# William Feller

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

## Early life and education

Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian-Austrian Catholic, and Eugen Viktor Feller, who was born to a Polish Jew named David Feller and an Austrian named Elsa Holzer.^{[1]} Eugen was a famous chemist and created *Elsa fluid* named after his mother. According to Gian-Carlo Rota, Feller's father's surname was a "Slavic tongue twister", which William changed at the age of twenty^{[2]}—but as can be seen, this claim was false. His christened name, Vilibald, was chosen by his Catholic mother for the saint day of his birthday.^{[3]} In his school documentation, the small municipality of Donja Stubica in Zagorje is mentioned. This is the birthplace of his father, who was an apothecary and owner of a company producing hygienic utensils and cosmetics.

William finished his elementary and middle education in Zagreb, as well as two years of his math study. From 1925, he continued his study in Göttingen, Germany where he gained the doctoral degree in 1926 under the supervision of Richard Courant, with his work *Über algebraisch rektifizierbare transzendente Kurven*.

## 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

- ↑ William Feller's Origins
- ↑ Rota, Gian-Carlo (1996).
. Birkhäuser. ISBN 0-8176-3866-0.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>**Indiscrete Thoughts** - ↑ O'Connor, John J.; Robertson, Edmund F., "William Feller",
*MacTutor History of Mathematics archive*, University of St Andrews<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. - ↑ "Biography of William Feller".
*History of William Feller*. Retrieved 2006-06-27.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ 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)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ (Siegmund-Schultze 2009, p. 135)
- ↑ Preface to his
*Mathematical Methods of Statistics*. - ↑ Page 199:
*Indiscrete Thoughts*. - ↑ 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.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ "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.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

## External links

Wikiquote has quotations related to: William Feller |

- 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<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. - "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

- CS1 maint: ref=harv
- 1906 births
- 1970 deaths
- 20th-century American mathematicians
- 20th-century Croatian people
- Croatian mathematicians
- Presidents of the Institute of Mathematical Statistics
- Researchers in stochastics
- Probability theorists
- Brown University faculty
- Cornell University faculty
- Princeton University faculty
- University of Göttingen alumni
- Faculty of Science, University of Zagreb alumni
- National Medal of Science laureates
- Croatian refugees
- American people of Polish-Jewish descent
- Croatian Austro-Hungarians
- Croatian people of Austrian descent
- Croatian people of Polish-Jewish descent
- People from Zagreb
- Yugoslav emigrants to the United States
- American people of Croatian-Jewish descent