Norbert Wiener was born on November 26, 1894, and died on March 18, 1964. He was an American scientist, mathematician, and philosopher. Wiener became a professor of mathematics at the Massachusetts Institute of Technology (MIT). As a child, he showed great talent in learning. Later in life, he studied random and noise-related processes in mathematics, which helped advance fields like electronic engineering, communication, and control systems.

Wiener is known as the creator of cybernetics, a field that studies how communication works in living things and machines. This work had effects on engineering, systems control, computer science, biology, neuroscience, philosophy, and how societies are organized. His research influenced many important figures, including computer scientist John von Neumann, information theorist Claude Shannon, and anthropologists Margaret Mead and Gregory Bateson.

Wiener was among the first to suggest that intelligent behavior results from feedback mechanisms, which are ways systems respond to information. This idea was an important early step in the development of modern artificial intelligence.

Biography

Norbert Wiener was born in Columbia, Missouri, as the first child of Leo Wiener and Bertha Kahn. His parents were Jewish immigrants from Lithuania and Germany. Through his father, Wiener was related to Maimonides, a famous rabbi, philosopher, and physician from Al Andalus, and to Akiva Eger, who was the chief rabbi of Posen from 1815 to 1837.

Wiener met his paternal grandfather, Solomon Wiener, only once in New York. Solomon was a journalist who tried to replace Yiddish with German in his daily life. He was born in Krotoschin and later married a woman from a family of Jewish tanners. The family moved to Byelostok, where Wiener’s father was born in 1862. Wiener learned that his family had once been minor nobles in Russia, and his grandmother’s house was chosen as a temporary residence for the Russian Tzar.

Wiener’s paternal grandmother’s family was different from his grandfather’s. His father developed strong, practical habits that helped him manage the family well. However, his father also had an idealistic side. By age 13, because of their family situation and Jewish traditions, his father began supporting the family as a private tutor. His father attended a Lutheran school and learned several languages.

Later, his father left the Minsk Gymnasium to study in Warsaw, Poland. There, he formed friendships with Polish students and became involved with the Polish resistance movement. His father was a contemporary of Zamenhof, the creator of Esperanto, and studied the language early on. His father later studied medicine at the University of Warsaw but switched to engineering at the Polytechnicum in Berlin. Relatives in Berlin tried to convince his father to work in banking, but he refused. Instead, he adopted a Tolstoyan ethic, which influenced his decision to move to the United States and led to Wiener’s vegetarianism. Wiener later felt upset about his father’s strictness on this issue.

His father planned to create a commune in Central America based on his ideas but was abandoned by his companion. He traveled to Hartlepool, Liverpool, Havana, and New Orleans, learning English and Spanish along the way. Eventually, his father became a language teacher and studied philology. He later met Wiener’s mother, Bertha Kahn, in St. Joseph, Missouri.

Wiener’s maternal grandfather was a German Jewish immigrant from the Rhineland. His wife, whose family name was Ellinger, had moved to the United States many years earlier. Wiener noted that his maternal grandmother’s mother was not Jewish and that men on his mother’s side often married non-Jewish women. The family also had roots in the American South. Wiener mentioned that some men in this part of the family left their families suddenly, and one relative was rumored to have become a Western bandit.

In his autobiography, Wiener described the melting pot culture he grew up in, which was different from the more uniform Old American culture of the past. He believed this new culture offered more freedom and opportunity compared to the rigid systems in Eastern Europe.

Wiener’s father taught him at home until 1903, using his own methods except for a short time when Wiener was seven. He earned a living teaching German and Slavic languages and built a large personal library. He also taught his son mathematics until Wiener left home. In his autobiography, Wiener described his father as calm and patient, unless Wiener gave incorrect answers, which made his father angry.

In a paper he wrote at age 10, titled "The Theory of Ignorance," Wiener argued that humans cannot know everything for certain and that all knowledge is based on approximations.

Wiener graduated from Ayer High School in 1906 at age 11 and entered Tufts College, where he earned a BA in mathematics in 1909 at age 14. He studied zoology at Harvard before switching to philosophy at Cornell in 1910. He graduated from Cornell in 1911 at age 17.

The next year, he returned to Harvard to continue his philosophy studies. There, he was influenced by Edward Vermilye Huntington, who studied both math and engineering. Harvard awarded Wiener a PhD in 1913 at age 19 for a dissertation on mathematical logic, comparing the work of Ernst Schröder with that of Alfred North Whitehead and Bertrand Russell. His dissertation introduced the idea that ordered pairs can be defined using elementary set theory, a concept later simplified by Kazimierz Kuratowski in 1921.

In 1914, Wiener traveled to Europe to study with Bertrand Russell and G. H. Hardy at Cambridge University and with David Hilbert and Edmund Landau at the University of Göttingen. At Göttingen, he also attended courses with Edmund Husserl on Kant’s ethics and phenomenology.

Between 1915 and 1916, Wiener taught philosophy at Harvard, worked as an engineer for General Electric, and wrote for the Encyclopedia Americana. He briefly worked as a journalist for the Boston Herald, writing about poor working conditions for mill workers in Lawrence, Massachusetts. However, he was fired for refusing to write positive stories about a politician the newspaper’s owners supported.

Although Wiener later became a pacifist, he supported the war effort during World War I. In 1916, as the United States prepared to enter the war, Wiener attended a military training camp but did not receive a commission.

Work

Norbert Wiener was an early researcher of random and mathematical noise patterns, contributing work important to engineering, communication, and control systems. He proposed modeling a signal as a special kind of noise, giving it a clear mathematical foundation. An example often used is that English text can be seen as a random sequence of letters and spaces, where each letter and space has a specific probability. However, Wiener worked with analog signals, where such a simple example does not apply. His early research on information theory and signal processing focused on analog signals and was largely forgotten after the rise of digital theory.

Wiener was one of the main creators of cybernetics, a concept that describes feedback and has applications in engineering, systems control, computer science, biology, philosophy, and society. While he said the field developed during his own work, it has roots in the ideas of Leibnitz, Babbage, Maxwell, and Gibbs. His work influenced Gregory Bateson and Margaret Mead, and through them, anthropology, sociology, and education.

A simple mathematical model of Brownian motion, called the Wiener equation, assumes the speed of a fluid particle changes randomly.

For signal processing, the Wiener filter is a tool designed by Wiener in the 1940s and published in 1942 as a secret document, funded by the National Defense Research Committee. Its goal is to reduce noise in a signal by comparing it to a predicted noise-free signal. Wiener created the filter at MIT’s Radiation Laboratory to help predict the location of German bombers using radar data. This work led to a general mathematical theory for predicting the future based on incomplete past information. It used Wiener’s earlier research on integral equations and Fourier transforms.

Wiener studied polynomial chaos, including the Hermite-Laguerre expansion, detailed in Nonlinear Problems in Random Theory. He applied this expansion to understand and control nonlinear systems by inputting white noise and analyzing the output’s Hermite-Laguerre expansion.

Wiener was deeply interested in the mathematical study of Brownian motion, named after Robert Brown. He proved results now widely known, such as the fact that Brownian motion paths are not smooth. The one-dimensional version of Brownian motion is called the Wiener process. It is a well-known type of Lévy process, a class of mathematical models used in many areas, including physics and economics.

Wiener’s tauberian theorem, from 1932, advanced Tauberian theorems in summability theory by showing how many results could be explained using harmonic analysis. Though the theorem now seems unrelated to Tauberian theorems, which deal with infinite series, translating results from integrals or functional analysis is a standard process.

The Paley–Wiener theorem connects the growth of entire functions on the complex plane to the Fourier transformation of compactly supported distributions.

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

An abstract Wiener space is a mathematical object used to define a well-behaved, positive, and finite measure on an infinite-dimensional vector space. Wiener’s original method applied only to the space of continuous paths on a time interval, known as classical Wiener space. Leonard Gross later extended this idea to general separable Banach spaces.

The concept of a Banach space was discovered independently by Wiener and Stefan Banach around the same time.

Views

Because of his family background, Judaism had a big influence on his personality and how he saw himself. His father and Wiener were not religious, but he believed that Jewish traditions and community life helped shape parts of his growth. He wrote: "Jews seem to me mainly a group of people and a social group, even though many of them also followed a religion." Even as Jewish and non-Jewish communities became more connected, he noticed that some traditions and ways of life within Jewish culture remained unchanged.

Wiener described Jewish family relationships as stronger compared to those in Europe and America. He said that being a minority and facing prejudice historically changed how Jewish people thought and lived. He believed that Judaism placed more value on learning and education than Christianity did in the past. This, he thought, helped certain physical and cultural traits stay strong over time, while Christianity had more mixing of traits.

Because of these patterns in Jewish culture, Wiener thought Jewish scholars were more likely to have large families. This, he and his friend J. B. S. Haldane believed, helped certain biological and cultural traits become more common in the Jewish community. He was unsure about Jewish nationalism and Zionism and did not connect Jewish identity to these movements. He believed Jewish identity was not based on these groups.

His family claimed to be descendants of Moses Maimonides, who valued learning. However, he was more certain that he was related to Aqiba Eger, who was a respected religious leader but disagreed with Maimonides' ideas.

In popular culture

• His work with Mary Brazier is mentioned in Avis DeVoto's book As Always, Julia.
• A ship named after him is briefly mentioned in the book Citizen of the Galaxy by Robert Heinlein.
• The song "Dedicated to Norbert Wiener" is the second song on the 1980 album Why? by G.G. Tonet (Luigi Tonet), released by the Italian It Why label.
• He is mentioned in Dan Simmons' science fiction novel Hyperion when discussing artificial intelligence and God.

Publications

Wiener wrote many books and hundreds of articles:

• 1914, "A Simplification in the Logic of Relations." Published in the Proceedings of the Cambridge Philosophical Society, Volume 13, pages 387–390. Reprinted in van Heijenoort, Jean (1967). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press, pages 224–227.
• 1930, Wiener, Norbert (1930). "Generalized Harmonic Analysis." Acta Mathematica, Volume 55, Issue 1, pages 117–258. DOI: 10.1007/BF02546511.
• 1933, The Fourier Integral and Certain of Its Applications. Published by Cambridge University Press. Reprinted in 1988 by Dover and CUP Archive. ISBN 0-521-35884-1.
• 1942, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. A wartime classified report known as "the yellow peril" because of its yellow cover and complex content. Published in 1949 by MIT Press after the war.
• 1948, Cybernetics: Or Control and Communication in the Animal and the Machine. Published in Paris (Hermann & Cie) and Cambridge, Massachusetts (MIT Press). ISBN 978-0-262-73009-9. Second revised edition published in 1961.
• 1950, The Human Use of Human Beings. Published by The Riverside Press (Houghton Mifflin Co.).
• 1958, Nonlinear Problems in Random Theory. Published by MIT Press and Wiley.
• 1964, God & Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion. Published by MIT Press.
• 1966, Generalized Harmonic Analysis and Tauberian Theorems. Published by MIT Press.
• 1993, Invention: The Care and Feeding of Ideas. Written in 1954 but not completed. Published posthumously by MIT Press in 1993.

Wiener's papers are collected in the following works:

• 1964, Selected Papers of Norbert Wiener. Published by MIT Press and SIAM in Cambridge, Massachusetts.
• 1976–1984, The Mathematical Work of Norbert Wiener. Edited by Masani P, 4 volumes published by MIT Press in Cambridge, Massachusetts. Volume 1 includes mathematical philosophy, potential theory, Brownian movement, Wiener integrals, ergodic and chaos theories, turbulence, and statistical mechanics (ISBN 0262230704). Volume 2 includes generalized harmonic analysis, Tauberian theory, classical harmonic and complex analysis (ISBN 0262230925). Volume 3 includes the Hopf-Wiener integral equation, prediction and filtering, quantum mechanics and relativity, and other mathematical papers (ISBN 0262231077). Volume 4 includes cybernetics, science, and society; ethics, aesthetics, and literary criticism; book reviews and obituaries (ISBN 0262231239).

• 1959, The Tempter. Published by Random House. Discusses Oliver Heaviside's invention for reducing distortion on telegraph lines and his conflict with AT&T over recognition of his work.

• 2018, Norbert Wiener — A Life in Cybernetics. Edited by Kline, Ronald. Published by MIT Press. Includes both volumes of Wiener's autobiography.
• 1953, Ex-Prodigy: My Childhood and Youth. Published by MIT Press.
• 1956, I Am a Mathematician. Published by Gollancz in London.

Under the name "W. Norbert":

• 1952, *