Phys. Rev. Lett. (in the press); preprint at http://arxiv.org/abs/1608.03679
More than one hundred years ago, German mathematician Bernhard Riemann proposed a conjecture about the nontrivial zeroes of the Riemann zeta function: they all lie on a line in the complex plane that has a real part of 1/2. The Riemann hypothesis, as it's known, features on the list of 23 unsolved problems that David Hilbert published in 1900. Proving it would turn hundreds of mathematical statements into bona fide theorems — but a rigorous proof is still missing.
Carl Bender and colleagues have paved the way to a possible solution by exploiting a connection with physics. The Hilbert–Pólya conjecture supposes the existence of a Hamiltonian whose eigenvalues correspond to the imaginary parts of the nontrivial zeroes of the zeta function. Bender et al. constructed an operator that plays the role of this Hamiltonian. And with further analysis of the properties of this Hamiltonian, physics may yet shed light on the Riemann hypothesis, bringing new insights into this century-old mathematical problem.
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Li, Y. Heroes of zeroes. Nature Phys 13, 321 (2017). https://doi.org/10.1038/nphys4099