Jerzy Neyman (1894-1981) was a scholar, teacher, and pioneer of statistical mathematics and probability. He helped establish the field of statistical mathematics through the innovative Neyman-Pearson theory and by being a tireless advocate for its legitimacy.

# Jerzy Neyman

Neyman was born on April 16, 1894, in Bendery, Russia. He was the second of four children of Czeslaw Splawa-Neyman and Kazimiera Lutoslawaska, who were Polish and Roman Catholics. Neyman's father was a judge, and the family frequently moved about Russia as required by his father's occupation. Neyman did not begin his formal education until he was ten, when he enrolled in school in Simferopol, located in Crimea. Although he lagged behind his classmates in Russian history and geography, young Neyman displayed advanced knowledge of Polish, Russian, French, German, and Ukranian, among other subjects.

In 1906, Neyman's father died suddenly of a heart attack. To secure an income, Neyman's mother moved the family to Kharkov in the Ukraine, where she was employed as the manager of an estate belonging to her late husband's relatives. Enrolling in the local school, Neyman proved a superior student and graduated in 1912.

## Moved to Poland

Neyman entered the University of Kharkov (later Maxim Gorki University). Although he intended to study mathematics, he was temporarily drawn to physics by the groundbreaking work of Albert Einstein and Marie Curie. However, when Neyman was introduced to the advancements in calculus made by French mathematician Henri-Leon Lebesgue, he refocused his studies on mathematics and continued in the field for the remainder of his life. Although he did not meet Lebesgue until 1926, Neyman considered him his mentor. For his undergraduate thesis he submitted a paper entitled "Integral of Lebesgue," which was awarded a gold medal. He also studied mathematics and probability under S. N. Berstein. Graduating in September 1917, Neyman enrolled in the graduate school in mathematics at the University of Kharkov and also became a lecturer in mathematics at the Kharkov Institute of Technology.

The next four years were eventful for Neyman. It was a turbulent period politically in Russia, with the Communist Revolution and subsequent turmoil. During the Russian-Polish conflict, Neyman was imprisoned for a time as an enemy of the state due to his Polish heritage. He also was arrested for selling matches on the black market. On May 4, 1920, Neyman married Olga Solodovnikova, a Russian of the Orthodox faith.

Although official academic degrees were no longer bestowed under Soviet rule, examinations were still given as evidence of educational achievements. In the fall of 1920, Neyman passed the examinations for his master's degree at the University of Kharkov and remained at the university to teach a variety of mathematical courses. However, by the end of his first year of teaching, Neyman received word that he was about to be arrested again. As a result, he moved with his wife, mother, and grandmother out of Russia to Poland.

## Early Work in Mathematics

In Poland, he accepted a position as the senior statistical assistant for the National Agricultural Institute in Bydgoszcz. During the two years he spent there, Neyman began working on numerous papers that applied mathematical probability to agricultural problems.

In 1923 Neyman accepted an offer to direct the Biometric Laboratory of the Nencki Institute for Experimental Biology in Warsaw and began lecturing at the Central College of Agriculture in Warsaw. He also continued his advanced studies and graduated with his doctoral degree in mathematics from the University of Warsaw in 1924. Continuing his interest in statistical probability, Neyman submitted his dissertation in two papers that addressed issues of probability related to agricultural experimentation. Written in Polish and summarized in French, the papers were titled "On the Applications of the Theory of Probability to Agricultural Experiments" and "Memoir on the Application of Mathematical Statistics on Resolving Some Agricultural Problems." The papers provided a careful analysis of problems in estimation, including a preliminary discussion of "true value." However, because Neyman was at that time unaware of groundbreaking statistical work being done in England, the impact of his work was limited.

Having received his Ph.D., Neyman began teaching mathematical and statistical courses at the University of Warsaw, the Central College of Agriculture, and the University of Kharkov. In the fall of 1925, with the help of a postdoctoral fellowship from the University of Warsaw, Neyman traveled to London to study at the Biometric Laboratory at University College. The laboratory was run by Karl Pearson, author of the influential mathematical work *Grammar of Science* and commonly considered the founder of modern statistics. During his year in London, Neyman worked with those on the leading edge of mathematics, including William S. Gosset.

## The Neyman-Pearson Theory

Neyman's most influential relationship in London was with Karl Pearson's son, Egon Pearson, with whom he would collaborate in the study of hypothesis testing, leading to significant advancements in modern statistical methodology. The two decided to continue their investigation via letters and occasional meetings. What resulted from their combined work between 1928 and 1933 became known as the Neyman-Pearson theory, or the Neyman-Pearson fundamental lemma. Their first joint paper was published in 1928. It was followed by a series of ten published papers that culminated in 1933 with the publication of "On the Problem of the Most Efficient Tests of Statistical Hypotheses." According to L. E. Lehmann in "The Neyman-Pearson Theory After Fifty Years," his contribution to the *Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer* (1985), "Despite the fact that these ideas had their forerunners in the work of [English mathematician R. A.] Fisher, the Neyman-Pearson paradigm formulated for the first time a clear program and provided a completely novel approach to hypothesis testing, the first 'exact' small-sample theory of its kind."

The goal of the Neyman-Pearson theory is to draw conclusions regarding a hypothesis even though there exists the possibility of error. Neyman and Pearson distinguished two error types. A Type I error occurs when a true hypothesis is deemed false (false negatives), and a Type II error occurs when a false hypothesis is deemed true (false positives). When a decision must be made under uncertain conditions, Neyman's methodology provided a means to lessen the occurrence of error, even when the outcome was based solely on chance, by establishing what Neyman referred to as "confidence intervals."

## Economic Struggles

In 1926 Neyman continued his postdoctoral studies, spending the academic year in Paris with the support of a Rockefeller Fellowship. The next year he returned to Poland and assumed his position as faculty docent at the University of Warsaw. He also worked diligently to establish a small biometric laboratory at the Nencki Institute for Experimental Biology. Although his fame as a mathematician and statistician eventually placed him among the elite of the academic world, he was never offered a full professorship in Poland, and his economic situation in Poland proved precarious. In "The Neyman-Pearson Story: 1926-1934," an article in *Research Papers in Statistics* (1966), Egon Pearson quotes Neyman from a personal letter, dated June 23, 1932: "I simply cannot work; the crisis and the struggle for existence takes all my time and energy. I am not sure that next year I shall not be obliged to take some job, I do not know where—in trade, perhaps, selling coal or handkerchiefs."

At the end of 1933, Pearson invited Neyman to join him on the faculty of the University College in London, and Neyman accepted. At first he was a visiting professor, but in 1935 he was promoted to reader. In 1936 he was given a full professorship and put in charge of the university's statistical laboratory. During his tenure at University College, Neyman wrote two significant papers. One, published in 1934, laid the foundation for the sampling techniques that subsequently influenced the development of modern day public opinion polling. The other, published in 1937, expounded on his theory of confidence intervals. Neyman applied his statistical probability methodology, using randomized testing, to such practical areas as the spread of disease during epidemics, agricultural problems, and issues in chemistry, biology, physics, and medicine.

## Years at Berkeley

After a successful speaking tour of the United States in 1937, Neyman the following year accepted an offer from the University of California at Berkeley to join its faculty as a professor of statistical mathematics and to start a statistical laboratory. Neyman remained associated with the University of California for the remainder of his life. Although he was eager to establish his program at the university, World War II interrupted his plans, and by March 1942, Neyman had turned his attention to military research, namely bomb sights and targeting accuracy and patterns. In 1944, Neyman became a citizen of the United States. In 1950 he and wife, with whom he had one child, separated. They never legally divorced and lived within several miles of each other.

Once his attention was returned to the development of statistical studies at the University of California and its Berkeley Statistical Laboratory, Neyman methodically developed his work. Known as a generous and personable man, Neyman was steadfast in creating an intellectually superior program in mathematical statistics. In 1945 he established the Berkeley Symposia in Mathematical Statistics and Probability, which drew the best statistical minds in the world as speakers. He also diligently pressed University officials for recognition, funding, and resources for his work. In 1954, he succeeded in establishing the Department of Statistics as a separate program, and he was named as chair of the new department. None of his publications, during his tenure at Berkeley, had the impact of his previous published work. Yet he made an indelible mark on the field of statistics and probability as mentor and teacher to 39 Ph.D. students, several of whom became leading statisticians at Berkeley, including Erich Lehmann, Joseph Hodges, and Elizabeth Scott. Neyman retired from teaching at Berkeley in 1961 but remained as director of the Statistical Laboratory.

Neyman was highly influential in the development of statistical mathematics as both a scholar of original thought and as an ambassador for the field of study. His personality won him many friends and inspired him to take some difficult stands on issues outside the field of mathematics. After World War II, when the University of California required all faculty members to sign loyalty oaths, stating that they were not involved in any activities to overthrow the U.S. government, Neyman, who signed the oath, nonetheless supported those who refused to sign it. In the 1960s he became involved in the opposition to American involvement in the war in Vietnam.

For his numerous and important contributions, Neyman was awarded the Cleveland Prize of the American Association for the Advancement of Science in 1958 and the Samuel S. Wilks Medal by the American Statistical Association in 1964. He refused to attend the 1964 medal ceremony because it was held at an army base. In 1968, he was given the National Medal of Science. He was also the recipient of honorary degrees from the University of Chicago (1953), the University of California at Berkeley (1963), the University of Stockholm (1964), and the University of Warsaw (1974). Neyman remained active until the end of his life. He died of a heart attack on August 5, 1981, in Oakland, California.

## Books

*American Men and Women of Science,* Jacques Cattell Press/R.R. Bowker Co., 1972.

*American National Biography,* Volume 16, edited by John A. Garraty and Mark C. Carnes, Oxford University Press, 1999.

*McGraw-Hill Modern Scientists and Engineers,* edited by Jay E. Greene, McGraw-Hill, 1980.

*Proceedings of the Berkeley Conference in Honor of Jerzy Newman and Jack Kiefer,* Volume 1, edited by Lucien Le Cam and Richard A. Olshen, Wadsworth, 1985.

*Research Papers in Statistics,* edited by F.N. David, John Wiley and Sons, 1966.

## Online

"Jerzy Neyman," *Contemporary Authors Online,* http://www.galenet.com (January 18, 2001).

"Jerzy Neyman," *The Scribner Encyclopedia of American Lives, Volume 1: 1981-1985,* http://www.galenet.com (January 18, 2001).