The Most Beautiful Equation

Euler's Identity is one of the most popular math equations. In this video you'll learn what it really means.

Chapters:
00:00 Intro
00:33 Pi
01:28 i
02:07 Derivative
10:00 e

This video was sponsored by Brilliant

[gruk]

This is absolutely incredible. I just finished Calculus II, and when we talked about Taylor Series they were explained very poorly. This not only made me completely understand how Taylor series are formed, but also what e^ipi really means (something I’ve been wondering for a very long time). People like you make the world of learning a better place. Thank you

[victoryfirst]

If only my math teacher explained this so well.

[mustafayigitkartal]

This might be the most concise (and perhaps the prettiest) explanation of euler's identity that I've ever seen. I love how you show each derivation (pun intended) step by step and using first principles, really shows that you're not just listing off an arbitrary set of rules but actually understand what each of them mean.

[swdhags]

Derivative, Taylor seires, sin cosine, iota, pie all in one video!! Incredible

[Kaspa]

You did an amazing job explaining It! I tried many times to understand the Euler's identity, but I couldn't because other people didn't do what you did. You explained everything from the basics, and It really helped a lot.

[i_have_no_pronouns]

Dude, this is the beauty of math that an engineer like me won’t truly be able to experience. We learn a lot of stuff without proper explanation so it’s nice to see a video like this

[OmarElsayedd]

The animation, the explanation and the way you covered so many topics in one video is just amazing.

[kennethbrack]

Oh my gosh. That equation was a wonder to me when I was a teenager and very good at math. Now I am a senior citizen and have understood it for the first time. Thank you for your excellent explanation.

[OKchromia]

This channel is too underrated, this was explained flawlessly

[mario-pxpb]

This is the most beautiful thing i have ever seen. Amazing explanation. Thank you!

[endlesswick]

A really good explanation. I have heard of solving Euler's Identity with the Taylor series before, but you really went into detail explaining how the Taylor series works, how to turn sin, cos, and e^x into Taylor series, and finally bringing it all home equating the Taylor series of e^x to that of sin and cos. All in 13 minutes. Impressive.

[among-us-in-tetris]

this has been my favorite equation since i read it on a math book, but now is the first time i actually understood the process of it. most useful 14 minutes of math in my life

[ЛевАронов]

it's like magic...
I first saw this equation in the video "Math vs Animation". Since I am just in 11th grade, I know nothing about complex numbers or eulers number e. So I never understood what those complex equations mean. But now when you wrote e^ipi = cosx + isinx I was shocked, because I remember this equation from that video. This is so well done, thank you so much for the explanation!

[thomaskember]

We can go further by writing the identity as e^ipi = -1 and from that write ipi = ln(-1) then dividing both sides by I we get pi = ln(-1) /i or pi = ln(-1) / square root of-1 which is a new definition of pi. I am sorry my keyboard doesn’t have much in the way of mathematical notation.

[supremeclamitas]

That was the best explanation of the derivative limit I've ever seen!

[fun-damentals]

so this guy actually explained radians, calculus and other stuff in 13 minute video. he explained them well enough to actually understand the subject matter. you sir are a legend. so damn rare to find content like this. hats off man

[YoutubeBorkedMyOldHandle_why]

Thank you sir. This is the most elegant and understandable explanation I've seen, which ties these important concepts together. It is truly amazing that Euler and others understood these things some 3 centuries ago, yet we still struggle with them today.

[fano]

You explain so much about complex numbers in this little video, which never been told in any maths class. Thats brilliant!

[JD-eedf]

This is insane, there's about 5 different concepts in this video that I understood for the first time despite years of studying Maths and having to take these things for granted. Amazing video, thank you.

[uchiaru]

me who understood nothing, but still found it cool 😂