# Norbert Wiener

## Tufts Degree 1909, Honorary Degree 1946

To celebrate our distinguished alumnus, the Tufts University Mathematics Department has instituted the Norbert Wiener Lectures, initially funded by an anonymous gift to the University, as well as the Wiener Award for an especially gifted student.

Norbert Wiener may be the Tufts alumnus of most enduring fame. He was a world-renowned mathematician and founder of the science of cybernetics and made some of the most important contributions to mathematics in the 20th century. Wiener was born in Columbia, Missouri, November 26, 1894. His father, Leo Wiener, was a Russian who became a self-taught philologist of importance, acquiring a chair in Slavic languages at Harvard soon after Norbert's birth. Wiener's mother Bertha was born in Missouri. The father personally took charge of his son's education, and Norbert was home-schooled until enrolling in high school in Ayer, Massachusetts, near his family's home in the rural town of Harvard, Massachusetts.

### Tufts

When he was 11 the family moved to Medford Hillside, so he could enter Tufts. He enrolled at Tufts in 1906 and graduated in 1909 at age 14. His major was mathematics, and he had a strong interest in physics and chemistry, and finally biology. At 15 he entered the graduate program in zoology at Harvard. His eyesight and coordination made him a failure at laboratory work. After changing to philosophy he moved closer to mathematics with a doctoral thesis (at Harvard) on mathematical logic, obtained while working with Professor Karl Schmidt at Tufts.

### Travels

In 1913 (at age 18) he moved to Cambridge University where he worked with Bertrand Russell, and then to Göttingen in the same academic year to work with David Hilbert until the onset of World War I. Via Cambridge, London, and Columbia he returned to the Harvard Philosophy department. He tried to enlist in the military but was rejected for poor eyesight. After trying out officer training and teaching at the University of Maine he worked for General Electric in Lynn and at Aberdeen Proving Ground. For a few months he was a reporter for the Boston Herald.

### MIT

Then, in Spring 1919, still at the tender age of 24, he joined the faculty at the Massachusetts Institute of Technology, where he was to spend the remainder of his career. He began to produce spectacular results in mathematics that garnered him world-wide fame in due course and made him one of the most famous faculty members of MIT.

Wiener did highly innovative and fundamental work on what is now called stochastic processes and, in particular, on the theory of Brownian motion--that is, the construction of a rigorous mathematical description of a physical process that is subject to random change--and on generalized harmonic analysis--that is, the analysis of functions into periodic components and the generalizations of such an analysis--as well as significant work on other problems of mathematical analysis. From a long list of published works, three papers stand out: "Differential Space," Journal of Mathematics and Physics, 58:131-174 (1923); "Generalized Harmonic Analysis," Acta Mathematica, 55:117-258 (1930); and "Tauberian Theorems," Annals of Mathematics, 33:1-100 (1932). In 1933 Wiener was elected to the National Academy of Science but soon resigned, repelled by some of the aspects of institutionalized science he encountered in the Academy. In the same year, he shared the Bôcher Prize, offered every five years by the American Mathematical Society, and was honoured by the society by being invited to present the Colloquium Lectures, published in 1934 as "Fourier Transforms in the Complex Domain." Much of the work appearing in this volume had been done in collaboration with Raymond E.A.C. Paley, who was killed a year before the book was finished. Wiener's mathematical work was so influential that by now literally thousands of mathematical research publications refer to him. The main threads of his work are woven throughout the fabric of contemporary mathematics.

During World War II Wiener worked on gunfire control, the problem of pointing a gun to fire at a moving target. The ideas that evolved led to "Extrapolation, Interpolation, and Smoothing of Stationary Time Series" (1949), which first appeared as a classified report and established Wiener as a codiscoverer, with the Russian mathematician A.N. Kolmogorov, of the theory on the prediction of stationary time series. It introduced certain statistical methods into control and communications engineering and exerted great influence in these areas. This work also led him to formulate the concept of cybernetics. The term he coined is the root of neologisms such as cyberspace.

In 1948 his book "Cybernetics: or, Control and Communication in the Animal and the Machine" appeared. For a scientific book it was extremely popular, and Wiener became known in a much broader scientific community. Cybernetics is interdisciplinary in nature; based on common relationships between humans and machines, it is used today in control theory, automation theory, and computer programs to reduce many time-consuming computations and decision-making processes formerly done by human beings. Wiener worked at cybernetics, philosophized about it, and propagandized for it the rest of his life, all the while keeping up his research in other areas of mathematics.

After the war Wiener continued to contribute new ideas to widely divergent subjects, including mathematical prediction theory and quantum theory, providing the latter a possible solution to a difficulty that had been debated by the physicists Niels Bohr and Albert Einstein. Applying his theoretical description of Brownian movement to quantum phenomena, he showed how quantum theory, to the extent that it is based on probability, is consistent with other branches of science. A few weeks before his death, Wiener was awarded the National Medal of Science by President Lyndon B. Johnson.

### Appreciation

His colleague Dirk Struik, who was born in the same year, was also a good friend of the mathematics department at Tufts. When asked by David Rowe in a 1987 interview for the Mathematical Intelligencer what qualities he most admired in Wiener, Struik replied:

I would say his courage and his sensitivity. He was a man of enormous scientific vitality which the years did not seem to diminish, but this was complemented by extreme sensitivity; he saw and felt things for which most of us were blind and unfeeling. I think this was partly due to the overly strict upbringing he had as a child prodigy. Wiener was a man of many moods, and these were reflected in his lectures, which ranged from among the worst to the very best I have ever heard. Sometimes he would lull his audience to sleep or get lost in his own computations---his performance in Göttingen was notoriously bad. But on other occasions I have seen him hold a group of colleagues and executives at breathless attention while he set forth his ideas in truly brilliant fashion. Wiener was among those scientists who recognized the full implications of the scientist's unique role in modern society and his responsibilities to it in the age of electronic computers and nuclear weapons. I well remember how upset he was the day after Hiroshima was bombed. When I remarked that because of Hiroshima the war against Japan should now come to a speedy close without much further bloodshed---a common sentiment at the time and the official justification still heard today---he replied that the explosion signified the beginning of a new and terrifying period in human history, in which the great powers might prove bound to push nuclear research to a destructive potential never dreamed of before. He also recognized and detested the racism and arrogance displayed in using the bomb against Asians.

He just saw further than the rest of us. In Wiener's day robots were largely the stuff of fiction. His favorite parables concerned such robots or similar devices with the capability of turning against those who built them: Rabbi Loew's Golem, for example, or Goethe's Sorcerer's Apprentice, the Genie of the Arabian Nights, and W. W. Jacobs' Monkey's Paw. Today we all know that cybernetics, the science of self-controlling mechanisms, has an increasing impact on industry and employment, on warfare and the welfare of human beings.

### Sources and Further Reading

From the Notices of the American Mathematical Society: Wiener's life and Wiener's work in mathematics.

From the Encyclopedia Britannica: Wiener's biography and article about cybernetics.

From Mathematical Reviews (subscription only): partial bibliography and a listing of thousands of articles referring to Wiener and his work.