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!
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.
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?
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.
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... 👍
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.
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
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).
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
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.
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!
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!
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.
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.
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!
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.
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.
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
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
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 .
For more videos of math (theory) & explanations, I recommend UA-cam 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).
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.
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.
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.
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.
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😢
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.
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?
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!
Why Art Matters. The documentation of the human experience? Some forms of art, there is a cross over in art and mathematics and the way we perceive aesthetic principles. At school I studied 19th Century French Academic Art. That sort of art you need to know a bit about the observation of light and proportions, for example. It is through Artistic expression, that humans learnt about beauty and aesthetics. It is through Art, that mathematicians learnt about beauty. And it is through Art, that humans learnt about the observation of nature. Some of the first observations of nature are cave paintings using the language of art. Without art, there would be no mathematics. Some scientists forget that.
Richard Feynman impressed on his students that it was *irrelevant* whether an equation was reasonable, elegant; or even 'beautiful'. It had to be *correct* and must be testable and reproducible. Occasionally it might look 'pretty' is all.
But here we are talking about mathematics, not physics. Fundamentally, maths is about patterns, independent of the real world, and humans are pattern-seeking creatures, so we can see that it might be the most beautiful science. Moreover, in fact, there is no consensus about the definition of maths. Some academics even believe that mathematics is an art.
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?
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.
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
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!
just saw your comment, i wrote the same above
I can’t begin to tell you how important these videos are for keeping our minds work. Thanks again Professor.
Well, MY mind's work is definitely enhanced by these videos......she said, trying hard not to be a Grammar Police agent.
Its 4AM in vietnam and I still decide to watch this :D the most beautiful equation ever
No matter how many descriptions or explanations I read/see of Euler's formula, it amazes me every single time. Thanks for this!
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.
These studies are ART! Love the eloquence in language! My mom had said to hang out with smarter friends. I'm 63+
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?
I don't believe it has that connection to displacement
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.
"Read Euler, read Euler, he truly is the master of us all. Pierre Simon Marques De' Laplace.
Your excitement is infectious, Professor. Thank you!
This equation ALSO has a product AND a power in it, PLUS as sum, so it has even many basic operators included!
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... 👍
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.
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
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).
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
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.
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!
Can you make this page downloadable somehow so that we can look at this on our own time. Great video btw!
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!
I loved that! It’s my favorite theorem, so beautiful! And Brian derived it so logically and clearly.
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.
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.
This is the one I’ve been waiting for and you excelled yourself. Exquisite. Thank you so much 👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻
Taylor's Theorem just doesn't get enough credit.
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!
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.
Hey there! Could you point me to a place I can get an overview of the other equation? Thanks!
This equation is what opens the door to things like i^i, ln i, sin x = 2, and other amazing concepts.
Beautiful! I never saw this beauty when I was studying high level math
The leg work was a little overwhelming but it is absolutely elegant and you did a beautiful job as a teacher in communicating that
Wow, after being an engineer for 50 years I finally understand this strange identity. Thanks for a great presentation.
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.
Thanks for touching my life with all these fabulous and exciting information
I remember how much I enjoyed discovering this in my calculus course as part of an assignment we had.
Wonderful. The identity is so beautiful, well worth emblazoning it on a T-shirt. Thx.
Much excited to listen mathematical tools in physics... Thank you Dr. Brian Greene for starting this amusements
Thank you professor Brian.
I'm also from india...
is it possible to write an exam if I tattooed this formula
Its always treat to watch your videos. I was knowing this but how beautifully you explain.
This is the fundamental values of varies and constant is based on the ruler formula nice video 👏👍
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
Bravo!! it just keeps getting better
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!
Bravo Euler! Bravo Brian!
Very cool explanation, thanks professor Green... I wish you will have a conversation with yuval Noah Harari in world science festival
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
Yeah thanks professor🙏 you chose the equation I suggested in last video's chat section☺☺☺☺
Euler - you see that number everywhere! Awesome!!!
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.
There's a special place in heaven for the teacher.
Yes, they all represent identities!
Thanks for another great, and very generous video, Professor!
hey professor greene plz give a link for the mathematical derivation of E=MC^2
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 .
For more videos of math (theory) & explanations, I recommend UA-cam 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).
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.
It is really a beautiful equation without any doubt ..great work sir
Kya equation bnayi h shri shri shri brian greene ji
Formulae of compound interest p x ( r/100) whole sq equals to??
Great content! Thank you very much Dr. Greene
Thank you, i will go back and look at my calculus text book and see why Taylor's theorem works.
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.
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
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.
I actually do have this tattooed on my arm.
Oh man i so badly want it on my arm now
@@vikranttyagiRN Get it man. I'm a boss when people ask me about it and I'm able to explain it.
@@michaelwaskiewicz1 😂😂😂😂😂😂😂😂😂😂😂😂
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.
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😢
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.
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.
I like it very much , sir.
frankly, i dont understand anything because im only in 8th grade but i just enjoy the beauty of these symbols
8th should already finish calculus 3 and differential equations, study hard man!
When he talks about "the third derivative" (or f ' ' ') - is he referring to a third-order differential equation ?
I must say that I was pleasantly overwhelmed as we arrived at the final (and gorgeous) expression.
Muito sensacional !!! :-D
Greetings from Brazil.
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?
Lucky to learn from you sir
Very logical n acccurate in no time
Sir
Brian is lovable !
Thank you Brian .... Awesome
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?
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!
could you do a video on the Fourier transform?
Incredible and enjoyable explanation👌
if you share a pdf link obout equations it will be good for us. Thanks for your good teaching
very nice explication
The fundamental beauty of any or all equations is =, how could anything else compare? =
Why Art Matters. The documentation of the human experience? Some forms of art, there is a cross over in art and mathematics and the way we perceive aesthetic principles. At school I studied 19th Century French Academic Art. That sort of art you need to know a bit about the observation of light and proportions, for example. It is through Artistic expression, that humans learnt about beauty and aesthetics. It is through Art, that mathematicians learnt about beauty. And it is through Art, that humans learnt about the observation of nature. Some of the first observations of nature are cave paintings using the language of art. Without art, there would be no mathematics. Some scientists forget that.
Thank you Brian!
Richard Feynman impressed on his students that it was *irrelevant* whether an equation was reasonable, elegant; or even 'beautiful'. It had to be *correct* and must be testable and reproducible. Occasionally it might look 'pretty' is all.
But here we are talking about mathematics, not physics. Fundamentally, maths is about patterns, independent of the real world, and humans are pattern-seeking creatures, so we can see that it might be the most beautiful science. Moreover, in fact, there is no consensus about the definition of maths. Some academics even believe that mathematics is an art.
so much time using e, and havimg no idea where it's comes and what it's means. Thanks for that
e is just the natural number of science. We couldn’t have an earth without it. Think of it as mathematical oxygen.
Think of it like pi. It’s a constant, roughly 2.72
Your handwriting is so interesting.
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?
Amazing
Euler didnt leave behind information. The universe did.
I wonder what was euler's reaction when he discovered this
can you do a video about uncertainty principle?
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.
Art expands the mind and lets you think out of the box, right?
Can you explain the 3-body problem in a video?
Professor, the lower stamp is actually East German (DDR). Have a good day.
I'm so excited 😁
Love it 😍
...wow!, thank you Sir, it is never late to learn ...
5:27 theoretically speaking, if you WERE to do an infinite number of daily equation videos, that would be a countable infinite 😜😅