Claude Elwood Shannon


Born: 30 April 1916 in Gaylord, Michigan, USA
Died: 24 February 2001 in Medford, Massachusetts, USA

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Claude E Shannon's father was also named Claude Elwood Shannon and his mother was Mabel Catherine Wolf. Shannon was a graduate of the University of Michigan, being awarded a degree in mathematics and electrical engineering in 1936. Although he had not been outstanding in mathematics, he then went to the Massachusetts Institute of Technology where he obtained a Master's Degree in electrical engineering and his Ph.D. in mathematics in 1940. Shannon wrote a Master's thesis A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. His doctoral thesis was on population genetics.

At the Massachusetts Institute of Technology he also worked on the differential analyser, an early type of mechanical computer developed by Vannevar Bush for obtaining numerical solutions to ordinary differential equations. Shannon published Mathematical theory of the differential analyzer in 1941. In the introduction to the paper he writes:-

The most important results [mostly given in the form of theorems with proofs] deal with conditions under which functions of one or more variables can be generated, and conditions under which ordinary differential equations can be solved. Some attention is given to approximation of functions (which cannot be generated exactly), approximation of gear ratios and automatic speed control.

Shannon joined AT&T Bell Telephones in New Jersey in 1941 as a research mathematician and remained at the Bell Laboratories until 1972. Johnson writes in [4] that Shannon:-

... became known for keeping to himself by day and riding his unicycle down the halls at night.

D Slepian, a colleague at the Bell Laboratories wrote:-

Many of us brought our lunches to work and played mathematical blackboard games but Claude rarely came. He worked with his door closed, mostly. But if you went in, he would be very patient and help you along. He could grasp a problem in zero time. He really was quite a genius. He's the only person I know whom I'd apply that word to.

Working with John Riordan, Shannon published a paper in 1942 on the number of two-terminal series-parallel networks. This paper extended results obtained by MacMahon who had published his early contribution in the Electrician in 1892.

Shannon published A Mathematical Theory of Communication in the Bell System Technical Journal (1948). This paper founded the subject of information theory and he proposed a linear schematic model of a communications system. This was a new idea. Communication was then thought of as requiring electromagnetic waves to be sent down a wire. The idea that one could transmit pictures, words, sounds etc. by sending a stream of 1s and 0s down a wire, something which today seems so obvious as we take this information from a server in St Andrews, Scotland, and view it anywhere in the world, was fundamentally new.

Shannon considered a source of information which generates words composed of a finite number of symbols. These are transmitted through a channel, with each symbol spending a finite time in the channel. The problem involved statistics with the assumption that if xn is the nth symbol produced by the source the xn process is a stationary stochastic process. He gave a method of analysing a sequence of error terms in a signal to find their inherent variety, matching them to the designed variety of the control system. In A Mathematical Theory of Communication , which introduced the word "bit" for the first time, Shannon showed that adding extra bits to a signal allowed transmission errors to be corrected. Slepian, in the introduction to [2], writes:-

Probably no single work in this century has more profoundly altered man's understanding of communication than C E Shannon's article, "A mathematical theory of communication", first published in 1948. The ideas in Shannon's paper were soon picked up by communication engineers and mathematicians around the world. They were elaborated upon, extended, and complemented with new related ideas. The subject thrived and grew to become a well-rounded and exciting chapter in the annals of science.

On 27 March 1949 Shannon married Mary Elizabeth Moore. They had three sons and one daughter; Robert, James, Andrew Moore, and Margarita. He continued his work showing how Boolean algebra could be used to synthesise and simplify relay switching circuits. He also proved results on colouring the edges of a graph so that no two edges of the same colour meet at a vertex. Another important paper, published in 1949, was Communication theory of secrecy systems.

In 1952 Shannon devised an experiment illustrating the capabilities of telephone relays. He had held a position as a visiting professor of communication sciences and mathematics at the Massachusetts Institute of Technology in 1956, then from 1957 he was appointed to the Faculty there, but remained a consultant with Bell Telephones. In 1958 he became Donner Professor of Science [1]:-

When he returned to MIT in 1958, he continued to threaten corridor-walkers on his unicycle, sometimes augmenting the hazard by juggling. No one was ever sure whether these activities were part of some new breakthrough or whether he just found them amusing. He worked, for example, on a motorised pogo-stick, which he claimed would mean he could abandon the unicycle so feared by his colleagues ...

R G Gallager, a colleague who worked at the Massachusetts Institute of Technology, wrote:-

Shannon was the person who saw that the binary digit was the fundamental element in all of communication. That was really his discovery, and from it the whole communications revolution has sprung.

His later work looked at ideas in artificial intelligence. He devised chess playing programs and an electronic mouse which could solve maze problems. The chess playing program appeared in the paper Programming a computer for playing chess published in 1950. This proposal led to the first game played by the Los Alamos MANIAC computer in 1956. This was the year that Shannon published a paper showing that a universal Turing machine may be constructed with only two states.

Latterly he felt that the communications revolution, which he had played a major role in starting, was going too far. He wrote:-

Information theory has perhaps ballooned to an importance beyond its actual accomplishments.

Marvin Minsky described Shannon as follows:-

Whatever came up, he engaged it with joy, and he attacked it with some surprising resource which might be some new kind of technical concept or a hammer and saw with some scraps of wood. For him, the harder a problem might seem, the better the chance to find something new.

He also applied his inventing genius to other areas [1]:-

... he once invented a two-seater version of his unicycle, and it is probably true that no one was anxious to share it with him. A later invention, the unicycle with an off-centre hub, would bring people out into the corridors to watch him as he rode it, bobbing up and down like a duck.

Shannon received many honours for his work. Among a long list of awards were the Alfred Nobel American Institute of American Engineers Award in 1940, the National Medal of Science in 1966, the Audio Engineering Society Gold Medal in 1985, and the Kyoto Prize in 1985. He was awarded the Marconi Lifetime Achievement Award by the Guglielmo Marconi International Fellowship Foundation in 2000. It was the first time that organization, known for its annual Fellowship Prize, gave this particular award.

He was afflicted by Alzheimer's disease, and he spent his last few years in a Massachusetts nursing home.

Article by: J J O'Connor and E F Robertson

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List of References (7 books/articles)

A Poster of Claude E Shannon

Mathematicians born in the same country

Additional Material in MacTutor

  1. Obituary: The Times
  2. Obituary: The Guardian
  3. Obituary: The New York Times

Honours awarded to Claude E Shannon
(Click below for those honoured in this way)
AMS Gibbs Lecturer1963

Cross-references in MacTutor

  1. Chronology: 1940 to 1950

Other Web sites
  1. AMS (registration required)
  2. E Weisstein
  3. Shannon's 1948 paper (pdf)
  1. A D Wyner
  2. Mathematical Genealogy Project

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