Gerardus 't Hooft, as a doctoral student under the supervision of Martinus Veltman at Utrecht University, proves in 1971 that the electroweak theory of Glashow, Salam, and Weinberg — which unifies electromagnetism and the weak nuclear force — is "renormalizable": that is, that the mathematical infinities appearing when precisely calculating its predictions can be consistently eliminated using rigorous mathematical techniques, just as Feynman, Schwinger, and Tomonaga had achieved two decades earlier for quantum electrodynamics. Before this work, calculations in weak-interaction theory produced physically meaningless infinite probabilities, leaving electroweak theory as a mathematically problematic proposal, incapable of generating precise, verifiable numerical predictions despite its conceptual elegance. The work's immediate origin traces to summer 1970, when 't Hooft, at a physics meeting in Corsica, asked specialists how renormalization ideas should be applied to the new non-abelian gauge theories; the answer he received was "if you're Veltman's student, ask him" — Veltman was recognized as understanding renormalization better than almost anyone, and had also developed his own symbolic-calculation program, Schoonschip (created back in 1963, during a stay at Stanford), one of the earliest computer-algebra systems in history, designed to evaluate the complex field-theory contributions these calculations required. With Schoonschip's help, Veltman verified the partial results 't Hooft was obtaining, and together they developed in detail the complete calculation method. 't Hooft and Veltman also develop calculation techniques — including the dimensional regularization method — that would become standard calculation tools throughout later theoretical particle physics. The proof of renormalizability transforms electroweak theory from a speculative proposal into a rigorous predictive framework, providing the solid mathematical foundations on which the Standard Model of particle physics would be built, and allowing precise calculation of the expected masses and properties of the W and Z bosons, which Rubbia and van der Meer would confirm experimentally at CERN a decade later, as well as, later still, the mass of the top quark, directly observed in 1995. For this work, 't Hooft and Veltman receive the 1999 Nobel Prize in Physics "for elucidating the quantum structure of electroweak interactions".