How Imaginary Numbers Were Invented

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.

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References:
Some great videos about the cubic:

Cardano, G (1545), Ars magna or The Rules of Algebra, Dover (published 1993), ISBN 0-486-67811-3

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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

[ongka]

I wholeheartedly believe that giving context to the history and slowly guiding students through the mindset of mathematicians is objectively better than spoon-feeding them equations.

[StevenHe]

This video makes me want to do math. It’s inspiring in the best way

[TheGrimSmile]

I can't believe that now, a decade after struggling to understand it, I finally know what "completing the square" means.

[willclark]

It's shocking how thoroughly you managed to deceive me into thinking I almost understood this topic. You, sir, are phenomenal!

[FinFET]

Imagine minding your own business as a mathematician and suddenly someone challenges you to MATH DUEL, that can make you lose your job. Man, the older times were really intense for mathematicians.

[DanielVCOliveira]

Man, change "depressed quadratic" to an obscure magic spell and you literally get a fantasy duel story, complete with a sage old mentor, an underdog protagonist, an enchantment and a boastful proud villain wtf

[DarkRavenhaft]

Visualizing "i" as describing a value that cancels itself out and seeing the CG of e^ix described as a spiraling 3-dimensional waveform with the X & Y functions 90° out of phase may have contributed more to my understanding of physics and mathematics than the entirety of my college calculus courses.

[Srioll]

I have a masters degree in physics, so I'm confident in saying I'm pretty good at maths. You describing the completing the square method of solving a quadratic just genuinely blew my mind. I never understood where any of it was coming from and opted instead just to use the quadratic formula and ignore completing the square. I just thought it was entirely irrelevant. But holy wow it makes so much sense now, I see where the steps all come from, and it's actually extraordinarily elegant. It makes soo much more sense now!

Just goes to show how much influence a teacher has on their students and why so many people think they're bad at maths. I hope more teachers start teaching things they way you did there. Thank you!

[kevinmatheka]

"I did not deem him capable of finding such a rule on his own." Savage 😂

[Factnomenal]

A History, Math and Science smoothie blended to perfection. Well done 👏

[the_Googie]

I was one of the worst math graduates in my highschool class but recently I had a spark of love for maths and reteach myself everything. This video is nothing short of amazing. Its just mindblowing!!

[CrikeyArchie]

"Only by giving up maths' connection to reality could it guide us to a deeper truth about how the universe works." Bravo!
A thoroughly professional presentation from algebraic dependence on visual geometry through Mediterranean ego vignettes segueing into physics, with remarkable insights along the way, culminating in the quote above.

[JJOOOOSSSSSSSSHHHHHHHHHHHHHHHH]

As someone who's really bad with math, these visuals have helped me realize a lot of what I didn't understand with basic algebra and trig functions from school as a kid.

[izzynobre]

Dude makes math sound absolutely riveting... Incredible

[mathieud]

It just feels like I've uncovered some chunk of fundamental knowledge of absolute purity. Thank you for letting us fools taste the beauty of maths in a 23-minute video.

[ViciandoCodigo]

This video was incredible, I cannot put into words the fantastic journey I experienced in these last few minutes, thinking about the realities of mathematicians, how problems that have been considered to be impossible for thousands of years are solved, and how we naturalize the legacy of these incredible minds. Thanks my friend

[TheFinalRevelation]

Most of your work is educational yet highly entertaining but this particular video deserves an award. One of my favorite channels on the platform. Proud to have subscribed to it over 10 years ago.

[welovfree]

History of mathematics should be taught as early as in middle school, and this video tells exactly the reason why it would immensely help students appreciate what they are taught.

[sampsontendaimutsago]

I thought I was just going to browse the video but here am i going through it all and even rewinding. Thanks it was very engaging and brilliantly undertaken.

[Angarayan]

Superb in everyway. This is how mathematics should be taught. You deserve a prestigious award.