Your Daily Equation #11: Euler's Identity or The Most Beautiful of all Equations

Episode 11 #YourDailyEquation: Euler's Identity is widely viewed as the most beautiful of all mathematical equations, combining a handful of disparate fundamental quantities into a single mathematical formula. In this episode of Your Daily Equation, Brian Greene derives the identity, one that is second to none in capturing the poetry of mathematics.

Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.

The World Science Festival (WSF) is an innovative multi-media organization that produces original live and digital content straddling the arenas of science, technology, the arts, media, performance and education. With the goal of radically transforming public perceptions of science, WSF creates world-class programming, both live on stage and televised, featuring inspired collaborations, outstanding talent and novel production techniques that bring scientific discovery, insight and perspective to a broad general audience.

[BarryKort]

Besides having the arithmetic constants, 0 and 1, plus the imaginary number, i, along with the mathematical constants, pi and e, you also have the fundamental operations of addition, multiplication, and exponentiation, plus the concept of equality. How fabulous is that!

[stephenjones]

I can’t begin to tell you how important these videos are for keeping our minds work. Thanks again Professor.

[Vestiger]

Its 4AM in vietnam and I still decide to watch this :D the most beautiful equation ever

[ahx]

No matter how many descriptions or explanations I read/see of Euler's formula, it amazes me every single time. Thanks for this!

[richiethesailor]

These studies are ART! Love the eloquence in language! My mom had said to hang out with smarter friends. I'm 63+

[portcreditdave]

Your excitement is infectious, Professor. Thank you!

[antoniomonsanto]

Dr. Greene. Thanks for covering so smoothly the various concepts and their articulations reaching the "unexpected", singular and meaningful Euler's identity in a twenty minute exposition. Your obviously a great teacher and communicator. A role model to all engaged with teaching and educational tasks.

[trevormugalu]

"Read Euler, read Euler, he truly is the master of us all. Pierre Simon Marques De' Laplace.

[navstar]

Super presentation! Thanks so much. The "Daily Equation" format is brilliant - enough depth to be very satisfying (& memory jogging, for some of us!) and yet brief enough to consistently incorporate into days of everyday life... 👍

[marcwong]

Dr. Greene, thanks so much for giving non-physicists like myself insight into the wonder of the universe!

My question is about displacement and relevant equations.

I picture Archimedes in that bath tub noticing the water levels rise. Is displacement a thing in Einstein's theories? When a massive object distorts space, is this a sort of displacement?
Is there a galactic bathtub that contains a volume of space? Can space spill over the sides of some causality container (sorry for the surely inaccurate words)?
In other words, do gravitational waves spill over the side, or bounce back, or continue forever?
I think about Archimedes in a boundless ocean, would displacement exist?

[inj]

It's a pleasure to see you alive. I thank to Nature for keeping you safe in New York city. Also thanks to you professor for explaining these physical laws with examples, in layman's terms.

[JO-mgxc]

Dr. Green is a great teacher! For those who have some background education like college students this is fantastic! The students can overcome the deficit of their own local professors. Who’s Wavefunction to the Square is always zero

[martijn]

This equation ALSO has a product AND a power in it, PLUS as sum, so it has even many basic operators included!

[vedmitraupadhyay]

Thank u prof Brian for lively time on Euler's identity. Wonderful to experience the beauty once again at the age of 68 years. Amazes me at the power of human intellect. God keep u safe

[joaopaulomelo]

With each passing day, the videos are more interesting. I am from Brazil and I would like all people here, regardless of social class, to have the opportunity to watch this in our mother tongue, Portuguese, and really appreciate the beauty of these discussions.

[Meurantbotha]

Can you make this page downloadable somehow so that we can look at this on our own time. Great video btw!

[s_patzz]

This series needs to become a book! 2, 3, 5, pages of explanation per equation, as you describe it here but I would LOVE to have something like that to dip in and out of!

[samali]

Dear Greene, I must say that I have watched dozens of videos on Euler's identity, from mathologer to 3b1b and numerous I won't list here. But I can tell you that the way you explained it just out of this world. Thank you.
(Disclaimer: I am not a mathematician or physicist).

[sarathnair]

Beautiful! I never saw this beauty when I was studying high level math

[atessakrak]

Thanks for touching my life with all these fabulous and exciting information