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 Most beautiful math result?
 Posted 2020-08-28, 01:39 PM What is the most beautiful math result in your opinion?* *Can't be $\reverse e^{i \pi}+1 = 0$ Personally, I usually like approaches that allow you to solve a problem in an indirect way. My favorite result is probably the uniqueness of the Poisson equation (I don't see why this wouldn't hold for other differential equations too, but as a physics guy this is the area I saw it applied so I'm just going with that) as it allows for the method of images. I don't think there is any other result which when I first saw applied made me go WTF. For similar reasons, I think the residue theorem is quite cool too. Who would have thought that to solve real integrals you would need to move off the real line and look for singularities elsewhere. I mean, it's quite amazing if you think about how that must have developed historically. An unrelated result which I quite like, which you introduced me to Chruser, are the Borwein integrals.
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Demosthenes

 Posted 2020-09-16, 09:16 AM in reply to Demosthenes's post "Most beautiful math result?" $\reverse \sum_{n=1}^{\infty} n*-1^{n + 1} = -1/12$ Last edited by Asamin; 2020-09-16 at 09:35 AM.
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 Asamin

Posted 2020-11-01, 10:47 PM in reply to Demosthenes's post "Most beautiful math result?"
This means nothing in reality.

Quote:
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D3V

Posted 2020-11-02, 09:43 AM in reply to D3V's post starting "This means nothing in reality."
D3V said: [Goto]
 This means nothing in reality.
What means nothing in reality?
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Demosthenes

 Posted 2020-11-13, 03:28 PM in reply to Demosthenes's post "Most beautiful math result?" Sorry for the late response. I've been busy breaking math (more on that in a while). Anyway, I don't think I could pick a single #1 result in terms of beauty, so here are a few different ones. 1: Tartaglia's solution of the cubic equation. The first demonstration of modern(ish) man doing something mathematically significant that the ancients could not. This opened the floodgates for future discoveries. 2: Great Picard's theorem. It proves that $\reverse e^{1/z}$ is infinitely HBTQ-inclusive around the origin, with the exception of at most one gender (the null gender?) (Genders are complex, right?) 3: Let P(d) be the probability that a random walk on a d-dimensional lattice returns to the origin. Pólya proved that P(1) = P(2) = 1, but P(d) < 1 for d > 2. Oh yeah, and Obviously. Probably Kuratowski's theorem as well (it has some nice generalizations to surfaces with holes), along with various results on the classical Hopf fibration, monstrous moonshine, and the Riemann zeta function. "Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
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Chruser

 Posted 2020-11-13, 05:36 PM in reply to Chruser's post starting "Sorry for the late response. I've been..." If we’re being honest, most beautiful of all is A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+ A+A+A+A+A+A+A+A+A+A+A+A+A+A+A=4.0
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WetWired

Posted 2020-11-13, 09:05 PM in reply to WetWired's post starting "If we’re being honest, most beautiful..."
WetWired said: [Goto]
 If we’re being honest, most beautiful of all is A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+A+ A+A+A+A+A+A+A+A+A+A+A+A+A+A+A=4.0
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram
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Chruser

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