He was born in Columbia, Missouri, the first child of Leo and Bertha Wiener. Leo was an Instructor in Slavic Languages at Harvard. Norbert was educated at home until he was seven, he entered school only briefly before resuming the majority of his studies at home. In 1903 he returned to school, graduating from Ayer High School in 1906.
In September 1906, aged eleven, he entered Tufts College to study mathematics. He received his degree from Tufts in 1909 and entered Harvard. At Harvard he studied zoology but in 1910 he transferred to Cornell to begin graduate studies in philosophy, he then returned to Harvard the next year to continue his philosophy studies. Wiener received his Ph.D. from Harvard in 1912 for a dissertation on mathematical logic.
From Harvard he went to Cambridge, England and studied under Bertrand Russell and G. H. Hardy. In 1914 he studied at Göttingen, Germany under David Hilbert and Edmund Landau. He then returned to Cambridge and then back to the USA. In 1915-16 he taught philosophy courses at Harvard, worked for General Electric and then Encyclopedia Americana before working on ballistics at the Aberdeen Proving Ground, Maryland. He remained in Maryland until the end of the war, when he took up a post as instructor in mathematics at MIT.
While working at MIT he frequently travelled to Europe. In 1926 he married Margaret Engemann and then returned to Europe as a Guggenheim scholar. He spent most of his time at Göttingen or with Hardy at Cambridge. He worked on Brownian motion, the Fourier integral, Dirichlet's problem, harmonic analysis and Tauberian theorems among other problems. He won the Bocher Prize in 1933.
During WW II he worked on gunnery control which encouraged him to synthesize his interests in communication theory into cybernetics.
Published works include The Human Use of Human Beings (1950), Ex-Prodigy (1953), I am a Mathematician (1956), Nonlinear Problems in Random Theory (1958), and God & Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion (1964).