Richard Feynman, at Cornell, Julian Schwinger, at Harvard, and Sin-Itiro Tomonaga, at the University of Tokyo and isolated by the consequences of World War II, independently develop between 1947 and 1949 three mathematically equivalent formulations of quantum electrodynamics (QED), the theory describing the interaction between light and matter with extraordinary precision. The original quantum theory of the 1920s and 1930s produced, when rigorously applied to certain calculations, infinite and physically meaningless results — a problem known as ultraviolet divergences that threatened the coherence of all quantum field theory. The three physicists solve the problem through the technique of "renormalization", which mathematically absorbs those infinities by reabsorbing them into the definition of the electron's mass and charge, producing finite predictions that match experiment to ten decimal places of precision — among the most accurate predictions ever verified in all of physics. Feynman also develops a graphical method, Feynman diagrams, which visually represents interactions between particles as lines and vertices, becoming a universal calculation and teaching tool in particle physics. Tomonaga had completed his work in isolation in Japan during the war, without access to Western scientific publications, and his chronological priority is only fully recognized once his results reach the United States after the end of the conflict.