Richard W. Hamming
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Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for
computer engineering Computer engineering (CoE or CpE) is a branch of electrical engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers ...
and telecommunications. His contributions include the
Hamming code In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the sim ...
(which makes use of a
Hamming matrix In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the sim ...
), the
Hamming window In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several '' window functions'' can be defined, based on ...
,
Hamming numbers Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 ×&nb ...
,
sphere-packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...
(or
Hamming bound In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of pack ...
),
Hamming graph Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let be a set of elements and a positive integer. The Hamming graph has vertex set , ...
concepts, and the
Hamming distance In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to chan ...
. Born in Chicago, Hamming attended
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
,
University of Nebraska A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...
and the
University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Universit ...
, where he wrote his doctoral thesis in mathematics under the supervision of
Waldemar Trjitzinsky Waldemar, Valdemar or Woldemar is an Old High German given name. It consists of the elements ''wald-'' "power", "brightness" and ''-mar'' "fame". The name is considered the equivalent of the Slavic name Vladimir, Volodymyr, Uladzimir or Włod ...
(1901–1973). In April 1945 he joined the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
at the
Los Alamos Laboratory The Los Alamos Laboratory, also known as Project Y, was a secret laboratory established by the Manhattan Project and operated by the University of California during World War II. Its mission was to design and build the first atomic bombs. Ro ...
, where he programmed the IBM
calculating machines A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators we ...
that computed the solution to equations provided by the project's physicists. He left to join the
Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...
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
Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...
in 1968, being its third recipient. After retiring from the Bell Labs in 1976, Hamming took a position at the
Naval Postgraduate School The Naval Postgraduate School (NPS) is a public graduate school operated by the United States Navy and located in Monterey, California. It offers master’s and doctoral degrees in more than 70 fields of study to the U.S. Armed Forces, DOD ci ...
in
Monterey, California Monterey (; es, Monterrey; Ohlone: ) is a city located in Monterey County on the southern edge of Monterey Bay on the U.S. state of California's Central Coast. Founded on June 3, 1770, it functioned as the capital of Alta California under bo ...
, where he worked as an
adjunct professor An adjunct professor is a type of academic appointment in higher education who does not work at the establishment full-time. The terms of this appointment and the job security of the tenure vary in different parts of the world, however the genera ...
and
senior lecturer Senior lecturer is an academic rank. In the United Kingdom, Ireland, New Zealand, Australia, Switzerland, and Israel senior lecturer is a faculty position at a university or similar institution. The position is tenured (in systems with this concep ...
in
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, 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

Richard Wesley Hamming was born in Chicago, Illinois, on February 11, 1915, the son of Richard J. Hamming, a credit manager, and Mabel G. Redfield. He grew up in Chicago, where he attended Crane Technical High School and
Crane Junior College Malcolm X College, one of the City Colleges of Chicago, is a two-year college located on the Near West Side of Chicago, Illinois. It was founded as Crane Junior College in 1911 and was the first of the City Colleges. Crane ceased operations at ...
. Hamming initially wanted to study engineering, but money was scarce during the
Great Depression The Great Depression (19291939) was an economic shock that impacted most countries across the world. It was a period of economic depression that became evident after a major fall in stock prices in the United States. The economic contagio ...
, and the only scholarship offer he received came from the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
, which had no engineering school. Instead, he became a science student, majoring in mathematics, and received his Bachelor of Science degree in 1937. He later considered this a fortunate turn of events. "As an engineer," he said, "I would have been the guy going down manholes instead of having the excitement of frontier research work." He went on to earn a Master of Arts degree from the
University of Nebraska A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...
in 1939, and then entered the
University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Universit ...
, where he wrote his doctoral thesis on ''Some Problems in the Boundary Value Theory of Linear Differential Equations'' under the supervision of
Waldemar Trjitzinsky Waldemar, Valdemar or Woldemar is an Old High German given name. It consists of the elements ''wald-'' "power", "brightness" and ''-mar'' "fame". The name is considered the equivalent of the Slavic name Vladimir, Volodymyr, Uladzimir or Włod ...
. His thesis was an extension of Trjitzinsky's work in that area. He looked at
Green's function In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential ...
and further developed
Jacob Tamarkin Jacob David Tamarkin (russian: Я́ков Дави́дович Тама́ркин, ''Yakov Davidovich Tamarkin''; 11 July 1888 – 18 November 1945) was a Russian-American mathematician best known for his work in mathematical analysis. Biography ...
's methods for obtaining characteristic solutions. While he was a graduate student, he discovered and read
George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ire ...
's ''
The Laws of Thought ''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'' by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathe ...
''. 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, immediately after she was awarded her own Master of Arts in English literature. They would remain married until his death, and had no children. In 1944, he became an assistant professor at the J.B. Speed Scientific School at the
University of Louisville The University of Louisville (UofL) is a public research university in Louisville, Kentucky. It is part of the Kentucky state university system. When founded in 1798, it was the first city-owned public university in the United States and one of ...
in
Louisville, Kentucky Louisville ( , , ) is the largest city in the Commonwealth of Kentucky and the 28th most-populous city in the United States. Louisville is the historical seat and, since 2003, the nominal seat of Jefferson County, on the Indiana border ...
.


Manhattan Project

With
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
still ongoing, Hamming left Louisville in April 1945 to work on the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
at the
Los Alamos Laboratory The Los Alamos Laboratory, also known as Project Y, was a secret laboratory established by the Manhattan Project and operated by the University of California during World War II. Its mission was to design and build the first atomic bombs. Ro ...
, in
Hans Bethe Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel Prize ...
's division, programming the IBM
calculating machines A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators we ...
that computed the solution to equations provided by the project's physicists. His wife Wanda soon followed, taking a job at Los Alamos as a
human computer The term "computer", in use from the early 17th century (the first known written reference dates from 1613), meant "one who computes": a person performing mathematical calculations, before electronic computers became commercially available. Ala ...
, working for Bethe and
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care fo ...
. Hamming later recalled that: Hamming remained at Los Alamos until 1946, when he accepted a post at the
Bell Telephone Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...
(BTL). For the trip to New Jersey, he bought
Klaus Fuchs Klaus Emil Julius Fuchs (29 December 1911 – 28 January 1988) was a German theoretical physicist and atomic spy who supplied information from the American, British and Canadian Manhattan Project to the Soviet Union during and shortly aft ...
's old car. When he later sold it just weeks before Fuchs was unmasked as a spy, the
FBI The Federal Bureau of Investigation (FBI) is the domestic Intelligence agency, intelligence and Security agency, security service of the United States and its principal Federal law enforcement in the United States, federal law enforcement age ...
regarded the timing as suspicious enough to interrogate Hamming. Although Hamming described his role at Los Alamos as being that of a "computer janitor", he saw
computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
s of experiments that would have been impossible to perform in a laboratory. "And when I had time to think about it," he later recalled, "I realized that it meant that science was going to be changed".


Bell Laboratories

At the Bell Labs Hamming shared an office for a time with
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-o ...
. The Mathematical Research Department also included
John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...
and Los Alamos veterans Donald Ling and
Brockway McMillan Brockway McMillan (March 30, 1915 – December 3, 2016) was an American government official and scientist, who served as the eighth Under Secretary of the Air Force and the second Director of the National Reconnaissance Office. McMillan was ...
. Shannon, Ling, McMillan and Hamming came to call themselves the Young Turks. "We were first-class troublemakers," Hamming later recalled. "We did unconventional things in unconventional ways and still got valuable results. Thus management had to tolerate us and let us alone a lot of the time." Although Hamming had been hired to work on
elasticity theory In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are a ...
, he still spent much of his time with the calculating machines. Before he went home on one Friday in 1947, he set the machines to perform a long and complex series of calculations over the weekend, only to find when he arrived on Monday morning that an error had occurred early in the process and the calculation had errored off. Digital machines manipulated information as sequences of zeroes and ones, units of information that Tukey would christen "
bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s". If a single bit in a sequence was wrong, then the whole sequence would be. To detect this, a
parity bit A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes) ...
was used to verify the correctness of each sequence. "If the computer can tell when an error has occurred," Hamming reasoned, "surely there is a way of telling where the error is so that the computer can correct the error itself." 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 In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...
into another, which is today known as the
Hamming distance In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to chan ...
. Hamming thereby created a family of mathematical
error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...
s, which are called
Hamming code In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the sim ...
s. This not only solved an important problem in telecommunications and computer science, it opened up a whole new field of study. The
Hamming bound In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of pack ...
, also known as the sphere-packing or volume bound is a limit on the parameters of an arbitrary
block code In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definit ...
. It is from an interpretation in terms of
sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...
in the Hamming distance into the
space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
of all possible words. It gives an important limitation on the
efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
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 equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s, Hamming studied means of numerically integrating them. A popular approach at the time was Milne's Method, attributed to
Arthur Milne Edward Arthur Milne FRS (; 14 February 1896 – 21 September 1950) was a British astrophysicist and mathematician. Biography Milne was born in Hull, Yorkshire, England. He attended Hymers College and from there he won an open scholarship ...
. 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 Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component tha ...
, devising a new filter, the
Hamming window In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several '' window functions'' can be defined, based on ...
, 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 The IBM 650 Magnetic Drum Data-Processing Machine is an early digital computer produced by IBM in the mid-1950s. It was the first mass produced computer in the world. Almost 2,000 systems were produced, the last in 1962, and it was the first ...
, 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 The IBM 704 is a large digital mainframe computer introduced by IBM in 1954. It was the first mass-produced computer with hardware for floating-point arithmetic. The IBM 704 ''Manual of operation'' states: The type 704 Electronic Data-Pro ...
in 1957. In ''A Discipline of Programming'' (1976),
Edsger Dijkstra Edsger Wybe Dijkstra ( ; ; 11 May 1930 – 6 August 2002) was a Dutch computer scientist, programmer, software engineer, systems scientist, and science essayist. He received the 1972 Turing Award for fundamental contributions to developing progra ...
attributed to Hamming the problem of efficiently finding
regular numbers Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 ×&nb ...
. The problem became known as "Hamming's problem", and the regular numbers are often referred to as Hamming numbers in Computer Science, 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."


Later life

Hamming served as president of the
Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ...
from 1958 to 1960. In 1960, he predicted that one day half of the Bell Lab's budget would be spent on computing. None of his colleagues thought that it would ever be so high, but his forecast actually proved to be too low. His philosophy on scientific computing appeared as the motto of his ''Numerical Methods for Scientists and Engineers'' (1962): In later life, Hamming became interested in teaching. Between 1960 and 1976, when he left the Bell labs, he held visiting or adjunct professorships at
Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
,
Stevens Institute of Technology Stevens Institute of Technology is a private research university in Hoboken, New Jersey. Founded in 1870, it is one of the oldest technological universities in the United States and was the first college in America solely dedicated to mechanical ...
, the
City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...
, the
University of California at Irvine The University of California, Irvine (UCI or UC Irvine) is a public land-grant research university in Irvine, California. One of the ten campuses of the University of California system, UCI offers 87 undergraduate degrees and 129 graduate and pr ...
and
Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
. As a Young Turk, Hamming had resented older scientists who had used up space and resources that would have been put to much better use by the young Turks. Looking at a commemorative poster of the Bell Labs' valued achievements, he noted that he had worked on or been associated with nearly all of those listed in the first half of his career at Bell Labs, but none in the second. He therefore resolved to retire in 1976, after thirty years. In 1976 he moved to the
Naval Postgraduate School The Naval Postgraduate School (NPS) is a public graduate school operated by the United States Navy and located in Monterey, California. It offers master’s and doctoral degrees in more than 70 fields of study to the U.S. Armed Forces, DOD ci ...
in
Monterey, California Monterey (; es, Monterrey; Ohlone: ) is a city located in Monterey County on the southern edge of Monterey Bay on the U.S. state of California's Central Coast. Founded on June 3, 1770, it functioned as the capital of Alta California under bo ...
, where he worked as an
Adjunct Professor An adjunct professor is a type of academic appointment in higher education who does not work at the establishment full-time. The terms of this appointment and the job security of the tenure vary in different parts of the world, however the genera ...
and
senior lecturer Senior lecturer is an academic rank. In the United Kingdom, Ireland, New Zealand, Australia, Switzerland, and Israel senior lecturer is a faculty position at a university or similar institution. The position is tenured (in systems with this concep ...
in
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
. He gave up research, and concentrated on teaching and writing books. He noted that: Hamming attempted to rectify the situation with a new text, ''Methods of Mathematics Applied to Calculus, Probability, and Statistics'' (1985). In 1993, he remarked that "when I left BTL, I knew that that was the end of my scientific career. When I retire from here, in another sense, it's really the end." And so it proved. He became
Professor Emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
in June 1997, 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. Hamming's final recorded lecture series is maintained by
Naval Postgraduate School The Naval Postgraduate School (NPS) is a public graduate school operated by the United States Navy and located in Monterey, California. It offers master’s and doctoral degrees in more than 70 fields of study to the U.S. Armed Forces, DOD ci ...
along with ongoing work that preserves his insights and extends his legacy.


Appearances

* Hamming takes part in the 1962 TV series ''The Computer and the Mind of Man''


Awards and professional recognition

*
Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...
,
Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ...
, 1968. * * Member of the
National Academy of Engineering The National Academy of Engineering (NAE) is an American nonprofit, non-governmental organization. The National Academy of Engineering is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy ...
, 1980. *
Harold Pender Award The Harold Pender Award, initiated in 1972 and named after founding Dean Harold Pender, is given by the Faculty of the School of Engineering and Applied Science of the University of Pennsylvania to an outstanding member of the engineering professio ...
,
University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
, 1981. *
IEEE Richard W. Hamming Medal The IEEE Richard W. Hamming Medal is presented annually to up to three persons, for outstanding achievements in information sciences, information systems and information technology. The recipients receive a gold medal, together with a replica in ...
, 1988. * Fellow of the
Association for Computing Machinery The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional member ...
, 1994. * Basic Research Award,
Eduard Rhein Foundation The Eduard Rhein Foundation was founded in 1976 in Hamburg (Germany) by Eduard Rhein. The goal of the foundation is to promote scientific research, learning, arts, and culture. This is done in particular by granting awards for outstanding achievemen ...
, 1996. The
IEEE Richard W. Hamming Medal The IEEE Richard W. Hamming Medal is presented annually to up to three persons, for outstanding achievements in information sciences, information systems and information technology. The recipients receive a gold medal, together with a replica in ...
, named after him, is an award given annually by the
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...
(IEEE), for "exceptional contributions to
information sciences Information science (also known as information studies) is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. ...
,
systems A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
and
technology Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, science, ...
", 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

* * ; second edition 1983

* * ; second edition 1986. * *: Unconventional introductory textbook which attempts to both teach calculus and give some idea of what it is good for at the same time. Might be of special interest to someone ''teaching'' an introductory calculus course using a conventional textbook in order to pick up some new pedagogical viewpoints. * * *: Entertaining and instructive. Hamming tries to extract general lessons—both personal and technical – to aid one in having a successful technical career by telling stories from his own experiences.


Notes


References

* * * * * * * * * * *


External links

* * {{DEFAULTSORT:Hamming, Richard 1915 births 1998 deaths 20th-century American mathematicians American information theorists Coding theorists Naval Postgraduate School faculty Numerical analysts Manhattan Project people Turing Award laureates Fellows of the Association for Computing Machinery Presidents of the Association for Computing Machinery Fellow Members of the IEEE University of Chicago alumni University of Illinois Urbana-Champaign alumni University of Nebraska–Lincoln alumni City College of New York faculty Scientists from Chicago University of Louisville faculty Mathematicians from Illinois