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.
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[@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!

[@martijn130370]

just saw your comment, i wrote the same above

[@stephenjones796]

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

[@altareggo]

Well, MY mind's work is definitely enhanced by these videos......she said, trying hard not to be a Grammar Police agent.

[@Vestiger]

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

[@richiethesailor629]

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

[@marcwong7964]

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?

[@DANGJOS]

I don't believe it has that connection to displacement

[@martijn130370]

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

[@ahx5287]

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

[@pandabearguy1]

I remember how much I enjoyed discovering this in my calculus course as part of an assignment we had.

[@JO-mg6xc]

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

[@portcreditdave]

Your excitement is infectious, Professor. Thank you!

[@sarathnair5883]

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

[@nickbutcherx]

This is the one I’ve been waiting for and you excelled yourself. Exquisite. Thank you so much 👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻

[@antoniomonsanto3925]

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.

[@inj1979]

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.

[@marykarensolomon7103]

I loved that! It’s my favorite theorem, so beautiful! And Brian derived it so logically and clearly.

[@eggonwalterlewinsshirt1071]

Yeah thanks professor🙏 you chose the equation I suggested in last video's chat section☺☺☺☺

[@rickcygnusx1]

One more thanks so much Dr. Greene! I just discovered this series today, only because I hadn't noticed the red WSF symbol at the top left, now I'm hooked!

[@Meurantbotha]

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

[@atessakrak8432]

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

[@mskEduTech]

Its always treat to watch your videos. I was knowing this but how beautifully you explain.

[@bkkfootball]

Great content! Thank you very much Dr. Greene

[@lilydog1000]

Wonderful. The identity is so beautiful, well worth emblazoning it on a T-shirt. Thx.

[@ShailendraKumar-ug4tn]

Thank you professor Brian.

[@adityajha9665]

I'm also from india...

[@stephenbrown40]

At my school, two standard math curriculum where available, the school chose the one that has no calculus. A group of us after trying to change this, had to do extra lesson's, After school, one teacher Mr Speed, taught 9 out of a class of 32, twice a week for a year. He was OK even though he had never taught calculus officially, he was supposed to teach Biology to collage level, he had to teach science to kids who wanted to do anything else but be taught anything.The next year he did teach biology for the first time, As we all wanted to learn, he taught us up to A level way above what was needed. The next year he left to teach Biology in another school. What amazes me is he left it so long, 10 yrs filling in.

[@mrsvspin]

Bravo!! it just keeps getting better

[@logicom4]

Thank you Brian!

[@lahockeyboy]

Thanks for another great, and very generous video, Professor!

[@digetalised]

Thank you Brian .... Awesome

[@samali786]

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).

[@vedmitraupadhyay1947]

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

[@muhammadshuraim9007]

Much excited to listen mathematical tools in physics... Thank you Dr. Brian Greene for starting this amusements

[@s_patzz8212]

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!

[@joaopaulomelo6620]

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.

[@samferrer]

Yes, they all represent identities!

[@danielbachour9987]

Amazing as always Professor Brian! Thank you so much! Enjoyed the video a lot! ... The energy that you always bring with you in every video is incredible! That makes the video even better! You make things look easy! That makes you who you are, an excellent physicist and professor! Thank you for your time! ... I would like to do an equation suggestion. As you mentioned in previous videos, we can propose an equation, following this idea, I would like you to explain "The Geodesic Deviation Equation". I find it very interesting. Too much physics in it! Thank you again Professor!

[@BookOnThrough]

The aesthetics of symbols are beautiful, and the cultural celebrations of the discoveries of the past greats are beautiful... but imo, the real deal beauty is in the comprehension.

[@jsbllrt]

Bravo Euler! Bravo Brian!

[@HebrewYisrael]

Euler - you see that number everywhere! Awesome!!!

[@matyasmeszaros1904]

Thank you!

[@alexisc6136]

The leg work was a little overwhelming but it is absolutely elegant and you did a beautiful job as a teacher in communicating that

[@paulneeds]

Dr. Greene - I am a self professed mathematical idiot - my teachers of some 42 years ago would probably extend that to arithmetical idiot also. But even so. In this presentation, for the very first time I’ve seen beauty in mathematics thank you for that! I’ve also for the first time found out the relationship of sin and cos to triangles! We were just taught that this angle is the sin of that one - and I handle things better when I know where they actually derive from - no matter the topic! So very many thanks, from Wales in the UK. Stay safe.

[@evanrodriguez6178]

These are so great, thank you! I have seen Euler's (my favorite equation for a few years now), and 1=.999... Looking forward to the rest. My question is if any equations out there attempt to tackle the shape of "functional infinity" versus conceptual it classic infinity. This is to say we have the infinitesimal mapped out with Planck's length and the lengths where quantum effects really take center stage, but are there any equations looking at where identifying (or conceiving of) a highest possible value within the realm might be more useful than simply using infinity as classically done? I can provide an example if you are interested, similar in a sense to the other side of the Zeno's Arrow Paradox coin.

[@Dr10Jeeps]

As I've mentioned before, I'm a psychology professor who is fascinated with physics. I can't thank Dr. Greene enough for all he does in promoting the beauty of science in general and physics in particular.

[@prayogdash3564]

please explain in the up coming videos about STEPHEN HAWKING's equation on finding the area of event horizon by the entropy of a black hole

[@annagorska1229]

Beautiful!

[@It_is_Aaditya]

This is the fundamental values of varies and constant is based on the ruler formula nice video 👏👍

[@gratefulamateur1393]

Wow, after being an engineer for 50 years I finally understand this strange identity. Thanks for a great presentation.

[@farhattabasum3542]

Lucky to learn from you sir

[@interVULife]

I'm so excited 😁

[@nawabpoya]

Incredible and enjoyable explanation👌

[@DipakDas-zq2in]

I like it very much , sir.

[@thoibaningthoujam8121]

Very logical n acccurate in no time Sir

[@sarmadnajim4839]

Amazing

[@nubesnegras10]

...wow!, thank you Sir, it is never late to learn ...

[@ChannelCtrlAltDefeat]

Thank you

[@abidmalik689]

It is really a beautiful equation without any doubt ..great work sir

[@nawabpoya]

Very cool explanation, thanks professor Green... I wish you will have a conversation with yuval Noah Harari in world science festival

[@mountainclimber48]

Agreed, the most beautiful equation in mathematics. For me the next one is the integral of e to the minus x squared from negative to positive infinity equaling the square root of pi. And both are so remarkably simple to derive. Thank you Dr. Greene, wonderful video.

[@theviscount9985]

Hey there! Could you point me to a place I can get an overview of the other equation? Thanks!

[@woody7652]

Bravo!

[@ProCoderIO]

This equation is what opens the door to things like i^i, ln i, sin x = 2, and other amazing concepts.

[@sethgilbertson2474]

Ok, I didn’t get any of this. But it did motivate me to start learning what I need to be able to. I want to understand this language! It is beautiful!

[@greggjackson2743]

There's a special place in heaven for the teacher.

[@sahojarkhan3411]

I am so EXCITED

[@adityajha9665]

It's awesome

[@srinivasjayanthy5946]

Brian is lovable !

[@HugoHabicht12]

Love it 😍

[@marcosgermano4737]

I must say that I was pleasantly overwhelmed as we arrived at the final (and gorgeous) expression. Muito sensacional !!! :-D Greetings from Brazil.

[@johnkechagais7096]

Thank you, i will go back and look at my calculus text book and see why Taylor's theorem works.

[@pipertripp]

Taylor's Theorem just doesn't get enough credit.

[@strikeblade6669]

hey professor greene plz give a link for the mathematical derivation of E=MC^2

[@mido3071]

It's easy, try using the definition of work F.ds and write it in terms of momentum and velocity, then plug in the momentum from special relativity and do the integration. you end up with E = mC^2 .

[@theklaus7436]

The first thing I thought was Bertrand Russell principia mathematica . Which is a classic about mathematical theories. I admit it is above my level but I get the point about beauty in math

[@michaelwaskiewicz1]

I actually do have this tattooed on my arm.

[@vikranttyagiRN]

Oh man i so badly want it on my arm now

[@michaelwaskiewicz1]

@@vikranttyagiRN Get it man. I'm a boss when people ask me about it and I'm able to explain it.

[@danieldorsz1047]

@@michaelwaskiewicz1 😂😂😂😂😂😂😂😂😂😂😂😂

[@BeckBeckGo]

Haha right before he said that I was thinking about doing that. I don't have any ink yet but I always come across things I'd be willing to stencil on my skin.

[@Amir-vw6rk]

frankly, i dont understand anything because im only in 8th grade but i just enjoy the beauty of these symbols

[@ybc8495]

8th should already finish calculus 3 and differential equations, study hard man!

[@SetemkiaFawn]

From a mathematician's perspective there is a quicker and easier way to show why we use natural logarithms. The exponential function exp(n)=e^n is a function f(x) such that (df/dx)(n)= f(n). That is, the function is its own derivative. The power series expansion of this function is Trivial and converges everywhere. From this received the exponent to an is equal to hyperbolic sine plus hyperbolic cosine. And we also find a familiar cosine + i sine

[@tonib5899]

thanks

[@casonkonzer8639]

could you do a video on the Fourier transform?

[@dontfollow4704]

Kya equation bnayi h shri shri shri brian greene ji Formulae of compound interest p x ( r/100) whole sq equals to??

[@Goldslate73]

Professor.... Could you please now take to the domain of particle physics???? Also... A question... Is it true to say that our mind uses or follows Heisenberg's uncertainty principle when we think about something happening and tell someone about it and then the thing never happens as planned.... In a long run?

[@kdkittehmama9490]

Can you explain the 3-body problem in a video?

[@Eztoez]

When he talks about "the third derivative" (or f ' ' ') - is he referring to a third-order differential equation ?

[@danielreed540]

For more videos of math (theory) & explanations, I recommend KZbin channels/publishers - 3Blue1Brown (excellent visualizations), & Mathologer (definitely presents advanced math theory & proofs & explanations, though sometimes does not state the conditions/limitations/assumptions under which what they present true, so can be confusing until they state or you figure out the conditions/limitations/assumptions under which it is true.) & check out suggested/related channels, or especially each channel's list of other channels, that are better quality (to me at least).

[@lindsaycoffey3327]

To see a “World in a grain of sand and heaven in a wild flower. To hold infinity in the palm of your hand, and eternity in an hour.” - William Blake.

[@yakupceliktas7739]

if you share a pdf link obout equations it will be good for us. Thanks for your good teaching

[@ahsanrubel2869]

Who are you, Brain!? How can you explain all the abstract ideas so eloquently..!? You are Feynman of our time... You are simply the best explainer by a considerable margin. You are the teacher I always missed. I can confidently say that now I understand the weirdness of special relativity because of you.. Your 11:30 hours lectures on special relativity are invaluable. I myself who graduated from business studies can follow your lectures...!! Just make General Relativity videos like those u made for special relativity.

[@KodamatiUdayaPrabhuKiran]

Brain Greene Bro! Plz explain equally weird expansion 1+2+3+4+.... = -1/12 which is being used string theory ( being you as one of the best string Theorists of our era). Note: All Physicists and Mathematicians are my Bros.

[@BeckBeckGo]

Oh I love this equation! I love seeing other people love it too. Best one yet. Also let's take a second and give that iPad a pat on the back.

[@hafismohammed5445]

can you do a video about uncertainty principle?

[@arisspenjian1220]

Your handwriting is so interesting.

[@chethannayak]

As a direct descendant of Euler, I have come up with my own little identity - p+ie=pie, where i is the square root of negative one, e is my great ancestor's constant and p is the secret ingredient which adds that unique flavour to that delicious snack called pie. Moreover, you can add other things to my identity to make customised snacks like apple pie, custard pie, etc. I know I deserve a Nobel prize but unfortunately they don't award it to mathematicians😢

[@phil97n]

Wonderful thanks. I may have to develop a love for tattoos so I can have that formula tattooed on my forehead.

[@equalat]

The fundamental beauty of any or all equations is =, how could anything else compare? =

[@muhammadshuraim9007]

Sir tell us that is numbers really exist or its just our tools to understand this universe. As you have written in your books "Until the end of Time......" that languages are evolved.. Tell me how evolving process do you think in mathematics. Is it also evolved?

[@kameronbriggs235]

I love what you are doing here. Sadly its hard to see the beauty of mathematics without really digging in. I slowly begin to realize - "Hey i can describe rates and changes, with calculus" -.... Then piece by piece its like... "Hey i can aim a tank gun while its moving" or "Hey i can create procedural algorithms to define trees" or "wow i can create descriptions of these sheets in structural geology" and so much more. Idk its just wicked cool.

[@noguera30]

so much time using e, and havimg no idea where it's comes and what it's means. Thanks for that

[@marykarensolomon7103]

e is just the natural number of science. We couldn’t have an earth without it. Think of it as mathematical oxygen.

[@bobross5716]

Think of it like pi. It’s a constant, roughly 2.72

[@mapeandrews3951]

I am a visual artist, I use science to inspire my practice. I was very surprised when you mentioned you had written an article about why art is important. I would love to read it, could you send me the link? I do not have a New York Times subscription and won't probably have it any time soon. I am a practicing artist, you can easily derive my purchasing power right there : D but seriously, would love to read what your thoughts are on the importance of art. I like how your brain works!

[@hackjokes9901]

I wonder what was euler's reaction when he discovered this

[@leon_noel1687]

There is a little mistake: (1+1/3)(1+1(3)(1+1/3) is actualy about 2,37. This imediatly popped into my eyes, because otherwise the line of numbers woudn´t make sence anymore.

[@sotomarkou9588]

I can see the resemblance :)

[@phalexasky5365]

Art expands the mind and lets you think out of the box, right?

[@Dr.JudeAEMasonMD]

I have a really stupid but honest question… if I may have a solution for one of the millennium prize problems, who do I contact?