How Imaginary Numbers Were Invented

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

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.

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

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

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.

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

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.

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!!

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

Instead of letter grades A through D, 8th graders should get a grade placement based on which century of Italian mathematics they most closely align with.

"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.

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!

Just had my mind blown learning that "complete the square" is literal.

All throughout grade school and college I struggled to understand the "why" portion of math beyond plug and chug. Usually professors couldn't give me an adequate explanation. Completing the square was one term that never really clicked for me. The first 3 minutes of this video are pure genius. So simple and understandable. This makes math so much more digestible.

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.

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

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.

This REALLY brought an eye opener to my "how the heck did they figure this out" during math classes. Awesome explanation. Thanks

@Veritasium A bit late to the party but in German we call them complex numbers and in my career as a physics uni student we never really considered them to be neither imaginary nor detached from reality. When we first came in contact with them in our first semester, for example when solving diff. equations, we just ‘used’ them as a tool to ‘simulate’ sin and cosin functions to help solve them.

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