What is the deepest statement that you’ve ever read? For me:
e^(pi*i)+1=0 - I have no idea what it means, and I’m pretty sure no one else does, either, but it is the most profound thing that I have ever seen in my life.

i'm - descartes

The four-color theorem
>given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color

>>17810503 (OP)
It is kind of obvious that five fundamental numbers would have to be related in some way though, lol.

>>17812135
How do?

>>17812135
Kinda meaningless statement. It's one thing to be related and another in such a deep way: the complex exponential function is essentially a combination of a rotation and the real exp

"America is a Nation that can be defined in a single word...Iwuzindfutmhmafut... Excuse me...the foothills of the Himalayas"

"Life is full of shit, and you are full of life"

>>17810503 (OP)
It can be made somewhat intuitive if you know that multiplying two complex numbers results in their angles being added and their lengths being multiplied.

So if you want a complex number of length 1 with a certain angle θ, you can, with a bit of handwaving, get to it by multiplying (1 + iθ/∞), or 1 plus an infinitesimal imaginary fraction of your desired angle, infinitely many times. So that would look like (1 + iθ/∞)^∞. And what's the limit definition of e^x? Well, for simplicity, if you just replace the numbers approaching infinity with infinity symbols, it would be (1+ x/∞)^∞. So the previous formula is actually just e^(iθ). And if you rotate 1 by an angle of π (or 180°) through the complex plane, you end up on the on the opposite side at -1. So e^(iπ) = -1. Hope that maybe helps a little.