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The conjecture (Montgomery's pair correlation conjecture, extended by Odlyzko and others) that the spacing and correlation statistics of the non-trivial zeros of the Riemann zeta function coincide with those of eigenvalues of large random Hermitian matrices from the Gaussian unitary ensemble (GUE). Claims about the conjecture's statement, evidence, numerical verification, refinements, and related

The spacing statistics of the zeros of the Riemann zeta function match those of eigenvalues of random Hermitian matrices.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Number theory Random matrix theoryimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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