Richard Hamming

Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, the sphere-packing or Hamming bound, Hamming graph concepts, and the Hamming distance.

Born in Chicago, Hamming attended the University of Chicago, the University of Nebraska and the University of Illinois at Urbana–Champaign, where he wrote his doctoral thesis in mathematics under the supervision of Waldemar Trjitzinsky (1901–1973). In April 1945, he joined the Manhattan Project at the Los Alamos Laboratory, where he programmed the IBM calculating machines that computed the solution to equations provided by the project's physicists. He left to join the Bell Telephone Laboratories in 1946. Over the next fifteen years, he was involved in nearly all of the laboratories' most prominent achievements. For his work, he received the ACM Turing Award in 1968, being its third recipient.

After retiring from Bell Labs in 1976, Hamming took a position at the Naval Postgraduate School in Monterey, California, where he worked as an adjunct professor and senior lecturer in computer science, and devoted himself to teaching and writing books. He delivered his last lecture in December 1997, just a few weeks before he died from a heart attack on January 7, 1998.

Early life

Hamming was born in Chicago, Illinois, on February 11, 1915, the son of Richard J. Hamming, a credit manager, and Mabel G. Redfield. His father was Dutch, and his mother was a Mayflower descendant. He grew up in Chicago, where he attended Crane Technical High School and Crane Junior College.

Hamming initially wanted to study engineering, but money was scarce during the Great Depression, and the only scholarship offer he received came from the University of Chicago, which had no engineering school. Instead, he became a science student, majoring in mathematics, and received his Bachelor of Science degree in 1937. While he was a graduate student, he discovered and read George Boole's The Laws of Thought.

The University of Illinois at Urbana–Champaign awarded Hamming his Doctor of Philosophy in 1942, and he became an instructor in mathematics there. He married Wanda Little, a fellow student, on September 5, 1942,

Hamming set himself the task of solving this problem, which he realised would have an enormous range of applications. Each bit can only be a zero or a one, so if you know which bit is wrong, then it can be corrected. In a landmark paper published in 1950, he introduced a concept of the number of positions in which two code words differ, and therefore how many changes are required to transform one code word into another, which is today known as the Hamming distance. Hamming thereby created a family of mathematical error-correcting codes, which are called Hamming codes. This not only solved an important problem in telecommunications and computer science, it opened up a whole new field of study.

The Hamming bound, also known as the sphere-packing or volume bound is a limit on the parameters of an arbitrary block code. It is from an interpretation in terms of sphere packing in the Hamming distance into the space of all possible words. It gives an important limitation on the efficiency with which any error-correcting code can utilize the space in which its code words are embedded. A code which attains the Hamming bound is said to be a perfect code. Hamming codes are perfect codes.

Returning to differential equations, Hamming studied means of numerically integrating them. A popular approach at the time was Milne's Method, attributed to Arthur Milne. This had the drawback of being unstable, so that under certain conditions the result could be swamped by roundoff noise. Hamming developed an improved version, the Hamming predictor-corrector. This was in use for many years, but has since been superseded by the Adams method. He did extensive research into digital filters, devising a new filter, the Hamming window, and eventually writing an entire book on the subject, Digital Filters (1977).

During the 1950s, he programmed one of the earliest computers, the IBM 650, and with Ruth A. Weiss developed the L2 programming language, one of the earliest computer languages, in 1956. It was widely used within the Bell Labs, and also by external users, who knew it as Bell 2. It was superseded by Fortran when the Bell Labs' IBM 650 were replaced by the IBM 704 in 1957.

In A Discipline of Programming (1976), Edsger Dijkstra attributed to Hamming the problem of efficiently finding regular numbers. The problem became known as "Hamming's problem"; in computer science, regular numbers are often referred to as "Hamming numbers", although he did not discover them.

Throughout his time at Bell Labs, Hamming avoided management responsibilities. He was promoted to management positions several times, but always managed to make these only temporary. "I knew in a sense that by avoiding management," he later recalled, "I was not doing my duty by the organization. That is one of my biggest failures." and delivered his last lecture in December 1997, just a few weeks before his death from a heart attack on January 7, 1998. He was survived by his wife Wanda. is maintained by Naval Postgraduate School along with ongoing work that preserves his insights and extends his legacy.

Awards and professional recognition

Turing Award, Association for Computing Machinery, 1968.
Member of the National Academy of Engineering, 1980.
Harold Pender Award, University of Pennsylvania, 1981.
IEEE Richard W. Hamming Medal, 1988.
Fellow of the Association for Computing Machinery, 1994.
Basic Research Award, Eduard Rhein Foundation, 1996.

The IEEE Richard W. Hamming Medal, named after him, is an award given annually by the Institute of Electrical and Electronics Engineers (IEEE), for "exceptional contributions to information sciences, systems and technology", and he was the first recipient of this medal. The reverse side of the medal depicts a Hamming parity check matrix for a Hamming error-correcting code.

Bibliography

; second edition 1973
; Hemisphere Pub. Corp reprint 1989; Dover reprint 2012
; second edition 1983; third edition 1989.
; second edition 1986.

Lectures

1991 - You and Your Research. Lecture sponsored by the Dept. of Electrical and Computer engineering, University of California, San Diego. Electrical and Computer Engineering Distinguished Lecture Series. Digital object made available by UC San Diego Library.

Notes

References

Reprinted, Dover Publications, 1986, .