Apart from two books devoted to his autobiography, two short stories and a novel, Norbert Wiener's works concern mainly logic and mathematics, cybernetics, mathematical physics and philosophical issues.

His papers on logic, written mainly at the beginning of his career, show a philosophical interest in mathematical thinking and its possible limitations. His contributions to mathematics and probability theory started in the early twenties with a mathematical modelling of Brownian motion introducing what was later to be called Wiener Measure. It gave rise to his concept of "differential space", which is akin to Banach space. These researches culminated in 1930 with his "generalized harmonic analysis" which allows the Fourier transform to be used for a large class of very irregular functions (of which periodic and almost periodic functions are special cases), also introducing their "covariance function" and "spectral distribution. He was inspired in that field both by J.Willard Gibbs as regards statistical physics, and by Henri Lebesgue, who propounded a famous generalization of the notion of integral. In a way, generalized harmonic analysis introduced what Wiener later (1938) called "homogeneous chaos", a notion not so far removed from what Jean Bass presented as "pseudo-aleatory functions" (1974, 1984).

The idea of "cybernetics" came to Wiener at the beginning of the forties, prompted by his work on anti-aircraft defence and by contacts with colleagues in Mexico ("Behavior, purpose and teleology" with A. Rosenblueth and J. Bigelow, Philos.Sci 1943). lt was made known to the world by the book Cybernetics or Control and Communication in the Animal and the Machine, published in l948 after contacts in l946 with M. Freymann of Hermann et Cie (Paris). Coined from the Greek "kubernetike" (the art of the steersman), cybernetics involves the theory of regulation and of signal transmission applied to technical devices, living beings and even societies. It may also concern the art of government, or "cybernetique" as Ampere conceived it in 1843, which Plato, using the already existent Greek word, compared to that of the captain of a ship. Two main ideas play a part in cybernetics: negative feedback with its stabilizing properties, and transmission of information, which helps to make a whole of the many parts of a complex system, whether living or not. The metaphor of the computer, with the role of Boolean logic, is also present in cybernetics. It is of interest to note that Wiener, remembering Leibniz's "calculus ratiocinator" and his construction, after Pascal, of a mechanical computer, considered him a patron saint of cybernetics, whereas Warren S. McCulloch favoured Descartes.

Research into the transmission of information is greatly indebted, as Wiener emphasized, to Claude E. Shannon's information theory (1948,1949), introducing the concept of quantity of information which involves a degree of formalism close to that of entropy in statistical mechanics. It is also linked to the theory of signal transmission in the presence of a perturbative noise, as developed by Wiener in 1942 in a classified monograph (nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject) and then in Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications (1949). In this book Wiener applies generalized harmonic analysis to stationary aleatory signals and solves the problem of optimal elimination of the perturbative noise and of optimal prediction of the signal itself, with the help of a filtering operator. Quite independently, A.N. Kolmogoroff had announced results in the same domain at a time (1941) when scientific communications were interrupted. Improvements regarding prediction were published by Wiener in collaboration with Pier Masani in 1959.

Norbert Wiener was also deeply attracted to mathematical physics. His interest originated in a collaboration with Max Born in 1926 on quantization and developed (1927,1928) in the direction of relativistic quantum theory and the use of a fifth dimension as proposed by Kaluza and Klein. Einstein's attempt to unify gravitation and electromagnetism also aroused his interest (1929). Later, Wiener returned to quantum mechanics with a theory of statistical hidden variables using his differential space and aiming at explaining the principles of quantum measurement. These researches were published, in collaboration with Armand Siegel, from 1953 to 1956and presented, along with other considerations, in a posthumous book (1966).

Wiener's interests were not limited to logic, mathematics, cybernetics or mathematical physics. He was also familiar with all the aspects of philosophy, from epistemology and metaphysics to morals. . With The Human Use of Human Beings (1950) he gives a presentation of cybernetics underlining its social aspects with some emphasis on the role of randomness and entropy. Another book, entitled God, Golem, Inc. A Comment on Certain Points where Cybernetics Impinges on Religion, published in the year of Wiener's death, shows, although he was a skeptic, his interest in theology. In a very different field, he wrote two short stories and a novel (The Tempter,1959). Wiener also published an autobiography in two parts: Ex-Prodigy: My Childhood and Youth (1953) and I Am a Mathematician (1956).