Mathematics Is Not Physics: Experiment Decides Models, Proof Certifies Routes

Experimental tests and mathematical proofs answer different questions. This paper uses Yang–Mills theory to illustrate the distinction. The discovery of the \(W\) and \(Z\) bosons, precision measurements at LEP and SLC, and QCD tests of asymptotic freedom and lattice predictions support the use of Yang–Mills dynamics in the Standard Model. The Clay problem asks a separate question. A rigorous construction of four-dimensional pure quantum Yang–Mills theory with a positive mass gap remains open. The moving-electron debate of 1903–1908 offers a historical parallel. Early beta-ray measurements appeared to favor Abraham’s rigid-electron model, while later measurements favored the Lorentz–Einstein account. The paper applies the author’s independently developed Scretching–Planck (SP) density–phase reformulation to established observables in quantum mechanics, QED, and the gauge sectors. It identifies the inputs used, reports discrepancies, and records a blind prediction for true muonium. The proposed uniform gap bound, Conjecture C, remains open. For students, the distinction is practical. When evaluating a theory, ask which predictions survive comparison with measurements and which conclusions follow rigorously from its assumptions.