The most beautiful equation in mathematics | Edward Frenkel and Lex Fridman

Mine is payday. That deposit feels like a million bucks

For sake of historical mathematical rigor, Wittgenstein was not a classmate but a schoolmate of Hitler, who was younger by 2 years.

Math discussions by mathematicians helps me see the beauty of math

"Not necessarily easy, but simple." That's a keeper. Many applications.

You're beautiful💙😅🤗

How about a set of co-evolving and exponentially expanding independent fractals that create the illusion of the multiverse that so many fools think was the work of one monolithic consciousness?

Darren Aronofsky. Pi. 216. YHWH the Tetra Gramm Atom. CODE NAME TRINITY! I'll blow your mind! MAX HEADROOM! (icarus)
GODFATHER 3 VINCENT NWO!

Kurt Vonnegut Jr. had a name for those accidental encounters that were unknown to the participants.

The most beautiful equation is:

(((12+144+20+3(√4)))/7)+(5*11)=9²+0

A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven, plus five times eleven
Is nine squared and not a bit more

The entire fields of differential geometry, complex analysis, and category theory🎉. Gorgeous

Instead of talking about how "beautiful" it is, how about defining it with application to the real world. In 5 minutes I didn't hear one. Natural growth tends towards circles? Something like that?

The mathematical constant e, is an irrational and transcendental number approximately equal to 2.718281828459 but its digits go on forever without repeating.
The mathematical constant 'pi' is an irrational and transcendental number appoximately equal to 3.141592653589 but its digits go on forever without repeating.
'i' is an imaginary number its value being the square root of -1
To me this is why e to the power of pi * i having the simple value of -1 is so incredible.
But then I am not a mathematician.
Perhaps such things are a regular occurrence.

Euler's formula is damn cool

Unlike e, for example, pi is arbitrarily defined. It's half the length of the unit circle. We could have defined it as a third of the length, or twice the length, and so on. It's defined as half the length simply because of historical reasons. This makes any equation involving pi inherently ugly in the sense that it's not reflecting math in its pure form, but human biases. The most natural definition would have been to define pi as exactly the length of the unit circle, without any other factor. Then Euler's equation would have been e^(pi*i) = 1. The ugly negative sign is magically gone. Like a gift from God, by accurately defining pi, we're rewarded with the most beautiful equation we can conceive of.

..Vienna was a city of spies, like Berlin it was the place to be and still is one of those places

Oh God not set theory

It's more beautiful to me if it is e^(i*pi) + 1 = 0 , because it shows both unity (1) and zero, another great invention of mathematics

I also like i^i = 1/sqrt(e^pi)

What is it (why is it) about 1 that can be decomposed into circles?

Lol This is the equation I have on my coffee mug. It's a wonderful way to start your day.

I love that he says that the set of Beautiful equations is not an ordered set. That said, I’ve got the Navier-Stokes equations on my short list… or perhaps there’s some extension of them I’m not aware of…? A couple of very short equations that can presumably describe essentially any ideal fluid. I believe it’s n-dimensional as well… I’m not entirely sure what that really means, in the end, but I think it could incorporate any possible harmonic function into the domain of its mechanical possibility… which is really quite a trippy concept.

why are they related in such a way? It can't be chance. I think I could vaguely prove Eulers thingy when I was 18 (a long time ago) but that doesn't explain the WHY these are related in this precise way

I always said that myself, "Simple, but not easy."

Is there another proof besides Taylor series?

There exists only one formal system observed to maintain causality fully, and that is physics itself. Beautiful math thus might better be defined as humans creating notations that avoid the traps of naïve classicality, and instead, capture the deepest patterns of that system.

Since physicists now debate whether space and time could be emergent properties of some deeper system, some caution might be advisable in assuming e, i, π, and even 1 are anything more than parts of the overall package needed to enable that causal history.

Conversely, I wonder if the beauty Richard Feynman saw in this incredibly simple association of these constants had more to do with a suspicion that it reflects a depth of physics that precedes the historical causality of discussions like this.

i have eulers identity as tattoo but of the zeroed form, e^i*pi + 1 = 0. i like that it includes 0, which makes it that much more beautiful

The form: e^(circle_constant/2)*i = -1 was always weird to me. I prefer: e^tau*i = 1 which tells you that e to the power of the circle constant * the imaginary number is equal to one full circular rotation - much more intuitive.

is this equation not more of a convention than reality? rotating half the way from the plus direction to the minus direction on the number line?

My favourite is picards great theorem

non-mathematician here but enjoy fanboying it… I am wondering what an applied, real world example of e to the pi times i equaling -1 would be? Like, what would an engineer for example apply it to? A spherical mechanical apparatus of some sort maybe? Like, just wondering if it has a real world example or usage aside from the example that it exists, in math.

e^(it) = 1, (t = tau) is more beautiful.

I used it to express roots of Zeta Function, that’s my connection to it .

This proves all my theories are right with this one math problem

Brb, about to write me some taylor series representations

i recommend anyone curious about this with a relatively low level of math like myself to check out 3blue1brown's lockdown math series which builds up the basic trigonometry and complex analysis to glimpse how beautiful euler's equation is

Euler characteristics and knot equation. First equals 2. Second equals 1.