Imaginary Numbers Are Real [Part 2: A Little History]

Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.

Part 1: Introduction
Part 2: A Little History
Part 3: Cardan's Problem
Part 4: Bombelli's Solution
Part 5: Numbers are Two Dimensional
Part 6: The Complex Plane
Part 7: Complex Multiplication
Part 8: Math Wizardry
Part 9: Closure
Part 10: Complex Functions
Part 11: Wandering in Four Dimensions
Part 12: Riemann's Solution
Part 13: Riemann Surfaces

Part 2 especially owes a debt to Paul Nahin's excellent book: An Imaginary Tale: The Story of sqrt(-1). Nahin presents a very thorough account of the development of imaginary numbers, which was invaluable in creating this series.

[amohogride]

Imagine a mathematician running around the street carrying a sheet of questions finding an opponent.

This is basically Pokemon

[xxnotmuchxx]

Mathematicians should continue to have duels. That sounds pretty cool.

[Technomancr]

Why did you abandon calling them lateral numbers?

[HDitzzDH]

3:35 That is not quite correct, the current definition of the square root only accounts for the positive number whose square is the number inside the square root, the only time you inlude +/- is when you're solving an equation. The square root itself is only defined for one positive number.

[anarki]

Holy shit. Math duels? Are you serious? That's pretty hilarious.

[rabeebibrat]

A HUGE thumbs up for the historical context, which math texts don't provide. Interesting series!
Keep up the good work.

[wiredelectrosphere]

This math duel thing is presented like you can make an anime out of it

[sajjadulhaq]

Words are just not enough to explain how awesome these series are. Only true mathematician can understand that how difficult it is to prepare such lectures.
I have been searching for such kind of study from many years.
I am truly great-full for this series.

[trulyUnAssuming]

sqr(9) = 3 and sqr(9) != -3. At least in the usual definition. Since you define the squareroot as the inverse function of f: [0, infinity] -> [0, infinity]; x -> x². But the solution to x²=9 is x=+/-sqr(9)=+/-3

[beta]

This is gold. Never have I seen better VFX used in presentations for such a basic topic.

[Maceta]

Nerds before:
"I just murdered someone in a math duel and I'm on the 30th page solving this single equation"
Nerds now:
"Why this python code not work"

[julesverne]

How long did it take to cut out all the continents of the world?

[robertwilsoniii]

This playlist is awesome!! I love learning the history of the math while learning the math! This is how it should be taught in general.

[samkoesnadi]

This is very very useful. I like it a lot. Thank you for your hardwork on this video!

[alexanderherbertkurz]

I love the way this mixes history and math. And handwriting and computer animation. Absolutely brilliant. Should be one of my favourite math videos now. Added: It is actually almost addictive ... I am going to watch the rest of the videos even though I know the stuff.

[manjunathnavalgund]

wow....this series is addictive....I am binge revising my school algebra

[Qebton]

this video is so underrated man its so freaking amazing i'm going to show it to everyone i know

[WoLFx]

The square root of 9 is strictly 3. When approaching x^2 = 9, only when you square root do you get the plus-minus in front of the positive root to indicate +-3

[tankmaster]

LOVE THE FACT THAT YOU BRING MATH'S TO LIVE AND VISUALIZABLE

[niteshsingh]

I just watched this video and got amazed with the concept, everyone who has studied complex numbers has thought about its practical use but got no answers here I got something new.