Norbert Wiener

26 Nov 1894
18 Mar 1964
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Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was Professor of Mathematics at MIT.

A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.

Wiener is considered the originator of cybernetics, a formalization of the notion of feedback, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society.

Wiener was born in Columbia, Missouri, the first child of Leo Wiener and Bertha Kahn, Jews of Polish and German origin, respectively. Leo had educated Norbert at home until 1903, employing teaching methods of his own invention, except for a brief interlude when Norbert was 7 years of age.

Earning his living teaching German and Slavic languages, Leo read widely and accumulated a personal library from which the young Norbert benefited greatly.

Leo also had ample ability in mathematics and tutored his son in the subject until he left home. In his autobiography, Norbert described his father as calm and patient, unless he (Norbert) failed to give a correct answer, at which his father would lose his temper.

He became an agnostic. After graduating from Ayer High School in 1906 at 11 years of age, Wiener entered Tufts College. He was awarded a BA in mathematics in 1909 at the age of 14, whereupon he began graduate studies of zoology at Harvard. In 1910 he transferred to Cornell to study philosophy.

Wiener took a great interest in the mathematical theory of Brownian motion (named after Robert Brown) proving many results now widely known such as the non-differentiability of the paths. Consequently, the one-dimensional version of Brownian motion was named the Wiener process.

It is the best known of the Lévy processes, càdlàg stochastic processes with stationary statistically independent increments, and occurs frequently in pure and applied mathematics, physics and economics (e.g. on the stock-market).

Wiener’s Tauberian theorem, a 1932 result of Wiener, developed Tauberian theorems in summability theory, on the face of it a chapter of real analysis, by showing that most of the known results could be encapsulated in a principle taken from harmonic analysis.

In its present formulation, the theorem of Wiener does not have any obvious association with Tauberian theorems, which deal with infinite series; the translation from results formulated for integrals, or using the language of functional analysis and Banach algebras, is however a relatively routine process.

The Paley–Wiener theorem relates growth properties of entire functions on Cn and Fourier transformation of Schwartz distributions of compact support.

The Wiener–Khinchin theorem, (or Wiener – Khintchine theorem or Khinchin – Kolmogorov theorem), states that the power spectral density of a wide-sense-stationary random process is the Fourier transform of the corresponding autocorrelation function.

An abstract Wiener space is a mathematical object in measure theory, used to construct a “decent”, strictly positive and locally finite measure on an infinite-dimensional vector space.

Wiener’s original construction only applied to the space of real-valued continuous paths on the unit interval, known as classical Wiener space.

Leonard Gross provided the generalization to the case of a general separable Banach space.

The notion of a Banach space itself was discovered independently by both Wiener and Stefan Banach at around the same time.

The Norbert Wiener Center for Harmonic Analysis and Applications (NWC) in the Department of Mathematics at the University of Maryland, College Park is devoted to the scientific and mathematical legacy of Norbert Wiener. The NWC website highlights the research activities of the Center.

Further, each year the Norbert Wiener Center hosts the February Fourier Talks, a two-day national conference displaying advances in pure and applied harmonic analysis in industry, government, and academia.

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