Physical and mathematical systems have spectra — sequences like bar codes representing data such as atom energy levels, Riemann ζ function zeros, bus departure times etc. The spectra of such complex, correlated systems exhibit a precise balance of randomness and regularity known as universality. This fine balance also appears in a purely mathematical setting: It defines the spacing between the eigenvalues of random matrices — ie vast matrices filled with random numbers. It's about time to discover such a matrix underlying the ζ zeros and therefore the distribution of the primes!
In Mysterious Pattern, Math and Nature Converge | Quanta Magazine
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