Freeman Dyson, a young doctoral student at Cornell who knows Richard Feynman's work (his teacher) firsthand and has also followed the advances of Julian Schwinger and Sin-Itiro Tomonaga, observes that the three physicists have arrived at versions of quantum electrodynamics (QED) that seem completely different from one another: Feynman works with intuitive diagrams and path integrals, Schwinger with a rigorous but technically complex operational method, and Tomonaga with a covariant approach developed in isolation in Japan during the war. In "The Radiation Theories of Tomonaga, Schwinger, and Feynman" (Physical Review, 1949), Dyson shows that the three formulations are mathematically equivalent — they solve the same physical problem in different languages — and, beyond that demonstration, takes the theory a step further: he proves that the mathematical infinities appearing in QED calculations can be systematically eliminated at any order of perturbation theory, not just the first orders Schwinger and Tomonaga had treated, via renormalization of the electron's observed charge and mass. In the process, Dyson develops an elegant mathematical method based on the S-matrix (the so-called "Dyson series"), which would become a basic tool not only for QED but for more general field theories and for the quantum many-body problem in condensed-matter physics. Dyson's work is decisive for the physics community to fully accept and understand Feynman's diagrammatic approach, then still little known and poorly understood outside a small circle. For the original work on QED, Tomonaga, Schwinger, and Feynman received the 1965 Nobel Prize in Physics; Dyson, despite the recognized importance of his unifying contribution and the general proof of renormalizability, was not included in that prize — he would instead receive the Wolf Prize in Physics in 1981, together with his later work on the stability of matter.