He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations". Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it". He concludes his paper with the same question with which he began: The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. Later, Hilary Putnam explained these "two miracles" as being necessary consequences of a realist but not Platonist view of the philosophy of mathematics.

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He had an older sister, Bertha, known as Biri, and a younger sister Margit, known as Manci, [2] who later married British theoretical physicist Paul Dirac. During this period, Wigner developed an interest in mathematical problems. His parents sent him to live for six weeks in a sanatorium in the Austrian mountains, before the doctors concluded that the diagnosis was mistaken.

Religious education was compulsory, and he attended classes in Judaism taught by a rabbi. Weissenberg wanted someone to assist him with his work on x-ray crystallography , and Polanyi had recommended Wigner. Wigner nonetheless studied independently. The latter had written a standard text, Group Theory and Quantum Mechanics , but it was not easy to understand, especially for younger physicists.

The plus sign on the nodes indicates an anticlockwise reading of its surrounding lines. Due to its symmetries, there are many ways in which the diagram can be drawn. An equivalent configuration can be created by taking its mirror image and thus changing the pluses to minuses. In these works, Wigner laid the foundation for the theory of symmetries in quantum mechanics.

The theorem specifies how physical symmetries such as rotations, translations, and CPT symmetry are represented on the Hilbert space of states.

According to the theorem, any symmetry transformation is represented by a linear and unitary or antilinear and antiunitary transformation of Hilbert space. The representation of a symmetry group on a Hilbert space is either an ordinary representation or a projective representation. By , his papers were drawing notice in the world of physics. In , Princeton University recruited Wigner for a one-year lectureship, at 7 times the salary that he had been drawing in Europe.

Princeton recruited von Neumann at the same time. They anglicized their first names to "Eugene" and "John", respectively. The Technische Hochschule responded with a teaching assignment for the other half of the year. This was very timely, since the Nazis soon rose to power in Germany.

There he met his first wife, Amelia Frank, who was a physics student there. However she died unexpectedly in , leaving Wigner distraught. He therefore accepted a offer from Princeton to return there. Roosevelt to initiate the Manhattan Project to develop atomic bombs.

They remained married until her death in November At the time, reactors existed only on paper, and no reactor had yet gone critical. In July , Wigner chose a conservative MW design, with a graphite neutron moderator and water cooling. It was signed by the participants. Wigner was disappointed that DuPont was given responsibility for the detailed design of the reactors, not just their construction.

He threatened to resign in February , but was talked out of it by the head of the Metallurgical Laboratory , Arthur Compton , who sent him on vacation instead. As it turned out, a design decision by DuPont to give the reactor additional load tubes for more uranium saved the project when neutron poisoning became a problem. This is a swelling of the graphite moderator caused by the displacement of atoms by neutron radiation. Because he did not want to be involved in administrative duties, he became co-director of the laboratory, with James Lum handling the administrative chores as executive director.

Groves, Jr. In , he published a now classic article on the philosophy of mathematics and of physics, which has become his best-known work outside technical mathematics and physics, " The Unreasonable Effectiveness of Mathematics in the Natural Sciences ". Hans D. Wigner with Andrew Szanton. In it, 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. New York: Academic Press. Translation by J. Indiana University Press, Bloomington.

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## The Unreasonable Effectiveness of Mathematics in the Natural Sciences

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## Eugene Wigner

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