesome 👍🏼

Nipun Aggarwal
2022-11-27 17:15:56

We need to bring back the math duels

Jonah
2022-11-27 10:16:02

I love and hate this video so much

Fine Mathematics
2022-11-27 02:12:26

This is a great Math History lesson. Not only can one see the evolution of Math, but also get a fresh perspective of the capabilities of Math beyoond perspectives.
As mentioned in this video, complex numbers are part on QM equations, but they also work very well In Electodynamics as well, by making the Math much easier.
History gives the Math context so students can differentiate different types of Math.

Subuhi Nigar
2022-11-26 17:53:04

very interesting video and informative too .

Kimberly Heimann
2022-11-26 15:07:03

I can’t even comprehend this math and people call me the smartest kid in school

Dexter White
2022-11-26 09:00:58

You lost me at "the mathematics began..." Dang it!

I am a Rubik's cube
2022-11-26 07:09:14

cUzklzVXJwo&t=3m58s 3:58 You colour it the colour of the table and put it over the other squares.

Aaron F
2022-11-26 05:23:05

Excellent video!!

Tomodachi友達
2022-11-26 04:54:20

Shoutout to Gauss for calling imaginary numbers Lateral Numbers

Tomodachi友達
2022-11-26 04:50:42

cUzklzVXJwo&t=19m03s 19:03 what a fancy way of saying "trust me bro"

Spectrickx
2022-11-24 23:05:05

Abandon reality, to find its meaning.

Jombos DC
2022-11-24 04:39:32

The effort that went into this video :)

Zackary Grandstaff
2022-11-24 01:39:01

I’m learning this right now. I will definitely come back to this video many times.

Tyladron
2022-11-24 00:17:00

I wish that we had learned the history of mathematics in school, imaginary numbers just came up out of nowhere and felt like there was no reason for them.

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