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John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...
, best known for the development of the fast Fourier Transform (FFT) algorithm and
box plot In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are ca ...
. The Tukey range test, the
Tukey lambda distribution Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not us ...
, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term ''
bit The bit is the most basic unit of information in computing and digital communication. 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 represented as ...
'' and the first published use of the word ''
software Software consists of computer programs that instruct the Execution (computing), execution of a computer. Software also includes design documents and specifications. The history of software is closely tied to the development of digital comput ...
''.


Biography

Tukey was born in
New Bedford, Massachusetts New Bedford is a city in Bristol County, Massachusetts, United States. It is located on the Acushnet River in what is known as the South Coast region. At the 2020 census, New Bedford had a population of 101,079, making it the state's ninth-l ...
, in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a
B.A. A Bachelor of Arts (abbreviated B.A., BA, A.B. or AB; from the Latin ', ', or ') is the holder of a bachelor's degree awarded for an undergraduate program in the liberal arts, or, in some cases, other disciplines. A Bachelor of Arts degree ...
in 1936 and
M.S. A Master of Science (; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine ...
in 1937 in chemistry, from
Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...
, before moving to
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
, where in 1939 he received a
PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
in
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
after completing a doctoral dissertation titled "On
denumerability In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers ...
in
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
". During
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, Tukey worked at the Fire Control Research Office and collaborated with Samuel Wilks and William Cochran. He is claimed to have helped design the U-2 spy plane. After the war, he returned to Princeton, dividing his time between the university and
AT&T Bell Laboratories Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...
. In 1962, Tukey was elected to the
American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...
. He became a full professor at 35 and founding chairman of the Princeton statistics department in 1965. Among many contributions to
civil society Civil society can be understood as the "third sector" of society, distinct from government and business, and including the family and the private sphere.American Statistical Association The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts, on November 27, 1839, and is the second-oldest continuous ...
that produced a report critiquing the statistical methodology of the
Kinsey Report The Kinsey Reports are two scholarly books on human sexual behavior, ''Sexual Behavior in the Human Male'' (1948) and ''Sexual Behavior in the Human Female'' (1953), written by Alfred Kinsey, Wardell Pomeroy, Clyde Martin, and (for ''Sexual Beh ...
, ''Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male'', which summarized "A random selection of three people would have been better than a group of 300 chosen by Mr. Kinsey". From 1960 to 1980, Tukey helped design the NBC television network polls used to predict and analyze elections. He was also a consultant to the Educational Testing Service, the Xerox Corporation, and Merck & Company. During the 1970s and early 1980s, Tukey played a key role in the design and conduct of the
National Assessment of Educational Progress The National Assessment of Educational Progress (NAEP) is the largest continuing and nationally representative assessment of what U.S. students know and can do in various subjects. NAEP is a congressionally mandated project administered by the ...
. He was awarded the
National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavior ...
by President Nixon in 1973. He was awarded the
IEEE Medal of Honor The IEEE Medal of Honor is the highest recognition of the American Institute of Electrical and Electronics Engineers (IEEE). It has been awarded since 1917, and is presented to an individual or team of up to three who have made exceptional contri ...
in 1982 "For his contributions to the spectral analysis of random processes and the
fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in ...
(FFT)
algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
". Tukey retired in 1985. He died in
New Brunswick, New Jersey New Brunswick is a city (New Jersey), city in and the county seat of Middlesex County, New Jersey, Middlesex County, in the U.S. state of New Jersey.statistical Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
methods for computers at
Bell Labs Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...
, where he coined the word ''bit'' in 1947. His statistical interests were many and varied. He is particularly remembered for his development with
James Cooley James William Cooley (September 18, 1926 – June 29, 2016) was an American mathematician. Cooley received a B.A. degree in 1949 from Manhattan College, Bronx, NY, an M.A. degree in 1951 from Columbia University, New York, NY, and a Ph.D. degree ...
of the
Cooley–Tukey FFT algorithm The Cooley–Tukey algorithm, named after James Cooley, J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite number, composite size ...
. In 1970, he contributed significantly to what is today known as the jackknife—also termed Quenouille–Tukey jackknife. He introduced the
box plot In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are ca ...
in his 1977 book, "Exploratory Data Analysis".
Tukey's range test Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, : Also occasionally described as "honestly", see e.g. is a single-step multiple comparison p ...
, the
Tukey lambda distribution Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not us ...
,
Tukey's test of additivity In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA ( regression analysis involving two qualitative factors) to assess whether the factor variables ( categorical variables) are additively related to ...
, Tukey's lemma, and the
Tukey window In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a function (mathematics), mathematical function that is zero-valued outside of some chosen interval (mathematics), interval. T ...
all bear his name. He is also the creator of several little-known methods such as the
trimean In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: : TM= \frac This is equivalent to the arithmetic mean of ...
and median-median line, an easier alternative to
linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
. In 1974, he developed, with
Jerome H. Friedman Jerome Harold Friedman (born December 29, 1939) is an American statistician, consultant and Professor of Statistics at Stanford University, known for his contributions in the field of statistics and data mining.
, the concept of the
projection pursuit Projection pursuit (PP) is a type of statistical technique that involves finding the most "interesting" possible projections in multidimensional data. Often, projections that deviate more from a normal distribution are considered to be more intere ...
.


Data analysis and foundations of data science

John Tukey contributed greatly to statistical practice and data analysis in general. In fact, some regard John Tukey as the father of data science. At the very least, he pioneered many of the key foundations of what came later to be known as data science. Making sense of data has a long history and has been addressed by statisticians, mathematicians, scientists, and others for many many years. During the 1960s, Tukey challenged the dominance at the time of what he called "confirmatory data analysis", statistical analyses driven by rigid mathematical configurations. Tukey emphasized the importance of having a more flexible attitude towards data analysis and of exploring data carefully to see what structures and information might be contained therein. He called this "exploratory data analysis" (EDA). In many ways, EDA was a precursor to data science. Tukey also realized the importance of computer science to EDA. Graphics are an integral part of EDA methodology and, while much of Tukey's work focused on static displays (such as box plots) that could be drawn by hand, he realized that computer graphics would be much more effective for studying multivariate data. PRIM-9, the first program for viewing multivariate data, was conceived by him during the early 1970s. This coupling of data analysis and computer science is what is now called data science. Tukey articulated the important distinction between
exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or ...
and
confirmatory data analysis A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. T ...
, believing that much statistical methodology placed too great an emphasis on the latter. Though he believed in the utility of separating the two types of analysis, he pointed out that sometimes, especially in
natural science Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...
, this was problematic and termed such situations
uncomfortable science Uncomfortable science, as identified by statistician John Tukey, comprises situations in which there is a need to draw an inference from a limited sample of data, where further samples influenced by the same cause system will not be available. Mor ...
. A. D. Gordon offered the following summary of Tukey's principles for statistical practice: Tukey's lectures were described to be unusual. McCullagh described his lecture given in London in 1977:


Coining the term ''bit''

While working with
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
on early computer designs, Tukey introduced the word ''
bit The bit is the most basic unit of information in computing and digital communication. 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 represented as ...
'' as a portmanteau of ''binary digit''. The term ''bit'' was first used in an article by
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...
in 1948.


See also

*
List of pioneers in computer science This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do. Pioneers ~ Items marked with a tilde are circa dates. See also * Computer Pioneer Award * IEEE John von ...


Publications

* * * * * * * * * * * * * ; ''The collected works of John W Tukey'', edited by William S. Cleveland * * * * * * * * ;About John Tukey *
Interview of John Tukey about his experience at Princeton


References


External links


Royal Society obit. by Peter McCullagh

John W. Tukey: His Life and Professional Contributions
published in ''The Annals of Statistics''
John Wilder Tukey (1915–2000)
in ''
Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...
''
Memories of John Tukey


by Mary Bittrich *
"Remembering John W. Tukey"
special issue of ''
Statistical Science ''Statistical Science'' is a review journal published by the Institute of Mathematical Statistics. The founding editor was Morris H. DeGroot, who explained the mission of the journal in his 1986 editorial: "A central purpose of ''Statistical Sci ...
'' {{DEFAULTSORT:Tukey, John Wilder 1915 births 2000 deaths People from Massachusetts National Medal of Science laureates Presidents of the Institute of Mathematical Statistics Fellows of the American Statistical Association IEEE Medal of Honor recipients American statisticians Survey methodologists Exploratory data analysis Princeton University faculty Princeton University alumni Brown University alumni Burials at Princeton Cemetery Foreign members of the Royal Society Members of the United States National Academy of Sciences 20th-century American mathematicians Computational statisticians Members of the American Philosophical Society