Imaginary Numbers Are Real [Part 13: Riemann Surfaces]

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

Special thanks to the fantastic Charles Jackson Young for helping me get the motion rig done in time for this video. You Rock!

[scuti]

Episodes 1-10: “Ah this is quite easy and relaxing”
Episodes 11-12: “Um what are we even doing?”
Episode 13: “HOW THE HELL AM I SUPPOSE TO VISUALIZEE 4D SURFACES IN A 3D WORLD ON a 2D SCREEN IN MY 1-D BRAIN?!”

[nirmolmunvar]

Episode 1: what is a number
Episode 13: *COMPLEX MULTIDIMENSIONAL MATHEMATICS*

[adamsahib]

It took me over thirty years, two math degrees and a decade of teaching math to even know of this shadow's existence, much less the meaningful layers behind it. This was incredibly humbling and illuminating.

[artemkochnev]

Watching the series feels like a top detective-documentary about math. Brilliant work, stunning storytelling.

[amanmahendroo]

4D visualization in 3D + Bass in the background? you guys need some oscars man!

[ProdCharles]

I had to pause and cup my hands over my mouth multiple times while watching this video. Thank you for such a beautiful explanation.

[nprsem]

Best educational series I saw. Strong plot. Many catchy moments. Tons of history and examples. Astonishing visual effects. I want to rewatch this with every of my friends. Thank you.

[arjunsadananda]

Oh My GOD!!! You are amazing! I actually felt emotional at the end of the story "Imaginary Numbers are Real". This video series is beyond this 3d space we live in! :P
All the efforts you put into this videos series is truly apreciated.

[farloux]

This. Is. Always will be. My favorite video series I've ever watched.

I'm in university now working for a degree in Mechanical Engineering.
I never enjoyed math.
That has always made working for this degree difficult.

Ever since following this series, math is the most beautiful thing I've ever seen.

Thank you, Welch Labs.
You gave me something I've been desiring my whole life.

[AyratHungryStudent]

Teacher: This will be on the test so pay attention *shows part 1*
Test: *part 13*

[edwardsolomon]

I actually had tears in my eyes at the conclusion of this series. For the nearly two decades I've been studying mathematics, teaching, and using "lateral" numbers...I never truly grasped their meaning until the very end of this video, which ends where the entire series began.

Thank You so much, this was gorgeous and very well made.

[bboysil]

I have never seen a better series of on any subject anywhere else on youtube. This series was just perfectly made.
I recommend this to anyone even if their field is not math related.

[weekendresearcher]

This series deserves a field's medal. This is Graduate level Math for toddlers. You guys just exploded the power of imagination. This is education AS REAL AS IT CAN GET !! Thanks a ton !!

[sebbes]

8:18 This is exactly similar to how you CAN return to a place you have been to previously, but CAN NOT return the same _time_ AND _place_ simultaneously.

[eskay]

I binge watched all the 13 videos, amazing.Hats off to the creator.Every math class should show this to the students.

[naeemaleahmadi]

no way on earth anyone can explain complex number better than this. thumbs up, hats off, thank you.

[wakeatmethree]

Well done. I feel like i binged through a season of House of Cards.

Except this was actually useful and opened my eyes to lateral planes.

Thank you, good sir.

[Zyoutube]

watching this series after 6 years of its release, and i'm really impressed of how beautiful this is, one of the most fun and amazing series I've ever watched

[wolfgangschaltung]

For the first time in my life, I got the feeling I grasped what imaginary numbers are about. Thanks for creating this!

[gouravgagan]

This should be compiled into a movie.. and should be released in theaters so that other people will know how much interesting mathematics really is.. 😀