# Probability in the Department of Mathematics at Cornell: a brief history

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Florian Cajori’s wonderful account of the state of mathematics departments and mathematics higher education in the United States around 1890 tells us that, at Cornell, during the academic year 1888–1889, an elective course titled Theory of Probabilities and of Distribution of Errors was taught by Professor Oliver and Jones. James Oliver, the second chair of the Department of Mathematics and a member of the National Academy of Science, was interested in all kinds of applications of mathematics and the description of this elective course in probability mentions applications to sociology.

In 1902, Henry Lewis (Louis) Rietz received his Ph.D. from Cornell working in group theory under George Miller. After taking a position at the University of Illinois, Rietz developed a keen interest in actuarial science and mathematical statistics. In 1918, he joined the University of Iowa where he served until is retirement in 1948. Rietz is recognized as one of the key figures in the emergence and growth of statistical science in the United States. Rietz served as president of the Mathematical Association of America in 1924, vice-president of the American Statistical Association in 1925, and vice-president of the American Mathematical Society in 1928. He participated in the creation of the Institute of Mathematical Statistics and became its first president in 1935. Rietz was an invited speaker at the International Congress of Mathematicians in 1924. He has accumulated over a thousand academic descendants (including Samuel Wilks), a record among Cornell Ph.D.s.

Among the early Cornell mathematics faculty, James McMahon had a keen interest in applied mathematics including probability and statistics. At the end of his career, he took up a challenge suggested by Karl Pearson and wrote the article “Hyperspherical Geometry; and its Application to Correlation Theory for NN Variables" which was published posthumously in 1923 by Biometrika.

Robert H. Cameron obtained his Ph.D. at Cornell in 1932, working under Wallie A. Hurwitz on almost periodic functions. He was a faculty member at MIT from 1935 to 1945 and spent the rest of his career at the University of Minnesota. At MIT, he met W.T. Martin with whom he had a fruitful collaboration in which they developed the concept of Wiener space. The Cameron-Martin space is a fundamental notion in Wiener space theory. Although mostly an analyst, Cameron counts Monroe Donsker among his Ph.D. students at the University of Minnesota.

In 1937, Mark Kac received his Ph.D. from the University of Lwow under Hugo Steinhauss. He spent the year 1938–1939 at The Johns Hopkins University on a fellowship. During the summer of 1939, he accepted a visiting position at Cornell. He stayed at Cornell for the next 23 years, until 1962. Kac wrote colorfully about his life in Ithaca and as a Cornell faculty member in his book *Enigmas of Chance: An Autobiography*. At Cornell, Kac advised a number of outstanding graduate students including Daniel Ray (Professor at MIT, remembered for the Ray-Knight theorems on local times), Murray Rosenblatt (Professor at San Diego, member of the National Academy of Science), Robert M. Blumenthal (Professor at the University of Washington, author with R. Getoor of *Markov Processes and Potential Theory*) and Harry Kesten (Professor at Cornell, member of the National Academy of Science, and recipient of the 2001 Leroy Steele Prize for Lifetime Achievement).

After World War II, Kac was joined at Cornell by William Feller who stayed until moving to Princeton in 1950. The first volume of his celebrated treatise, *An introduction to Probability Theory and its Applications*, one of the most successful and influential texts ever published on probability theory, was written at Cornell and first published in 1950.

In 1949, Gilbert Hunt accepted a position at Cornell where he stayed until 1959. For a few years, he hesitated between Princeton and Cornell until he definitively moved to Princeton in 1965. At Cornell, he published some of his most important works including *Random Fourier series*, *Semigroups of measures on Lie groups*, and the series of articles *Markov processes and potentials*. After Feller’s departure in 1950, probability remained strong at Cornell with the arrival of Jacob Wolfowitz and Jack Kiefer and short-term appointments including Kai Lai Chung, Monroe Donsker, and Cornell’s Ph.D. Steven Orey.

Harry Kesten joined Cornell in the summer of 1956 as a graduate student. Two years later, he defended his Ph.D. and accepted a postdoctoral position at Princeton before taking a position at The Hebrew University in Jerusalem. As Harry and his wife Doraline were settling in Jerusalem, Cornell sent Harry an offer to join the department. A year and a half later, in the summer of 1961, Harry returned to Cornell as an assistant professor. He was joined at Cornell by Frank Spitzer. Around the same time, Mark Kac left Cornell for Rockefeller University in New York. For many years, Kesten and Spitzer embodied the outstanding strength of Cornell Probability and Spitzer’s book *Principles of Random Walks* provides another highlight of Cornell contributions to probability. Before Kesten’s return and Spitzer's arrival, Leonard Gross had joined Cornell as an assistant professor in 1960. From 1969 to 1975, Kiyoshi Ito worked at Cornell and, in 1976, Eugene Dynkin joined the department. Cornell’s Ph.D. Lawrence D. Brown held a professorship at Cornell from 1966 to 1972 and from 1976 to 1994. Richard Durrett served the department from 1985 to 2010.

The Cornell Probability Summer School was held each year from 2005 to 2014 with support from a grant from the National Science Foundation.

### Faculty in Probabilty and Statistics, past and present

The following is a complete list of mathematicians who have contributed to probability theory and statistics and have held a full professorship in the Mathematics Department at Cornell. The years in parentheses are those of appointment at Cornell.

Mark Kac (Cornell: 1939–62), American Academy of Arts and Sciences, National Academy of Science. Chauvenet Prize, 1950, 1968; Birkhoff Prize 1978. President of the Institute of Mathematical Statistics. Fellow of the Institute of Mathematical Statistics.

William Feller (Cornell: 1950–55), American Academy of Arts and Sciences, National Academy of Science, National Medal of Science. President of the Institute of Mathematical Statistics . Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1936, 1958 (plenary).

Gilbert Hunt (Cornell: 1949–59 and 1963–65). Speaker at the International Congress of Mathematicians, 1962. Hunt was also an exceptional tennis player. He reached the quarterfinals of the U.S. National Championships in 1938 and 1939.

Jacob Wolfowitz (Cornell: 1951–1970), American Academy of Arts and Sciences, National Academy of Science. President of the Institute of Mathematical Statistics. Fellow of the Institute of Mathematical Statistics.

Jack Kiefer (Cornell: 1952–1979), American Academy of Arts and Sciences, National Academy of Science. President of the Institute of Mathematical Statistics. Fellow of the Institute of Mathematical Statistics.

Roger Farrell (Cornell: 1959--1999), Fellow of the Institute of Mathematical Statistics.

Leonard Gross (Cornell: 1960–2013, now emeritus), American Academy of Arts and Sciences. Fellow of the American Mathematical Society.

Harry Kesten (Cornell: 1961–2005, now emeritus), American Academy of Arts and Sciences, National Academy of Science, Leroy Steele Prize for Lifetime Achievement, George Pólya Prize. Fellow of the American Mathematical Society. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1970, 1983, 2002 (plenary).

Frank Spitzer (Cornell: 1961–1991), National Academy of Sciences. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1974.

Kiyoshi Ito (Cornell: 1965–1970), Japan Academy. Foreign member of the National Academies of Science in the United States and France. Recipient of the Imperial Prize, the Japan Academy Prize, the Kyoto Prize, the Wolf Prize, and the Carl Friedrich Gauss Prize. Speaker at the International Congress of Mathematicians, 1962.

Lawrence D. Brown (Cornell: 1966–72 and 1976–94), American Academy of Arts and Sciences, National Academy of Science. President of the Institute of Mathematical Statistics. Fellow of the Institute of Mathematical Statistics.

Eugene Dynkin (Cornell: 1975–2010, now emeritus), American Academy of Arts and Sciences, National Academy of Science. Prize of the Moscow Mathematical Society. Leroy Steele Prize for Lifetime Achievement. Fellow of the American Mathematical Society. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1962 (plenary), 1970, 1974.

J.T. Gene Hwang (Cornell: 1979–2012, now emeritus). Fellow of the Institute of Mathematical Statistics.

Richard Durrett (Cornell: 1985–2009), American Academy of Arts and Sciences, National Academy of Science. Fellow of the American Mathematical Society. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1990.

Persi Diaconis (Cornell: 1996–1998), American Academy of Arts and Sciences, National Academy of Science, 1982 McArthur Fellow. Fellow of the American Mathematical Society. President of the Institute of Mathematical Statistics. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 1990, 1998 (plenary).

Laurent Saloff-Coste (Cornell: 1997–), American Academy of Arts and Sciences. Fellow of the American Mathematical Society. Fellow of the Institute of Mathematical Statistics.

Michael Nussbaum (Cornell: 1999–). Fellow of the Institute of Mathematical Statistics.

Gregory Lawler (Cornell: 2000–2005), American Academy of Arts and Sciences, National Academy of Science, Pólya Prize. Fellow of the American Mathematical Society. Fellow of the Institute of Mathematical Statistics. Speaker at the International Congress of Mathematicians, 2002.

Marten Wegkamp (Cornell: 2011–).

### Related Information

For a brief complementary history of statistics at Cornell, see http://stat.cornell.edu/about-us/history

For the past thirty years, the Departments of ORIE (Operations Research, part of the College of Engineering) and Mathematics (part of the College of Arts and Sciences) have collaborated to bring to Cornell an outstanding presence in the field of probability theory and its applications.