After earning his doctorate, in 1945, encouraged by a friend, he joined the Manhattan Project. A month after he arrived at Los Alamos he was joined by his wife, who was also employed on the Manhattan Project. Hamming was put in charge of the IBM calculating machines that played a vital role in the project. 

After the Manhattan Project ended Hamming remained at Los Alamos for six months, writing up details of the calculations they had done.

In 1946 he accepted a position in the mathematics department at the Bell Telephone Laboratories in New Jersey. At Bell Labs he was able to work with both Claude Shannon, with whom he shared an office, and John Tukey. Hamming often related how they had all been affected by growing up in the depression, and all learned new skills with their war work. It led them, he said, to do unconventional things in unconventional ways. Hamming, for example, lunched with the physics group rather than his mathematics group, and they were fascinated by his unorthodox ideas and views. Not all his colleagues were happy to tolerate his unconventional ways. Some have described him as egotistical, saying he sometimes went off "half-cocked, after some half-baked idea." Unconventional ideas sometimes produce flashes of brilliance, but they sometimes also lead to failures.

We first note the many and varied problems he worked on in Bell Labs. These include problems involving design of telephone systems, traveling wave tubes, the equalization of television transmission lines, the stability of complex communication systems, and the blocking of calls through a telephone central office. He continued to work for Bell Telephones until 1976, although he became increasingly interested in teaching, and held visiting or adjunct professorships at Stanford University, the City College of New York, the University of California at Irvine and Princeton University between 1960 and 1976. After retiring from Bell Labs in 1976, he became a professor of computer science at the Naval Postgraduate School at Monterey, California. At this point he gave up his research career and concentrated on teaching and writing books. He believed that the way mathematics was being taught was wrong, and that the only way to change it was to write textbooks with a new approach. Here are two examples of his views on mathematics teaching:

We live in an age of exponential growth in knowledge, and it is increasingly futile to teach only polished theorems and proofs. We must abandon the guided tour through the art gallery of mathematics, and instead teach how to create the mathematics we need. In my opinion, there is no long-term practical alternative.

and

The way mathematics is currently taught it is exceedingly dull. In the calculus book we are currently using on my campus, I found no single problem whose answer I felt the student would care about! The problems in the text have the dignity of solving a crossword puzzle - hard to be sure, but the result is of no significance in life.

His attempt to move to a new way of teaching calculus is exhibited in his 1985 book Methods of Mathematics Applied to Calculus, Probability, and Statistics. 

Richard Hamming is best known for his work at Bell Labs on error-detecting and error-correcting codes. His fundamental paper on this topic, Error detecting and error correcting codes, appeared in April 1950 in the Bell System Technical Journal. This paper created an entirely new field within information theory. Hamming codes, Hamming distance and Hamming metric, standard terms used today in coding theory and other areas of mathematics, all originated in this classic paper and are of ongoing practical use in computer design.

In 1956 Hamming worked on the IBM 650, an early vacuum tube, drum memory, computer. His work led to the development of a rudimentary programming language. Hamming also worked on numerical analysis, especially integration of differential equations. The Hamming spectral window, still widely used in computation, is a special type of digital filter designed to pass certain frequencies and discriminate against closely related frequencies.

In addition to the Turing Award, Hamming received many awards for his pioneering work. He was made a fellow of the Association for Computing Machinery in 1994. The Institute of Electrical and Electronics Engineers (IEEE) awarded him the Emanuel R Piore Award in 1979.

The IEEE created "The Richard W. Hamming Medal" in his honor. He was the first recipient of this $10,000 prize medal in 1988. He was elected a member of the National Academy of Engineering in 1980, and received the Harold Pender Award from the University of Pennsylvania in 1981. In 1996, in Munich, Hamming received the prestigious $130,000 Eduard Rheim Award for Achievement in Technology for his work on error correcting codes.

In 1997 Hamming retired from teaching at the Naval Postgraduate School and was made Distinguished Professor Emeritus. Shortly before he retired, he said that when he left Bell Labs, he knew that that was the end of his research career. It really would be the end, he said, when he retired from teaching. Indeed he was right, for having taught up to December 1997, he died of a heart attack in the following month. Richard Franke of the Naval Postgraduate School at Monterey wrote of Richard Hamming:

He will be long remembered for his keen insights into many facets of science and computation. I'll also long remember him for his red plaid sport coat and his bad jokes.

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