Because people that study math like this see how it lays the foundations for the world around us. Math makes things exist, often in very beautiful ways.
I have hated math all my life due to my lack of understanding of the complicated formulas, BUT I have to admit, math is beautiful when taught by the right person, like this guy. thanks!
That guy spoke at a math competition in Bergen Country Academies once, I remember him. He talked about how dice were much more than dice, and he used the same excitement there too.
lol this equation is ridiculous. He just put a complex number under exponential form. Look here it is dude, z= -1 theta of that is pie. Magnitude or modulus(think of it as absolute value) of that is 1. so it gives us 1e^ipie = -1 btw i goes before pie not after but anyways. So e^i*pie + 1 = 0. It's really ridiculous tbh.
This formula contains mathematical constants derived from arithmetic (0 and 1), geometry (pi), algebra (i), and calculus (e), as well as addition, multiplication, and exponentiation! And it's so concise! You just can't get better than that.
Well, e is often defined as the limit of (1+1/n)^n as n approaches infinity. Also, e is the number whose exponential function (e^x) is its own derivative. Limits and derivatives are perhaps the two most fundamental concepts in calculus.
Tyler Borgard you forgot about trigonometry. That e^ipi=cos pi + isin pi. So the whole equation turns in cos pi (negative 1) +isin pi(which is 0 because of the sin)+ 1 which is exactly 0.
Well, I tend to view trigonometry as a subset of geometry, but that is a good point. Who would have guessed that trigonometric functions could be expressed in terms of exponentials?
Tyler Borgard Forgive me for my lack of skill as far as math is concered, but how exactly does (1 + 0)^infinity become ~2.71 rather than just one? Not at all saying you're wrong, I'm just curious about how this works.
Well, 1^infinity is what's called an indeterminate form (kind of like 0/0), which means that simple plugging-and-chugging isn't going to help you find the limit. Here's an easy way to see why 1^infinity is indeterminate: 1^1=1 1^10=1 1^100=1 1^1000=1 ... So you'd think 1^infinity would also be 1. However... 2^infinity=infinity 1.5^infinity=infinity 1.1^infinity=infinity 1.01^infinity=infinity ... I'm using the '=' sign rather loosely here, since infinity isn't technically a number. However, these equations still make sense in the context of limits, so you could argue from them that 1^infinity is actually infinity. We don't have a clear answer, which means that we must evaluate the limits on a case-by-case basis using other means. For example, take the limit (2^(1/n))^n as n approaches infinity. This approaches the form (2^0)^infinity=1^infinity, which is indeterminate. But we can still find the limit pretty easily, as follows: For all positive numbers n, (2^(1/n))^n=2^(1/n*n)=2^1=2. Therefore, the limit is 2 (and not 1). Now, in our situation, e is defined as the limit of (1+1/n)^n as n approaches infinity. This also approaches the indeterminate form 1^infinity, so we can't evaluate the limit in this way. Now, there's not an easy way to analytically find the limit, since this limit is the very definition of our special number e, but if we evaluate the expression for large enough values of n, we can get a good decimal approximation for e. (1+1/1)^1=2 (1+1/2)^2=2.25 (1+1/3)^3=2.370370... (1+1/5)^5=2.48832 (1+1/10)^10=2.593742460... (1+1/100)^100=2.7048138294... (1+1/1000)^1000=2.7169239322... (1+1/10000)^10000=2.7181459268... (1+1/100000)^100000=2.7182682371... (1+1/1000000)^1000000=2.7182804691... As n gets arbitrarily large, this expression gets arbitrarily close to e=2.7182818284...
Even though I have used Euler's Identity for almost 4 years now (being an engineer), I never really stopped and thought about how one imaginary and two irrational numbers combine perfectly to give -1. The professor's excitement clearly shows his love for math and his appreciation of its beauty. Great video!
kave mustermann He's intelligent, has a friendly personality and has a passion. He'll have no problem finding dates (as long as he doesn't bring along a blackboard).
lucky doesn't necessarily mean chance, can also mean fortunate by method of skill or achievement when used in context with the correct expression. so yes, you could say he is lucky.
FYI, this guy is the head coach of math Olympiad team USA. A Chinese American lead a math team with majority Asians beat the Chinese team 2 years in a row. Team USA was champion in 2015 and 2016. Wish them luck in 2017.
here's another beautiful number I discovered myself (idk if anyone already mentioned this in the history of math ever but I haven't done my research at the time that I am writing this, so I will proceed) 142857. why? multiplied by two, becomes 285714 by three, 428571 by four, 571428 by five, 714285 by six, 857142 but by seven, becomes 999999 anymore than six, with the exceptions of joining the number 0 to the numbers 1-6 to form a two-digit number (e.g., 10, 20, 30, etc.) and multiplying them to 142857, and the special exception of multiplying seven to it (or 70 or any number of digits starting with 7) will result in one of the digits present in 142857 to be missing. more rules: the digits present in 142857 will be present in that order when dividing a number non-divisible by 7 once (meaning it will result in a number with decimals, not a whole number) in the resulting decimals. dividing the number with 142857 in its decimals already by 7 once more will result in not seeing the number 142857. edit: okay so I did my research and it turns out this number has been discovered by other people. if you didn't understand my explanation perhaps this might help: en.wikipedia.org/wiki/142,857
Symbol 'i' is the root of -1 which is not a real number and that is why Pi is telling it to "Get Real". On the other hand, Pi(3.141592654 which can't be expressed in a fraction form) isn't a rational number and that is the reason i telling it to "Be Rational".
This video inspire me ! Not in math by in job. Look at this math teacher when he explained this equation his eyes were bright and shiny. There is no doubt that he like math and enjoy math very much . I hope I can do my job(Linux management) like him. : )
I wish my math teacher could transfer even a tiny bit of the passion for math this guy radiates on to his students. I don't even understand what's going on in this video but it's much easier to show interest in a topic if it's taught by someone like this
For those of you who are confused, Euler's theorem states that for any real number x e^(i*x) = cos(x) + i*sin(x), given x in our case = Pi and substituting into this equation we obtain e^(i*Pi) = cos(Pi) + i*sin(Pi), where cos(Pi) = 1 and sin(Pi)=0, therefore e^(i*Pi) = -1 + 0*i where 0*i is just 0. Rearranging, e^(i*Pi) +1 = 0
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/1.gif)
If you're planning on doing something big in life, start by making sure you're happy as this guy.
Amazed that I am the first one to appreciate your comment through comment
Appreciate your words man 🙂🙇🙇
I love how he’s so excited about it
You can see he loves what he does.
The gap between how good he is and how terrible I am is astounding
0:47 that "e" was so satisfying
it's so cool to see how excited a person can be while explaining math
Rainbow Dash69 it is
Rainbow Dash69 yes I want a teacher like this, maybe i will start to like maths😂
I need him as my high school teacher for math I can imagine how well he explains maths in such a happy way you can clearly see it’s passion
Because people that study math like this see how it lays the foundations for the world around us. Math makes things exist, often in very beautiful ways.
I just liked to make it an even number
The excitement in him saying those is unreal, it really shows the passion that he has for numbers.
TooCoolForYou So his excitement is imaginary?
Sir Socket numbers are not imaginary
Jay Modi Imaginary ones are
Jay Modi are you out of grade school maths yet?
That is derogatory.
I've never seen anyone in my life who's so exited with maths.
you know what's more beautiful than this equation?
that dude's smile ;)
The guy is just happy doing maths 😅
So? You seem to be happy being one piece's fanboy
So??
quick maffs
2+2 is 4, minus 1 that's free. Quick maths
Who isn't?
I have hated math all my life due to my lack of understanding of the complicated formulas, BUT I have to admit, math is beautiful when taught by the right person, like this guy. thanks!
Faisal M well said
Faisal M d
how old are you?
Faisal M well said
what has he taught ?
Love his energy, it's contagious 😂
Indeed, I would love having him as my professor.
HIGH energy
It's too bad this equation isn't as simple or as beautiful as it should be.
Michael Hartl explains it better than me.
Bbl
Pink Plant he is the best!
That guy spoke at a math competition in Bergen Country Academies once, I remember him. He talked about how dice were much more than dice, and he used the same excitement there too.
This guy should do a stand up comedy on math.
If there’s one beautiful thing in this video it’s not the equation...
It’s his damn handwriting
iuhfiuqwefq
lol
Define beauty for me
..
Tru dat
DuKiP I
DuKiP ikr
I just love this guy's enthusiasm!
ElAshtonio )
666 likes, illuminati confirmed
ElAshtonio All the mess in the universe makes -1
ElAshtonio ikr it hype af
Sandra Norman (
No idea what he's talking about, but clearly loves his work and is sparkling with enthusiasm; which is always nice to see.
It wasn't that hard to understand tho, he explained it concisely.
Dynamic3DLtd I
It was actually pretty simple to understand if u have taken courses in trigonometry, calculus...
SupermarketHobo in America? dont make me laugh
SupermarketHobo okay?
So?
This guy loves maths so much and is so happy it's great
Mathematics is a logical magic.....
If you know the logic,
You can enjoy the magic.
Here's the most beautiful thing I ever discovered:
my girlfriend is like √-100
a perfect ten, but also imaginary
I don't think she understands a thing he is saying.
Funny how everytime he writes he must put his left hand on his hip
He is touching a calculator in his shirt that projects an image inside of his glasses lens.
Joe Hughes i just noticed whhahegdh
joe hughes How fucking your mind is..........
when i dip you dip we dip (i cant load the comments thread to know if someone else said that)
kn00tcn ikr! i thought that only happened to me...
Wish I had a teacher that enthusiastic when I was in school.
Rick Deckard lucky..
Rick Deckard I did, lucky me...
Rick Deckard I do, it's great
Rick Deckard believe me.. U would not like it that much :) XD
Rick Deckard and your teacher kept wishing why aren't my students so enthusiastic
so here I am, stoned af watchin a guy that smiles as he is doing math... what
If you multiply pi, i, and e, you get πie, which spells pie.
I don't know why I wrote this comment.
I wish I loved something as this guy loves maths
I never knew that, that's actually quite fascinating.
My life finally has a meaning.
lol this equation is ridiculous. He just put a complex number under exponential form. Look here it is dude, z= -1
theta of that is pie. Magnitude or modulus(think of it as absolute value) of that is 1. so it gives us 1e^ipie = -1
btw i goes before pie not after but anyways. So e^i*pie + 1 = 0. It's really ridiculous tbh.
Your being sarcastic right 😂😂 indian kids learn this in iit coaching when they're 15 years old wtf😂😂
"e^ipie"
are you sure you know what you're talking about?
eπi=cosπ+isinπ=-1
Like, can we clone this guy's personality and talent and replace the teachers with the copies?
The *e* he draws on the chalkboard at 0:48 is so aesthetically pleasing
He's so ridiculously adorable during this 😂
Bunny Rawr 2:15 she was speechless
Bunny Rawr e^i.pi=cos(180)=-1 thats why when you add 1 is equal to 0
Bunny Rawr he's nerding out so bad. honestly I'm enjoying his reaction to this haha
He's inhumanly excited and I love it
Bunny Rawr ikr
This formula contains mathematical constants derived from arithmetic (0 and 1), geometry (pi), algebra (i), and calculus (e), as well as addition, multiplication, and exponentiation! And it's so concise! You just can't get better than that.
Well, e is often defined as the limit of (1+1/n)^n as n approaches infinity. Also, e is the number whose exponential function (e^x) is its own derivative. Limits and derivatives are perhaps the two most fundamental concepts in calculus.
Tyler Borgard you forgot about trigonometry. That e^ipi=cos pi + isin pi. So the whole equation turns in cos pi (negative 1) +isin pi(which is 0 because of the sin)+ 1 which is exactly 0.
Well, I tend to view trigonometry as a subset of geometry, but that is a good point. Who would have guessed that trigonometric functions could be expressed in terms of exponentials?
Tyler Borgard Forgive me for my lack of skill as far as math is concered, but how exactly does (1 + 0)^infinity become ~2.71 rather than just one?
Not at all saying you're wrong, I'm just curious about how this works.
Well, 1^infinity is what's called an indeterminate form (kind of like 0/0), which means that simple plugging-and-chugging isn't going to help you find the limit. Here's an easy way to see why 1^infinity is indeterminate:
1^1=1
1^10=1
1^100=1
1^1000=1
...
So you'd think 1^infinity would also be 1. However...
2^infinity=infinity
1.5^infinity=infinity
1.1^infinity=infinity
1.01^infinity=infinity
...
I'm using the '=' sign rather loosely here, since infinity isn't technically a number. However, these equations still make sense in the context of limits, so you could argue from them that 1^infinity is actually infinity.
We don't have a clear answer, which means that we must evaluate the limits on a case-by-case basis using other means.
For example, take the limit (2^(1/n))^n as n approaches infinity. This approaches the form (2^0)^infinity=1^infinity, which is indeterminate. But we can still find the limit pretty easily, as follows:
For all positive numbers n, (2^(1/n))^n=2^(1/n*n)=2^1=2. Therefore, the limit is 2 (and not 1).
Now, in our situation, e is defined as the limit of (1+1/n)^n as n approaches infinity. This also approaches the indeterminate form 1^infinity, so we can't evaluate the limit in this way. Now, there's not an easy way to analytically find the limit, since this limit is the very definition of our special number e, but if we evaluate the expression for large enough values of n, we can get a good decimal approximation for e.
(1+1/1)^1=2
(1+1/2)^2=2.25
(1+1/3)^3=2.370370...
(1+1/5)^5=2.48832
(1+1/10)^10=2.593742460...
(1+1/100)^100=2.7048138294...
(1+1/1000)^1000=2.7169239322...
(1+1/10000)^10000=2.7181459268...
(1+1/100000)^100000=2.7182682371...
(1+1/1000000)^1000000=2.7182804691...
As n gets arbitrarily large, this expression gets arbitrarily close to e=2.7182818284...
Never in my life thought I'd be laughing about a math joke
2:48 fakest laugh i've ever seen
I've never seen someone so happy talking about math
Even though I have used Euler's Identity for almost 4 years now (being an engineer), I never really stopped and thought about how one imaginary and two irrational numbers combine perfectly to give -1. The professor's excitement clearly shows his love for math and his appreciation of its beauty. Great video!
I wish i was as happy as him 😂
Joshua Biju just :)
Joshua Biju lolz
Joshua Biju 😂😂😂
i have an equation for that... i want to be happy+all day long= weed
2+2 is 4 minus 1 is 3 quick maths.
Ido Hager your dad is 44
Big Shaq
Ido Hager 😂😂😂
Everyday man's on the block, smoke trees
Lol
When I first saw the thumbnail I thought the equation was actually just +1 = 0
That would be mad.
that equation is so powerful...
im holding back tears
Samovar maker 0
OneEyedSleep boi shut your sensitive ass up
OneEyedSleep nevermind i just cried
You lnow if you order a pizza whichs radius is z and its thickness was A your equasion will be
PI*z*z*A
KAZ ._. unfortunately there's no pizza with thickness equal to A and radius equal to z, that would be very offensive for the pizza people.
Actually that makes no sense.
Great wish he was my maths teacher..
It’s refreshing to see someone with such a passion and excitement for what they do and love!
Most beuatiful eqution in math is
2+2 = 4 - 1 = 3
QUICK MATHZ
Jayden Dabral Must watch Channel Nikhil Nirmal Geometry Theorum of 18°72°90°
Mans not hot
Ting goes skrrraaaa popop kakaka
Skidika pop pop
And a purdrr purr pum
Don't want to but I have to correct you here, it's maff**
everyday man’s on the blok
I love how excited he is to explain maths. the world needs more profs like him 😃
That whole pie is just sitting there the whole time and neither take a bite? WTF man!
his enthusiasm is amazing
Sir you are inspiring me to learn mathematics.
This guy makes me so happy
His happiness and optimism and confidence is inspiring!
He seems so happy explaining that, everyone should love their jobs like this
this is the happiest video i've seen on Math lol
this is how he goes on dates
Jack Mabal haha
Better watch out before he steals all the girls ;)
maybe he has more important or fun (for him, at least) things to do than go on dates?
kave mustermann right! HAHA he's such a cutie
kave mustermann He's intelligent, has a friendly personality and has a passion. He'll have no problem finding dates (as long as he doesn't bring along a blackboard).
Beautiful! I am thankful and feel so blessed to have a son in this school!
Your son is so lucky
Leyla Sharafutdinova pretty sure he's just smart tho
lucky doesn't necessarily mean chance, can also mean fortunate by method of skill or achievement when used in context with the correct expression. so yes, you could say he is lucky.
iLandon what part of that does not make sense
it's money. money gets you everything.
He reminds me of my lecturer, very happy and energetic, every time he introduce something new, he gets very excited of how beautiful it is
He looks and seems so happy and kind :)
- people having him as a teacher must be so great full.
I love how passionate and enthusiastic he is about this! He's doing what he loves!
FYI, this guy is the head coach of math Olympiad team USA. A Chinese American lead a math team with majority Asians beat the Chinese team 2 years in a row. Team USA was champion in 2015 and 2016. Wish them luck in 2017.
*led
He's speakin' cursive.
Nyny 100 huh
here's another beautiful number I discovered myself (idk if anyone already mentioned this in the history of math ever but I haven't done my research at the time that I am writing this, so I will proceed)
142857.
why?
multiplied by two, becomes 285714
by three, 428571
by four, 571428
by five, 714285
by six, 857142
but by seven, becomes 999999
anymore than six, with the exceptions of joining the number 0 to the numbers 1-6 to form a two-digit number (e.g., 10, 20, 30, etc.) and multiplying them to 142857, and the special exception of multiplying seven to it (or 70 or any number of digits starting with 7) will result in one of the digits present in 142857 to be missing.
more rules:
the digits present in 142857 will be present in that order when dividing a number non-divisible by 7 once (meaning it will result in a number with decimals, not a whole number) in the resulting decimals. dividing the number with 142857 in its decimals already by 7 once more will result in not seeing the number 142857.
edit:
okay so I did my research and it turns out this number has been discovered by other people.
if you didn't understand my explanation perhaps this might help:
en.wikipedia.org/wiki/142,857
2:47 "hahaha * I dont get it* hahaha"
dummy
I is not a real number, and Pi is irrational.
Pi is a real number whilst i is rational
Symbol 'i' is the root of -1 which is not a real number and that is why Pi is telling it to "Get Real".
On the other hand, Pi(3.141592654 which can't be expressed in a fraction form) isn't a rational number and that is the reason i telling it to "Be Rational".
xander j. Pi isnt rational.. and i is an imaginary number.. that why pi says "get real" to i and i says get rational
I was so attentive to this guy's passion. I don't love Math, but this guy makes me want to haha
03:27 that laugh when u didn't get the joke
THIS MAN LOVES WHAT HE DOES.
WE need to learn from him
He looks so passionate about math. 😊
Not only is this very cool, but this guy has an enviable amount of energy and appreciation for mathematics.
What i understand from this is just Pie. Which i ate 5 mins ago.
What a hilarious comment!! :-)
Comment of the month. this made me laugh really hard. i wonder which flavour was it
Mohd Afiq. Pie.....aarggghhh
Mohd Afiq sqrt (-1) 2^3 E pi
Mohd Afiq u cant eat pi its irrational & infinite
I was expecting him to use the pie on the table at some point but oh well...
Aryamaan Singh 🤣🤣🤣🤣
There are only 2 types of people in this world: those who love math and those who don't understand its beauty.
GOLD 1515 depends who you get taught by. Have hated maths all my life, but love it this year because of my teacher. My grade jumped up 4 grades
GOLD 1515 So whats the other type?
tallarico I said there are two types. And I named those two types. Read it again.
GOLD 1515 Oh, my math sucks, nevermind
there are only 10 types of people in this world those who understand different numeral systems and those who don't.
I really love how enthusiastic about math he is :)
giving a thumbs up just because of how enthusiastic and happy the guys sounds when describing math
His eyes light up as he talk about math. You can tell this man LOVES what he does.
he is so exited lmao
Excited*
Seán Brennan its passion
This video inspire me ! Not in math by in job. Look at this math teacher when he explained this equation his eyes were bright and shiny. There is no doubt that he like math and enjoy math very much . I hope I can do my job(Linux management) like him. : )
He is so happy
Aaaawww, I love his energy, he's like a little kid trying to show off what he knows
HE'S SO HAPPY
It's so refreshing how excited about this he is, the interviewer tho......
He is so happy, its very nice to see people who are enthusiastic about math because math is important.
I love how much he is excited about tagging this. You know he loves this stuff.
he is SO hyped. I love it.
What a good guy
thanks would you like to have a battle
Johny Cage Wins Must watch Channel Nikhil Nirmal Geometry Theorum of 18°72°90°
These are the kind of math teachers we should all have. He actually enjoys what he's doing!
I wish my math teacher could transfer even a tiny bit of the passion for math this guy radiates on to his students. I don't even understand what's going on in this video but it's much easier to show interest in a topic if it's taught by someone like this
He's so likable. 😂
if any of my professors had this much enthusiasm for what they teach. I would love to be in their class.
You can tell that he has a real passion for mathematics. He was super inspired and excited about this equation, and honestly, who can blame him?
2:04 The happiest person on earth
in 2018 a random guy is having his most intense journey to find his scientific calculator for his exams tomorrow.
I love how happy he looks like :) it makes me smile. He really loves what he does
I've never seen someone so excited in all my life.
I'm in my senior year of highschool and we just learned about exponential function, this is so cool !
me 2
Crush: Impress me
Prof: *does this*
For those of you who are confused, Euler's theorem states that for any real number x
e^(i*x) = cos(x) + i*sin(x), given x in our case = Pi and substituting into this equation we obtain
e^(i*Pi) = cos(Pi) + i*sin(Pi), where cos(Pi) = 1 and sin(Pi)=0, therefore
e^(i*Pi) = -1 + 0*i where 0*i is just 0. Rearranging,
e^(i*Pi) +1 = 0
Is there anybody shows the proof of exist of imaginary number like i？I already checked wiki and youtube and Khal Academy but can't understand it still
Oh ya now i get it..
''cos(Pi)=1...''
My eyes, I'm bleeding !
Bin Wei No, it's an axiom like 1+1 = 2... But 1+1=2 has been proved by Bertrand Russell
It is in radian not degrees.
Edit: I feel I should elaborate more. Radian is another way to measure angles where pi in radian is 180 degrees.
just got this recommended and never saw a guy this happy about math
He spoke with passion so beautifully. It’s rare and motivating.
He is weirdly good at writing on a chalk board.. Such elegance, such grace.
Beautifully explained.
But e should say: "Why did I raise you into such negative numbers?"
His enthusiasm is contagious. He just makes me want to do some complex calculus all night long oh yes
Po-Shen went to my high school and gave our commencement speech. Great guy, he was even nice enough to teach my pre-calculus class for the day.
Man if I ever am half as happy doing anything as this guy's with math I'll know for sure I'm in the right place in life.
i love math but it doesnt loves me back :c