Random Matrix UniversalityFill a grid with random numbers, mirrored so it's symmetric, and ask where its eigenvalues land. Not randomly — they pile up into a smooth dome (the semicircle) and actively avoid sitting close together. Astonishingly the same dome and the same "spacing repulsion" show up for chaotic nuclei, chaotic drums, and even the zeros of the Riemann zeta function.Wigner modeled nuclear energy levels with random matrices in 1955, guessing their spacing statistics would be universal regardless of the messy details underneath. The semicircle law and level repulsion he found later turned up in chaotic quantum billiards, and in the spacing of nontrivial zeta zeros — the Montgomery–Odlyzko law — a still not fully understood bridge between random matrices, quantum chaos and prime numbers.