Editing Richard Hamming

{{short description|American mathematician and information theorist}}
{{distinguish|Richard Hammond}}
{{Use mdy dates|date=January 2025}}
{{good article}}
{{Infobox scientist
| name              = Richard Hamming
| image             = Richard Hamming.jpg
| image_size        =
| caption           = 
| birth_name        = Richard Wesley Hamming
| birth_date        = {{birth date|1915|2|11|mf=y}}
| birth_place       = Chicago, Illinois, U.S.
| death_date        = {{death date and age|mf=yes|1998|1|7|1915|2|11}}
| death_place       = [[Monterey, California]], U.S.
| field             = Mathematics
| work_institution  = {{hlist|[[University of Louisville]]|[[Manhattan Project]] (Los Alamos Laboratory, {{small|(1945-1946)}})|[[Bell Labs]] {{small|(1946–1976)}}|[[Naval Postgraduate School]] {{small|(1976–1998)}} }}
| education         = [[University of Chicago]] ([[Bachelor of Science|BS]])<br />[[University of Nebraska, Lincoln]] ([[Master of Arts|MA]])<br />[[University of Illinois, Urbana-Champaign]] ([[Doctor of Philosophy|PhD]])
| doctoral_advisor  = Waldemar Trjitzinsky
| thesis_title      = Some Problems in the Boundary Value Theory of Linear Differential Equations
| thesis_year       = 1942
| doctoral_students = 
| known_for         = {{hlist|[[Hamming code]]|[[Hamming window#Hamming window|Hamming window]]|[[Hamming numbers]]|[[Hamming distance]]|[[Hamming weight]]|[[Association for Computing Machinery]]}}
| awards            = [[Turing Award]] {{small|(1968)}}<br />[[IEEE Emanuel R. Piore Award]] {{small|(1979)}}<br />[[Harold Pender Award]] <small>(1981)</small> <br /> [[IEEE Richard W. Hamming Medal|IEEE Hamming Medal]] <small>(1988)</small>
| religion          = 
| signature         = <!--(filename only)-->
| footnotes         =  
}}

'''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 window|Hamming window]], [[Hamming numbers]], [[sphere-packing]] (or [[Hamming bound]]), [[Hamming graph]] concepts, and the [[Hamming distance]].

Born in Chicago, Hamming attended [[University of Chicago]], [[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 Labs|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 [[Turing Award]] in 1968, being its third recipient.<ref name="TuringAward">{{cite web |url=https://amturing.acm.org/award_winners/hamming_1000652.cfm |title=A.M. Turing Award, Richard W. Hamming |publisher=[[Association for Computing Machinery]] |access-date=August 1, 2022}}</ref>

After retiring from the 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,<ref name="IEEE">{{cite web |url=http://computer.org/computer-pioneers/hamming.html |archive-url=https://web.archive.org/web/20140903102828/https://www.computer.org/computer-pioneers/hamming.html |url-status=dead |archive-date=September 3, 2014 |title=Computer Pioneers – Richard Wesley Hamming |publisher=[[IEEE Computer Society]] |access-date=August 30, 2014}}</ref> the son of Richard J. Hamming, a credit manager, and Mabel G. Redfield.{{sfn|Carnes|2005|pp=220–221}} His father was [[Dutch people|Dutch]], and his mother was a [[Mayflower]] descendant.<ref>{{Cite book |last1=H. Loomis |first1=Herschel |url=https://nap.nationalacademies.org/read/10403/chapter/23 |title=Memorial Tributes: Volume 10 |last2=S. Potter |first2=David |publisher=[[National Academies Press]] |year=2002 |language=en |chapter=Richard W. Hamming|doi=10.17226/10403 |isbn=978-0-309-08457-4 }}</ref> He grew up in Chicago, where he attended [[Crane High School (Chicago)|Crane Technical High School]] and [[Malcolm X College|Crane Junior College]].{{sfn|Carnes|2005|pp=220–221}}

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,<ref name="ACM">{{cite web |url=http://amturing.acm.org/award_winners/hamming_1000652.cfm |title=Richard W. Hamming – A.M. Turing Award Winner |publisher=[[Association for Computing Machinery]] |access-date=August 30, 2014}}</ref> and received his Bachelor of Science degree in 1937.<ref name="IEEE" /> 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."<ref name="IEEE" />

He went on to earn a Master of Arts degree from the [[University of Nebraska]] in 1939, and then entered the [[University of Illinois at Urbana–Champaign]], where he wrote his doctoral thesis on ''Some Problems in the Boundary Value Theory of Linear Differential Equations'' under the supervision of [[Waldemar Trjitzinsky]].<ref name="ACM" /> His thesis was an extension of Trjitzinsky's work in that area. He looked at [[Green's function]] and further developed [[Jacob Tamarkin]]'s methods for obtaining [[Characteristic equation (calculus)|characteristic]] solutions.<ref name="St Andrews">{{cite web |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Hamming.html |title=Hamming biography |publisher=[[University of St Andrews]] |access-date=August 30, 2014}}</ref> While he was a graduate student, he discovered and read [[George Boole]]'s  ''[[The Laws of Thought]]''.{{sfn|Hamming|1998|p=643}}

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,<ref name="ACM" /> immediately after she was awarded her own Master of Arts in English literature. They would remain married until his death, and had no children.{{sfn|Carnes|2005|pp=220–221}} In 1944, he became an assistant professor at the [[J.B. Speed School of Engineering|J.B. Speed Scientific School]] at the [[University of Louisville]] in [[Louisville, Kentucky]].<ref name="ACM" />

== Manhattan Project ==
With [[World War II]] still ongoing, Hamming left Louisville in April 1945 to work on the [[Manhattan Project]] at the [[Los Alamos Laboratory]], in [[Hans Bethe]]'s division, programming the [[IBM]] [[calculating machines]] 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]], working for Bethe and [[Edward Teller]].<ref name="ACM" /> Hamming later recalled that:{{blockquote|Shortly before the first field test (you realize that no small scale experiment can be done—either you have a critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere." I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen—after all, there could be no experiments at the needed energy levels." He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, "What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?" I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, "Never mind, Hamming, no one will ever blame you."{{sfn|Hamming|1998|p=643}} }}

Hamming remained at Los Alamos until 1946, when he accepted a post at the  [[Bell Labs|Bell Telephone Laboratories]] (BTL). For the trip to New Jersey, he bought [[Klaus Fuchs]]'s old car. When he later sold it just weeks before Fuchs was unmasked as a spy, the [[FBI]] regarded the timing as suspicious enough to interrogate Hamming.{{sfn|Carnes|2005|pp=220–221}} Although Hamming described his role at Los Alamos as being that of a "computer janitor",{{sfn|Morgan|1998|p=972}} he saw [[computer simulation]]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".<ref name="IEEE" />

== Bell Laboratories ==
[[File:Hamming.jpg|thumb|upright=1.1|A two-dimensional visualisation of the [[Hamming distance]]. The color of each [[pixel]] indicates the [[Hamming distance]] between the [[binary representation]]s of its ''x'' and ''y'' coordinates, [[Modulo operation|modulo]] 16, in the 16-color system.]]
At the Bell Labs Hamming shared an office for a time with [[Claude Shannon]]. The Mathematical Research Department also included [[John Tukey]] and Los Alamos veterans Donald Ling and [[Brockway McMillan]]. Shannon, Ling, McMillan and Hamming came to call themselves the [[Young Turks (Bell Labs)|Young Turks]].<ref name="ACM" /> "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."<ref name="IEEE" />

Although Hamming had been hired to work on [[elasticity theory]], he still spent much of his time with the calculating machines.{{sfn|Morgan|1998|p=972}} 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.<ref name="Additional Materials" /> Digital machines manipulated information as sequences of zeroes and ones, units of information that Tukey would christen "[[bit]]s".{{sfn|Shannon|1948|p=379}} If a single bit in a sequence was wrong, then the whole sequence would be. To detect this, a [[parity bit]] 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."<ref name="Additional Materials">{{cite web |title=Richard W. Hamming Additional Materials |url=http://amturing.acm.org/info/hamming_1000652.cfm |publisher=[[Association for Computing Machinery]] |access-date=August 30, 2014}}</ref>

Hamming set himself the task of solving this problem,{{sfn|Carnes|2005|pp=220–221}} 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 (communication)|code word]] into another, which is today known as the [[Hamming distance]].{{sfn|Morgan|1998|pp=973–975}} Hamming thereby created a family of mathematical [[error-correcting code]]s, which are called [[Hamming code]]s. This not only solved an important problem in telecommunications and computer science, it opened up a whole new field of study.{{sfn|Morgan|1998|pp=973–975}}{{sfn|Hamming|1950|pp=147–160}}

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 (mathematics)|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.{{sfn|Ling|Xing|2004|pp=82–88}}{{sfn|Pless|1982|pp=21–24}}

Returning to [[differential equation]]s, Hamming studied means of numerically integrating them. A popular approach at the time was Milne's Method, attributed to [[Edward Arthur Milne|Arthur Milne]].<ref>{{cite web |last=Weisstein |first=Eric W. |title=Milne's Method |publisher=MathWorld |url=http://mathworld.wolfram.com/MilnesMethod.html |access-date=September 2, 2014}}</ref> 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 [[Linear multistep method|Adams method]].{{sfn|Morgan|1998|p=975}} He did extensive research into digital [[Filter (signal processing)|filters]], devising a new filter, the [[Hamming window]], and eventually writing an entire book on the subject, ''Digital Filters'' (1977).{{sfn|Morgan|1998|p=976–977}}

During the 1950s, he programmed one of the earliest computers, the [[IBM 650]], and with [[Ruth A. Weiss]] developed the [[L2 (programming language)|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.<ref>{{cite web |url=http://cm.bell-labs.com/cm/cs/cstr/99.html |archive-url=https://archive.today/20140902215751/http://cm.bell-labs.com/cm/cs/cstr/99.html |url-status=dead |archive-date=September 2, 2014 |title=Computing Science Technical Report No. 99 – A History of Computing Research at Bell Laboratories (1937–1975) |first1=Bernard D. |last1=Holbrook |first2=W. Stanley |last2=Brown |publisher=[[Bell Labs]] |access-date=September 2, 2014}}</ref>

In ''A Discipline of Programming'' (1976), [[Edsger Dijkstra]] attributed to Hamming the problem of efficiently finding [[regular numbers]].{{sfn|Dijkstra|1976|pp=129–134}} 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.<ref>{{cite web |url=http://c2.com/cgi/wiki?HammingProblem |title=Hamming Problem |publisher=Cunningham & Cunningham, Inc. |access-date=September 2, 2014}}</ref>

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."<ref name="IEEE" />

== Later life ==
Hamming served as president of the [[Association for Computing Machinery]] from 1958 to 1960.{{sfn|Morgan|1998|p=972}} In 1960, he predicted that one day half of the Bell Labs 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.{{sfn|Morgan|1998|p=977}} His philosophy on scientific computing appeared as the motto of his ''Numerical Methods for Scientists and Engineers'' (1962): {{blockquote|The purpose of computing is insight, not numbers.{{sfn|Hamming|1962|pp=vii, 276, 395}} }}

In later life, Hamming became interested in teaching. Between 1960 and 1976, when he left Bell Labs, he held visiting or adjunct professorships at [[Stanford University]], [[Stevens Institute of Technology]], the [[City College of New York]], the [[University of California at Irvine]] and [[Princeton University]].{{Sfnm|1a1=Carnes|1y=2005|1p=220–221|2a1=Tveito|2a2=Bruaset|2a3=Lysne|2y=2009|2p=59}} 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.<ref name="IEEE" />

In 1976 he moved to the [[Naval Postgraduate School]] in [[Monterey, California]], where he worked as an [[adjunct professor]] and [[senior lecturer]] in [[computer science]].{{sfn|Carnes|2005|pp=220–221}} He gave up research, and concentrated on teaching and writing books.<ref name="ACM" /> He noted that:
{{blockquote|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.<ref name="ACM" /> }}
Hamming attempted to rectify the situation with a new text, ''Methods of Mathematics Applied to Calculus, Probability, and Statistics'' (1985).<ref name="ACM" /> 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."<ref name="IEEE" /> And so it proved. He became [[Professor Emeritus]] in June 1997,<ref name="obit">{{cite news |url=http://www-history.mcs.st-and.ac.uk/Obits2/Hamming_NYTimes.html |newspaper=[[The New York Times]] |last=Fisher |first=Lawrence |date=January 11, 1998 |title=Richard Hamming, 82, Dies; Pioneer in Digital Technology |access-date=August 30, 2014 }}</ref> and delivered his last lecture in December 1997, just a few weeks before his death from a heart attack on January 7, 1998.{{sfn|Morgan|1998|p=972}} He was survived by his wife Wanda.<ref name="obit" />

Hamming's final recorded lecture series<ref>{{cite web |url=https://www.youtube.com/channel/UC6RujIChTIUawQ7WLCoogGA |title=Learning to Learn: The Art of Doing Science and Engineering lecture videos |publisher= [[Naval Postgraduate School]], YouTube |access-date=July 31, 2022}}</ref> is maintained by [[Naval Postgraduate School]] along with ongoing work<ref>{{cite web |url=https://hamming.nps.edu |title= Hamming Resources at NPS |publisher=[[Naval Postgraduate School]] |access-date=July 31, 2022}}</ref> that preserves his insights and extends his legacy.

== Awards and professional recognition ==
* [[Turing Award]], [[Association for Computing Machinery]], 1968.<ref>{{cite web |url=http://awards.acm.org/homepage.cfm?srt=all&awd=140 |title=A. M. Turing Award |publisher=[[Association for Computing Machinery]] |access-date=February 5, 2011 |url-status=dead |archive-url=https://web.archive.org/web/20091212132624/http://awards.acm.org/homepage.cfm?srt=all&awd=140 |archive-date=December 12, 2009 }}</ref>
*{{Awards|award=[[IEEE Emanuel R. Piore Award]]|year=1979|title="For introduction of error correcting codes, pioneering work in operating systems and programming languages, and the advancement of numerical computation."|role=|name=<ref>{{cite web |url=http://www.ieee.org/documents/piore_rl.pdf |title=IEEE Emanuel R. Piore Award Recipients |publisher=[[IEEE]] |access-date=March 20, 2021|archive-url=https://web.archive.org/web/20101124232834/http://ieee.org/documents/piore_rl.pdf |archive-date=November 24, 2010 |url-status=dead }}</ref>}}
* Member of the [[National Academy of Engineering]], 1980.<ref name="NAE">{{cite web|url=http://www.nae.edu/MembersSection/Directory20412/29268.aspx |title=NAE Members Directory – Dr. Richard W. Hamming |publisher=[[National Academy of Engineering]] |access-date=February 5, 2011}}</ref>
* [[Harold Pender Award]], [[University of Pennsylvania]], 1981.<ref>{{cite web |url=http://www.seas.upenn.edu/about-seas/lectures/pender.php |title=The Harold Pender Award |publisher=[[University of Pennsylvania School of Engineering and Applied Science|School of Engineering and Applied Science]], [[University of Pennsylvania]] |access-date=February 5, 2011 |archive-date=February 22, 2012 |archive-url=https://web.archive.org/web/20120222032929/http://www.seas.upenn.edu/about-seas/lectures/pender.php |url-status=dead }}</ref>
* [[IEEE Richard W. Hamming Medal]], 1988.<ref>{{cite web|url=http://www.ieee.org/documents/hamming_rl.pdf |archive-url=https://web.archive.org/web/20100620000223/http://ieee.org/documents/hamming_rl.pdf |url-status=dead |archive-date=June 20, 2010 |title=IEEE Richard W. Hamming Medal Recipients |publisher=[[IEEE]] |access-date=February 5, 2011}}</ref>
* Fellow of the [[Association for Computing Machinery]], 1994.<ref>{{cite web |url=http://fellows.acm.org/homepage.cfm?alpha=H&srt=alpha |title=ACM Fellows – H |publisher=[[Association for Computing Machinery]] |access-date=February 5, 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110124181313/http://fellows.acm.org/homepage.cfm?alpha=H&srt=alpha |archive-date=January 24, 2011 }}</ref>
* [[Eduard Rhein Award|Basic Research Award]], [[Eduard Rhein Foundation]], 1996.<ref>{{cite web |url=http://www.eduard-rhein-stiftung.de/html/Preistraeger_e.html |title=Award Winners (chronological) |publisher=[[Eduard Rhein Foundation]] |access-date=February 5, 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110718233021/http://www.eduard-rhein-stiftung.de/html/Preistraeger_e.html |archive-date=July 18, 2011 }}</ref>
<!-- * [[The Franklin Institute Awards|Certificate of Merit]], [[Franklin Institute]], 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]], [[information systems|systems]] and [[information technology|technology]]", and he was the first recipient of this medal.<ref>{{cite web|url=http://www.ieee.org/about/awards/medals/hamming.html |archive-url=https://web.archive.org/web/20100407141828/http://www.ieee.org/about/awards/medals/hamming.html |url-status=dead |archive-date=April 7, 2010 |title=IEEE Richard W. Hamming Medal |publisher=[[IEEE]] |access-date=February 5, 2011}}</ref> The reverse side of the medal depicts a Hamming parity check matrix for a Hamming error-correcting code.{{sfn|Morgan|1998|p=972}}

== Bibliography ==
* {{cite book |last=Hamming|first=Richard W. |title=Numerical Methods for Scientists and Engineers |url=https://archive.org/details/numericalmethods0000hamm|url-access=registration|location=New York |publisher=McGraw-Hill |year=1962|ref=none}}; [https://books.google.com/books/about/Numerical_Methods_for_Scientists_and_Eng.html?id=Y3YSCmWBVwoC second edition 1973]
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Calculus and the Computer Revolution |location=Boston |publisher=Houghton-Mifflin |year=1968}}
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Introduction To Applied Numerical Analysis |url=https://archive.org/details/introductiontoap0000hamm|url-access=registration|location=New York |publisher=McGraw-Hill |year=1971|isbn=9780070258891 }}; Hemisphere Pub. Corp reprint 1989; [https://books.google.com/books/about/Introduction_to_Applied_Numerical_Analys.html?id=osnZ9eiO-ngC Dover reprint 2012]
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Computers and Society |url=https://archive.org/details/computerssociety0000hamm|url-access=registration|location=New York |publisher=McGraw-Hill |year=1972}}
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Digital Filters |location=Englewood Cliffs, New Jersey |publisher=Prentice Hall |year=1977 |isbn=978-0-13-212571-0 }}; second edition 1983; [https://books.google.com/books/about/Digital_Filters.html?id=GQv9UOdeW9cC third edition 1989].
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=The Unreasonable Effectiveness of Mathematics |location=Washington, D.C. |publisher=The American Mathematical Monthly |year=1980}}
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Coding and Information Theory |location=Englewood Cliffs, New Jersey |publisher=Prentice Hall |year=1980|isbn=978-0-13-139139-0 }}; second edition 1986.
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=Methods of Mathematics Applied to Calculus, Probability, and Statistics |url=https://archive.org/details/methodsofmathema0000hamm|url-access=registration|location=Englewood Cliffs, New Jersey |publisher=Prentice Hall |year=1985 |isbn=978-0-13-578899-8 }}
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=The Art of Probability for Scientists and Engineers |location=Redwood City, California |publisher=Addison-Wesley |year=1991 |isbn=978-0-201-51058-4 }}
* {{cite book |last=Hamming|first=Richard W. |author-mask=1 |title=[[The Art of Doing Science and Engineering]]: Learning to Learn |location=Australia |publisher=Gordon and Breach |year=1997 |isbn=978-90-5699-500-3}}

== Lectures ==

* 1991 - [https://library.ucsd.edu/dc/object/bb4096852z 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 ==
{{Reflist|30em}}

== References ==
* {{cite book
|last = Carnes
|first= Mark C.
|year = 2005
|title = American National Biography. Supplement 2.
|location= New York
|publisher=Oxford University Press
|isbn= 978-0-19-522202-9
}}
* {{cite book
|last=Dijkstra
|first=Edsger W.
|author-link=Edsger W. Dijkstra
|title=A Discipline of Programming
|year=1976
|location=Englewood Cliffs, New Jersey
|publisher=Prentice-Hall
|isbn=978-0-13-215871-8
|url=https://archive.org/details/disciplineofprog0000dijk
|access-date=September 2, 2014
|url-access=registration
}}
* {{cite journal
|last = Hamming
|first = Richard W.
|mr = 0035935
|journal = [[Bell System Technical Journal]]
|pages = 147–160
|title = Error detecting and error correcting codes
|url = http://www.caip.rutgers.edu/~bushnell/dsdwebsite/hamming.pdf
|archive-url = https://web.archive.org/web/20060525060427/http://www.caip.rutgers.edu/~bushnell/dsdwebsite/hamming.pdf
|archive-date = May 25, 2006
|volume = 29
|issue = 2
|year = 1950
|doi=10.1002/j.1538-7305.1950.tb00463.x
|hdl = 10945/46756
|s2cid = 61141773
}}
* {{cite book
|last=Hamming
|first=Richard
|title=Numerical Methods for Scientists and Engineers
|year=1962
|location=New York
|publisher=McGraw-Hill
}} Reprinted, Dover Publications, 1986, {{isbn|978-0-486-65241-2}}.
* {{cite journal
|last=Hamming
|first=Richard
|title=The Unreasonable Effectiveness of Mathematics
|url=http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
|year=1980
|journal=[[American Mathematical Monthly]]
|volume=87
|doi=10.2307/2321982
|pages=81–90
|jstor=2321982
|issue=2
|hdl=10945/55827
|access-date=September 12, 2006
|archive-date=February 3, 2007
|archive-url=https://web.archive.org/web/20070203151259/http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
|url-status=dead
|hdl-access=free
}}
* {{cite journal
|last=Hamming
|first=Richard
|title=Mathematics on a Distant Planet
|journal=[[American Mathematical Monthly]]
|date=August–September 1998
|volume=105
|issue=7
|pages=640–650
|url=https://www.dropbox.com/s/xf0efns895cw98x/1998-hamming.pdf
|doi=10.2307/2589247
|jstor=2589247
}}
* {{cite book
|last1=Ling
|first1=San
|first2=Chaoping
|last2=Xing
|year=2004
|title=Coding Theory: a First Course
|location=Cambridge
|publisher=Cambridge University Press
|isbn= 978-0-521-82191-9
}}
* {{cite journal
|last=Morgan
|first=Samuel P.
|title=Richard Wesley Hamming (1915–1998)
|journal=Notices of the AMS
|date=September 1998
|volume=45
|issue=8
|pages=972–977
|issn=0002-9920
|url=https://www.ams.org/notices/199808/mem-morgan.pdf |archive-url=https://web.archive.org/web/20040215065757/http://www.ams.org/notices/199808/mem-morgan.pdf |archive-date=February 15, 2004 |url-status=live
|access-date=August 30, 2014
}}
* {{cite book
|last=Pless
|first=Vera
|author-link=Vera Pless
|year=1982
|title= Introduction to the Theory of Error-Correcting Codes
|title-link= Introduction to the Theory of Error-Correcting Codes
|location=New York
|publisher=Wiley
|isbn=978-0-471-08684-0
}}
* {{cite journal
|last=Shannon
|first=Claude
|title=A Mathematical Theory of Communication
|journal=The Bell System Technical Journal
|issue=3
|pages=379–423, 623–656
|date=July 1948
|volume=27
|doi=10.1002/j.1538-7305.1948.tb01338.x
|hdl=11858/00-001M-0000-002C-4314-2
|url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
|access-date=September 2, 2014
|archive-url=https://web.archive.org/web/20150328051218/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
|archive-date=March 28, 2015
|hdl-access=free
}}
* {{cite book
|last1=Tveito
|first1=Aslak
|last2=Bruaset
|first2=Are Magnus
|last3= Lysne
|first3=Olav
|year=2009
|title=Simula Research Laboratory: By Thinking Constantly about it
|location=New York
|publisher=Springer Science & Business Media
|isbn=978-3-642-01156-6
|page=59
}}

== External links ==
{{Wikiquote}}
* {{MacTutor Biography|id=Hamming}}
* {{MathGenealogy |id=4556}}

{{Richard W. Hamming Medal recipients}}
{{Turing award}}
{{Authority control}}
{{Portal bar|Biography|United States|Mathematics}}

{{DEFAULTSORT:Hamming, Richard}}
[[Category:1915 births]]
[[Category:1998 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:American information theorists]]
[[Category:American people of Dutch descent]]
[[Category:Coding theorists]]
[[Category:Naval Postgraduate School faculty]]
[[Category:Numerical analysts]]
[[Category:Manhattan Project people]]
[[Category:Turing Award laureates]]
[[Category:1994 fellows of the Association for Computing Machinery]]
[[Category:Presidents of the Association for Computing Machinery]]
[[Category:Fellows of the IEEE]]
[[Category:University of Chicago alumni]]
[[Category:University of Illinois Urbana-Champaign alumni]]
[[Category:University of Nebraska–Lincoln alumni]]
[[Category:City College of New York faculty]]
[[Category:Scientists from Chicago]]
[[Category:University of Louisville faculty]]
[[Category:Mathematicians from Illinois]]
[[Category:Crane High School (Chicago) alumni]]