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Squark comments on [Open Thread] Stupid Questions (2014-02-17) - Less Wrong
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Which are the most beautiful mathematical or physical equations?
I am interested in the elegance of the equation itself (not its visualization, e.g. the Mandelbrot set). Yeah, I know that there is a difference in opinions, but I hope there will be some correlation among experts. I would like to have, let's say, 5 candidates.
This is a specific example, and a very good candidate, IMHO:
e^(i π) + 1 = 0
I would like to have about 5 equations, not just one, so even if you agree with my choice, please post even the equations that seem a bit less impressive, but they still have some kind of beauty in them.
Okay, just to give you another anchor, this one is nice too, but much more simple:
a^2 - b^2 = (a + b).(a - b)
Off the top of my head:
Physics:
Einstein-Hilbert action:
Expectation values using Feynman's path integral:
Yang-Mills Lagrangian:
Deformation quantization (not sure what's the proper name for this, maybe Dirac's rule):
Fundumental thermodynamic relation:
Mathematics:
Stokes' theorem:
Riemann's functional equation:
L'Hopital's rule:
Taylor's series:
Lefschetz-Hopf theorem (unfortunatelly couldn't find one image of both sides of the equation):
Thank you!!!