I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed me.Wigner was born in 1902 and probably did not even meet Einstein until the 1930s. Those two "greatest inventions" were in 1905 and 1915. Wigner is famous for his contributions to quantum mechanics, which Einstein never appreciated. Einstein never accomplished anything after about 1920.
... But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jansci's brilliance, he never produced anything as original.
I would take Wigner seriously if he had some first-hand experience of Einstein's originality. Instead, Wigner is only crediting Einstein for originality that was reported in textbooks. As I explain in How Einstein Ruined Physics, very little of relativity was original to Einstein. Special relativity was due to Maxwell, FitzGerald, Lorentz, Poincare, and Minkowski. General relativity was due to Poincare, Grossmann, Hilbert, and Schwarzschild, with cosmological applications done by others. For more info, see Relativity priority dispute.
John von Neumann did invent ordinals (for use in axiomatic set theory), the Hilbert space formulation of quantum mechanics, operator algebras, game theory, and computers (for use in numerical simulations). A recent WSJ review of Turing's Cathedral: The Origins of the Digital Universe says:
The mathematician John von Neumann, born Neumann Janos in Budapest in 1903, was incomparably intelligent, so bright that, the Nobel Prize-winning physicist Eugene Wigner would say, "only he was fully awake." One night in early 1945, von Neumann woke up and told his wife, Klari, that "what we are creating now is a monster whose influence is going to change history, provided there is any history left. Yet it would be impossible not to see it through." Von Neumann was creating one of the first computers, in order to build nuclear weapons. But, Klari said, it was the computers that scared him the most.After von Neumann died, his Princeton IAS employer shut down the project and resolved to never do anything so practical again.
Update: Steve Hsu is another von Neumann fan.