>>11425393>>11425572>>11427504>>11427644>>11427661Dyson was a great physicist, universally recognized, and Weinberg said he was "fleeced" of the 1965 Nobel prize. His great work on electrodynamics explained the importance of operator dimensions, and he sketched the main reason for renormalizability--- that operators of dimensional analysis dimension 4 are special. This idea is central to modern renormalization theory, and it wasn't there in Feynman or Schwinger.
His dimensionality argument was criticized as insufficiently rigorous, because of the problem of "overlapping divergences", but this problem is superficial--- the overlapping divergences are really separate divergences as was understood in the 1950s by Zimmermann (but alas, nobody understood Zimmermann!), and later in a more transparent way by Wilson in the 1970s, further elaborated by Polchinsky in the 1980s. In mathematics, Zimmermann's ideas transmuted into the Connes Kreimer idea of using Hopf-algebras of point-collisions to organize the perturbation expansion renormalization, but the upshot of all that development is simply that Dyson had the right idea, the operator dimensions are sufficient to establish renormalizability.
Dyson did many other things, in engineering, like Orion, and just general nice thinking, like his ideas about origins of life, floating cities, and various mathematical things like his argument for the divergence of the perturbation series. But I think his immortal contribution was his extension of Wigner's Random Matrix theory into a real mathematical theory. This is where I think he was fleeced: of the 1963 Nobel prize, not the 1965 one, because Random Matrix theory is a much more distinctive unique contribution than the QED stuff, which, great as it was, would have been done by other people much the same way anyway.
