He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". Some contemporaries referred to Wigner as the Silent Genius and some even considered him the intellectual equal to Albert Einstein, though without his prominence. Wigner is important for having laid the foundation for the theory of symmetries in quantum mechanics as well as for his research into atomic nuclei, and for his several theorems.
In 1921, Wigner studied chemical engineering at the Technische Hochschule in Berlin (today the Technische Universität Berlin). He also attended the Wednesday afternoon colloquia of the German Physical Society. These colloquia featured such luminaries as Max Planck, Max von Laue, Rudolf Ladenburg, Werner Heisenberg, Walther Nernst, Wolfgang Pauli, and Albert Einstein. Wigner also met physicist Leó Szilárd, who at once became Wigner's closest friend. A third experience in Berlin was formative. Wigner worked at the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry (now Fritz Haber Institute), and there met Michael Polanyi, who became, after László Rátz, Wigner's greatest teacher.
In 1936, Princeton did not rehire Wigner, so he moved to the University of Wisconsin-Madison. There he met his first wife, a physics student named Amelia Frank. She died in 1937, leaving Wigner distraught. On January 8, 1937, Wigner became a naturalized citizen of the United States. Princeton University shortly invited Wigner back, and he rejoined its faculty in the fall of 1938. Though a professed political amateur, in 1939 and 1940 Wigner played a major role in agitating for the Manhattan Project, which developed the first atomic bomb. However, he was by personal preference a pacifist. He later contributed to civil defense in the U.S. In 1946, Wigner accepted a job as director of research and development at Clinton Laboratory (now Oak Ridge National Laboratory) in Oak Ridge, Tennessee. When this did not work out especially well, Wigner returned to Princeton.
In 1941 Wigner married his second wife, Professor Mary Annette Wheeler, of Vassar College. Professor Wheeler was also a physicist, with a Ph.D. from Yale in 1932. They were married until her death in 1977 and had two children.
In a 1987 appreciation of Professor Wigner, Alvin M. Weinberg stated: "…this trait of Wigner’s [giving credit to his young collaborators] explains why so much, not only of reactor theory but of theoretical physics from 1930 to 1965 — though it may not bear Wigner’s name — actually has origin in a suggestion made or question asked by Professor Wigner."
In 1960, Wigner gave a thought-provoking insight into the power of mathematics in his best-known essay outside physics, now a classic paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. He argued that biology and cognition could be the origin of physical concepts, as we humans perceive them, and that the happy coincidence that mathematics and physics were so well matched, seemed to be "unreasonable" and hard to explain. Even so, he found resistance to this theory, notably by distinguished mathematician Andrew M. Gleason. In 1963, Wigner received the Nobel Prize in Physics. He professed never to have even considered the possibility that this might occur, and added: "I never expected to get my name in the newspapers without doing something wicked." He later won the Enrico Fermi award, and the National Medal of Science. In 1992, at the age of 90, he published a memoir, The Recollections of Eugene P. Wigner with Andrew Szanton. Wigner died three years later in Princeton. One of his significant students was Abner Shimony.
Wigner was asked in the late 1970s "Do you remember Rátz?" (one of his early teachers). He answered: "There he is!" and pointed to a picture of Rátz on his office wall.
His third wife was Patricia Hamilton Wigner, widow of another physicist, Donald Ross Hamilton, retired Dean of the Graduate School at Princeton University who passed away in 1971.
Near the end of his life his thought turned more philosophical. In his memoir, Wigner said: "The full meaning of life, the collective meaning of all human desires, is fundamentally a mystery beyond our grasp. As a young man, I chafed at this state of affairs. But by now I have made peace with it. I even feel a certain honor to be associated with such a mystery." He became interested in the Vedanta philosophy of Hinduism, particularly its ideas of the universe as an all pervading consciousness In his collection of essays Symmetries and Reflections - Scientific Essays, he commented "It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness."
Wigner also conceived the Wigner's friend thought experiment, which is an extension of the Schrödinger's cat thought experiment. The Wigner's friend experiment asks the question: at what stage does a "measurement" take place? Wigner designed the experiment to highlight how he believed consciousness is necessary to the quantum mechanical measurement process.
Wigner was a committee chairman at Unification Church founder Sun Myung Moon's annual International Conference on the Unity of the Sciences (ICUS) for several years. At the 11th ICUS conference in Philadelphia, he was given the Founder's Award "for his outstanding contributions to science.