Wait! There’s an improved version:
Also, for the calculus-savvy, you’ll prefer this one:
Home page:
The enigmatic equation e^{pi i} = -1 is usually explained using Taylor’s formula during a calculus class. This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns one action into another.
For more information on viewing exponential functions in this new light, check out this article:
Music: “Wyoming 307” by Time For Three,
source
This video is not exactly my proudest work, I have since made an improved version of this video, giving some of the surrounding context and presenting things at a more reasonable pace. Check it out here: https://youtu.be/mvmuCPvRoWQ
(Edit 2 years later): And now yet another! If you're comfortable with calculus, I think this 3.14-minute explanation is the best way to understand it: https://youtu.be/v0YEaeIClKY
2026
Hey man! the video is pretty good!
Peu importe qu'il y ait une nouvelle version je suis tellement fan que j'ai décidé de toutes les regarder par ordre chronologique. Je ne comprends pas tout? Tant mieux le voyage a son lot de mystère et d'abstraction et c'est ça que l'on aime! Merci ❤
Beautiful video and gorgeous backgroud Irish music.
Welp time to watch this channel from beginning and be math expert
ah i see. incomplete-feeling at the end
This video helped me so much.
Before, I was really confused, and now I'm still very confused
I can see why this video has been disowned a bit compared to later videos, but it also contains by far the most sensible explanation of complex arithmetics I've seen yet
I try this on computer but it show me 23.140692632779263
The first video of a cool math person
School: These are numbers
Students: what are these numbers? why do they exist?
High-school: it helps you to count though
3b1b: number are the word of nature's mind.
Leaving me comment here on your first video hoping one day my channel gets as big as you❤
I don't understand it entirely, but to me, this is poetry.
I'm gonna do a rewatch of the whole channel in 2026!
His videos have mathematical topics that I would understand if the English spoken weren't so complex..
If anybody see this who can know this plz.explain i didn't understand anything?
3 years ago, I watched this clip without understand even a single instance 😅
Now I've learnt Cal 1, and I still cannot understand all of it 😂
Btw, great stuff
Where a legend was born 0:00
It's 2025 ❤❤
4:20 -> including the rotation action made it make sense.
From an engineering background, I "understood" it as just that raising something to an imaginary exponent is "exponential growth" but in a perpendicular direction, which is just rotation.
This didn't help. Need more examples of sliding and stretching of numberlines
A mathematician YouTuber was born
WTF since 10 years his all videos are legit
3:22 Finally found him use the Python walrus operator successfully
Wow!
pls make this vedio in hindi..❤
My calculator say undefined. I know better
thank you
does anyone know where the video at 5:53 can be found?
This video was so good that I accidentally clicked the like button 🔥
This reminds me of my thinking in trigonometry class that a real number can represent both how much a point spin and how far a point can go. For example, you could say you spin for a pi value(180 degrees) or you could also say i move pi value(~ 3.14), generally it sounds the same but depends on the frame of reference it gets a different meaning. This also applies to complex plane.
From the video I understand that: pi i means going on i axis pi value, and if you want pi i on the spinning frame of reference you will limit -pi i -> pi i and rotating by pi value will drive i axis to the other side of it. So in total the effect of pi in e^i is -1, because i axis rotated pi is -i, which means -1 x i, Im feeling like this is the same as real plane
its weird to not see the pi guys hanging around
Ok, so this is where I start. I'm going to finish this game by watching all of your videos
this is where it all started…
e^(pi times I)=-1
e^(pi) + e ^i=-1
-1-e^pi=e^i
e^i=????
This literally feels like nonsense, I didn't Understand a thing
I'm gonna fail my math exam
I got it!!!
am coming here to start my learning on Mathematics. Going to be a rough ride,,but I hope this will convince me enough to get a maths degree