William Feller

William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory.

Not to be confused with William Fellner.

William Feller
Born	Vilibald Srećko Feller July 7, 1906 (1906-07-07) Zagreb, Austro-Hungarian Monarchy (now Croatia)
Died	January 14, 1970 (1970-01-15) (aged 63) New York, New York, US
Nationality	Croatian–American
Alma mater	University of Zagreb University of Göttingen
Known for	Feller process Feller's coin-tossing constants Feller-continuous process Proof by intimidation Stars and bars
Awards	National Medal of Science (USA) in Mathematical, Statistical, and Computational Sciences (1969)
Scientific career
Fields	Mathematician
Institutions	University of Kiel University of Copenhagen University of Stockholm University of Lund Brown University Cornell University Princeton University
Doctoral advisor	Richard Courant
Doctoral students	Patrick Billingsley George Forsythe Robert Kurtz Henry McKean Lawrence Shepp Hale Trotter Benjamin Weiss David A. Freedman
Influences	Stanko Vlögel
Signature

Early life and education

Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian-Austrian Roman Catholic, and Eugen Viktor Feller, son of a Polish-Jewish father (David Feller) and an Austrian mother (Elsa Holzer).[1]

Eugen Feller was a famous chemist and created Elsa fluid named after his mother. According to Gian-Carlo Rota, Eugen Feller's surname was a "Slavic tongue twister", which William changed at the age of twenty.[2] This claim appears to be false. His forename, Vilibald, was chosen by his Catholic mother for the saint day of his birthday.[3]

Work

Feller held a docent position at the University of Kiel beginning in 1928. Because he refused to sign a Nazi oath,[4] he fled the Nazis and went to Copenhagen, Denmark in 1933. He also lectured in Sweden (Stockholm and Lund).[5] As a refugee in Sweden, Feller reported being troubled by increasing fascism at the universities. He reported that the mathematician Torsten Carleman would offer his opinion that Jews and foreigners should be executed.[6]

Finally, in 1939 he arrived in the U.S. where he became a citizen in 1944 and was on the faculty at Brown and Cornell. In 1950 he became a professor at Princeton University.

The works of Feller are contained in 104 papers and two books on a variety of topics such as mathematical analysis, theory of measurement, functional analysis, geometry, and differential equations in addition to his work in mathematical statistics and probability.

Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér.[7] His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota.[8] By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".

Results

Numerous topics relating to probability are named after him, including Feller processes, Feller's explosion test, Feller–Brown movement, and the Lindeberg–Feller theorem. Feller made fundamental contributions to renewal theory, Tauberian theorems, random walks, diffusion processes, and the law of the iterated logarithm. Feller was among those early editors who launched the journal Mathematical Reviews.

Notable books

• An Introduction to Probability Theory and its Applications, Volume I, 3rd edition (1968); 1st edn. (1950);[9] 2nd edn. (1957)[10]
• An Introduction to Probability Theory and its Applications, Volume II, 2nd edition (1971)

References

1. Zubrinic, Darko (2006). "William Feller (1906-1970)". Croatianhistory.net. Accessed 3 July 2018.
2. Rota, Gian-Carlo (1996). Indiscrete Thoughts. Birkhäuser. ISBN 0-8176-3866-0.
3. O'Connor, John J.; Robertson, Edmund F., "William Feller", MacTutor History of Mathematics archive, University of St Andrews.
4. "Biography of William Feller". History of William Feller. Retrieved 2006-06-27.
5. Siegmund-Schultze, Reinhard (2009). Mathematicians fleeing from Nazi Germany: Individual fates and global impact. Princeton, New Jersey: Princeton University Press. pp. xxviii+471. ISBN 978-0-691-14041-4. MR 2522825.CS1 maint: ref=harv (link)
6. (Siegmund-Schultze 2009, p. 135)
7. Preface to his Mathematical Methods of Statistics.
8. Page 199: Indiscrete Thoughts.
9. Wolfowitz, J. (1951). "Review: An introduction to probability theory and its applications, Vol. I, 1st ed., by W. Feller" (PDF). Bull. Amer. Math. Soc. 57 (2): 156–159. doi:10.1090/s0002-9904-1951-09491-4.
10. "Review: An introduction to probability theory and its applications, Vol. I, 2nd ed., by W. Feller" (PDF). Bull. Amer. Math. Soc. 64 (6): 393. 1958. doi:10.1090/s0002-9904-1958-10252-9.

External links

• William Feller at the Mathematics Genealogy Project
• A biographical memoir by Murray Rosenblatt
• Croatian Giants of Science - in Croatian
• O'Connor, John J.; Robertson, Edmund F., "William Feller", MacTutor History of Mathematics archive, University of St Andrews.
• "Fine Hall in its golden age: Remembrances of Princeton in the early fifties" by Gian-Carlo Rota. Contains a section on Feller at Princeton.
• Feller Matriculation Form giving personal details