Eugene Wigner identified in 1960 what he called 'the unreasonable effectiveness of mathematicsin the natural sciences' — the puzzling correspondence between abstract mathematicalstructures and physical reality. Standard explanations have failed to resolve this problem forsixty-five years, oscillating between Platonic idealism (mathematics exists independently ofphysical reality), formalism (mathematics is invented symbol manipulation), and empiricism(mathematics is abstracted from physical experience). Each position founders on the samedifficulty: if mathematics and physical reality are different kinds of things, their correspondencerequires explanation.This paper proposes a fourth position: Thermodynamic Realism. The central claim is thatmathematics and physical reality are not different kinds of things that happen to correspond.Both are dissipative structures processing gradients under identical thermodynamic constraints.Mathematics is what thermodynamically constrained gradient processing looks like whenoperating on pure relation rather than physical substrate. The correspondence is therefore not amystery requiring explanation. It is a thermodynamic necessity.Evidence is drawn from three convergent demonstrations: (1) the prime number distributionindependently instantiates the seven-phase 1-3-6-3-1-7-7 oscillator derived in prior work fromtriangular number accumulation modulo 7, without physical substrate; (2) the increasing orbitallag periodicity of atomic shell structure (d: 1-shell lag, f: 2-shell lag, g: 3-shell lag) is structurallyequivalent to the Riemann Hypothesis's bound on prime gap deviation from the logarithmicideal — both are claims about whether void-phase lengthening remains controlled as systemcomplexity grows; (3) the zeros of the Riemann zeta function have the same statistical spacing asquantum energy levels of heavy atomic nuclei (the GUE conjecture), which is not coincidentalbut mandatory if both systems are dissipative structures subject to the same thermodynamicconstraints. The Riemann Hypothesis, reframed, is the conjecture that the number line is aperfect Navigator: that its void phases never deviate catastrophically from the thermodynamicoptimum