#### Pioneering mathematician who transformed the use of statistics

The American John Tukey, who has died aged 85, was among the most inventive pure and applied mathematicians of the last 50 years. One of the most influential statisticians of his generation, he developed wide-ranging theories and ingenious techniques to analyse masses of complex data and compute series of numbers quickly.

His pioneering work for teasing out the hidden patterns and correlations in large amounts of data -- now called data mining -- had a profound impact in fields as diverse as electrical engineering, operations research, financial and business risk management, and the social sciences.

The early work for which Tukey was probably best known among his peers was his collaboration in 1965 with James Cooley, then working for IBM. Together, they developed the fast fourier transform, an algorithm (or mathematical procedure run on a computer) that was applicable to a wide range of physical sciences and engineering research. It helped astronomers, for example, to determine the spectrum of light from a star more quickly than previously possible.

An inspirational teacher, Tukey always told his students that "an approximate answer to the right question is worth a great deal more than a precise answer to the wrong question". His later work, on what statisticians call robust analysis, found ways of reaching credible conclusions even when working with flawed data.

The ideas and techniques he generated between 1946 and 1984, gathered in the eight volumes of The Collected Works Of John W Tukey, were the fruits of a career in which he held simultaneous posts as professor of statistics at Princeton University, and a researcher at the renowned Bell Laboratories. His work covered statistical topics, such as spectrum analysis, multiple comparisons and exploratory data analysis. His genius ranks alongside the like of Alan Turing in the advances he brought to communication theory and computing.

In 1944, Tukey coined the term "bit," an abbreviation of "binary digit", to describe the 1s and 0s that are the basis of the binary code in which all digital computer programs are produced. He was also credited with conceiving the word "software".

No stranger to controversy, Tukey was prepared to support unfashionable causes. In the 1950s, he attacked Alfred Kinsey's research on sexual behaviour, the conclusions of which he believed were seriously flawed because they relied on a sample of people who knew each other. Tukey said a random selection of three people would have been better than a group of 300 chosen by Kinsey.

In the 1970s, Tukey chaired a research committee that warned of the damage to the ozone layer from aerosol sprays. More recently, he recommended that the 1990 US census be adjusted by statistical formulae to compensate for the huge numbers of poor urban residents whom he believed it had missed. Always eager to apply statistics to new questions, from 1960 to 1980 he helped design the polls used by the NBC television network to predict and analyse American elections.

Tukey was born the only son of teachers in New Bedford, Massachusetts. His parents believed his talent would be best developed if he was educated at home, so his formal education began only when he entered Brown University, at Providence, Rhode Island. He graduated with a first in mathematics and chemistry and, in 1937, went to Princeton, where he obtained a PhD in mathematics in 1939 for a thesis on denumerability in topology.

During the second world war, he was engaged on strategic research that involved statistics, work he found fascinating, especially since it involved rubbing shoulders with other statisticians recruited to Princeton for the war effort. In particular, he met William Cochran, the brilliant Cambridge mathematician, who had moved to the US.

For Tukey, this was the start of a long and fruitful exchange of ideas with Cochran and other senior researchers. In 1945, he was offered a post in statistics within the mathematics department at Princeton, and, at the age of 35, was made a full professor. In 1965, he became founding chairman of Princeton's statistics department. One post was not, however, enough to absorb his energy, and, in 1945, he also joined Bell Laboratories.

The modern science of statistics is more than 100 years old. Tukey believed that, after the first 40 years, its practitioners lost sight of its original objectives of finding methods of analysing data that described patterns, trends, and relationships, and detected anomalies. In 1962, he maintained that mathematical statistics was ignoring real-world data analysis. He urged a return to the origins of scientific statistics, using modern methods in which the statistical description of the data was paramount.

Tukey proved his case by developing exploratory data analysis, a philosophy that returned to the original goals of statistics, but relied on modern computer methods. It is now a widely accepted technique, due, in large part, to the growth in desktop computers and the explosion of data for which traditional statistics is not suitable.

With an emphasis on graphic display, it initially gave mathematicians new ways to analyse and present data clearly. More refined versions of the technique let people with no statistical expertise discover what patterns, relationships or trends might lie hidden in the data they needed to examine.

One of those tools, the stem-and-leaf display, remains in the high school curriculum. Students use the technique to arrange a series of data points in rows and columns, and then make judgments about what techniques -- such as calculating the average or median -- would allow them to analyse the information intelligently. The method of displaying data confirmed Tukey's belief that mathematicians should start with their data, and then look for a theorem to interpret it.

Over the years, he became a hub for regular scientific meetings of a group of Princeton professors, including Lyman Spitzer, who inspired the Hubble space telescope. In his work on the philosophy of statistics and of research, Tukey balanced the usefulness and limitation of mathematical statistics.

Tukey had no immediate survivors. Elizabeth, his wife of 48 years, died in 1998.

[John Wilder Tukey, mathematician, born June 16 1915; died July 26 2000]

Pearce Wright, Wednesday August 16, 2000 © Guardian Newspapers Limited