Born in the Austrian capital of Vienna, Pauli was the son of a professor of physical chemistry at the university there and the godson of Ernst Mach. He was educated at the University of Munich, where he obtained his PhD in 1922. After further study in Copenhagen with Niels Bohr and at Göttingen with Max Born, Pauli taught at Heidelberg before accepting the professorship of physics at the Federal Institute of Technology, Zurich. Apart from the war years, which he spent working in America at the Institute of Advanced Studies, Princeton, he remained there until his early death in 1958.

Pauli was a physicist much respected by his colleagues for his deep insight into the newly emerging quantum theory. His initial reputation was made in relativity theory with his publication in 1921 of his Relativitätstheorie (Theory of Relativity). His name is mainly linked with two substantial achievements. The first, formulated in 1924, is known as the Pauli exclusion principle. It follows from this that as an electron can spin in only two ways each quantum orbit can hold no more than two electrons. Once both vacancies are full further electrons can fit only into other orbits. With this principle the distribution of orbital electrons at last became clear, that is, they could be explained and predicted in purely quantum terms.

The early model of the atom by Niels Bohr had been extended by Arnold Sommerfeld in 1915. In the Bohr–Sommerfeld atom, each electron orbiting the nucleus had three quantum numbers: n, l, and m. Pauli introduced a fourth quantum number (s), which could have values of +1/2 or –1/2 and corresponded to possible values of the ‘spin’ of the electron. Pauli's exclusion principle stated that no two electrons in an atom could have the same four quantum numbers (n, l, m, and s). The concept of electron spin was verified in 1926 by Samuel Goudsmit and George Uhlenbek. The exclusion principle explained many aspects of atomic behavior, including the spectral effects discovered by Pieter Zeeman. It has also been applied to other particles. It was for his introduction of the exclusion principle that Pauli was awarded the 1945 Nobel Prize for physics.

Pauli's second great insight was in resolving a problem in beta decay – a type of radioactivity in which electrons are emitted by the atomic nucleus. It was found that the energies of the electrons covered a continuous range up to a maximum value. The difficulty was in reconciling this with the law of conservation of energy; specifically, what happened to the ‘missing’ energy when the electrons had lower energies than the maximum? In 1930, in a letter to Lise Meitner, Pauli suggested that an emitted electron was accompanied by a neutral particle that carried the excess energy. Enrico Fermi suggested the name ‘neutrino’ for this particle, which was first tentatively observed in 1953 by Frederick Reines and whose existence was confirmed by Reines and Clyde Cowan in 1956.