Which is the most beautiful equation?

The most often cited beautiful equation among mathematicians is Euler's identity, ( e^{i\pi} + 1 = 0 ). Edward Frenkel and Keith Devlin both highlight its elegance and the surprising connection it unveils between fundamental constants like ( e ), ( \pi ), ( i ), ( 1 ), and ( 0 ). This equation ties together distinct areas of mathematics—exponential functions, geometry, and complex numbers—into a simple and profound identity.

Edward Frenkel admires Euler's identity for its element of surprise and inherent simplicity. He points out how different constants are harmonized in a way that is both unexpected and elegant 1 .

Keith Devlin also emphasizes this equation's beauty, noting its artistic quality and the deeper insights it provides into the connectivity within the mathematical structure 2 3 .

Overall, Euler's identity is often celebrated for its simplicity and profound implications, universally recognized among mathematicians as exemplary of mathematical beauty.