Short answers, pulled from the story.
Eugene Wigner 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. He shared the prize that year with Maria Goeppert-Mayer and J. Hans D. Jensen.
Wigner led a team at the Metallurgical Laboratory whose task was to design nuclear reactors to convert uranium into weapons-grade plutonium. In July 1942 he chose a conservative 100-megawatt design using a graphite moderator and water cooling. He was present on the 2nd of December 1942 when Chicago Pile One achieved the world's first controlled nuclear chain reaction beneath the stands at the University of Chicago's Stagg Field.
The Wigner effect is the swelling of a graphite moderator caused by the displacement of atoms through neutron radiation. It caused serious problems for the reactors at the Hanford Site after World War II, forcing production cutbacks and shutting down at least one reactor. It was eventually overcome through controlled heating and annealing.
The Wigner's Friend paradox is a thought experiment Wigner developed to illustrate the role of consciousness in quantum measurement. A friend inside a sealed laboratory performs a quantum measurement while Wigner, observing from outside, treats the friend and experiment as a combined quantum system, producing two seemingly incompatible descriptions. Wigner used the paradox to argue that consciousness is foundational to the quantum mechanical measurement process.
Published in 1960, the article argued that mathematics repeatedly describes physical reality with precision that seems impossible to explain - what Wigner called an 'unreasonable' coincidence. He suggested biology and cognition could be the deeper origin of physical concepts as humans perceive them. The paper prompted responses from researchers in computer science, molecular biology, data mining, physics, mathematics, and economics.
On the 2nd of August 1939, Wigner drove with Leó Szilárd to Albert Einstein's summer rental on Long Island to discuss nuclear fission. The meeting produced the Einstein-Szilárd letter to President Franklin D. Roosevelt, which warned that an atomic bomb was feasible and that Germany might be pursuing one. Roosevelt responded by authorizing the Advisory Committee on Uranium, the precursor to the Manhattan Project.