William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a

Croatia , image_flag = Flag of Croatia.svg , image_coat = Coat of arms of Croatia.svg , anthem = "Lijepa naša domovino"("Our Beautiful Homeland") , image_map = , map_caption = , capit ...

n- American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specializing in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

Early life and education

Feller was born in

Zagreb Zagreb ( , , , ) is the capital and largest city of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb stands near the international border between Croatia and Slov ...

to Ida Oemichen-Perc, a Croatian- Austrian

Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among the world's oldest and largest international institutions, and has played a ...

, and

Eugen Viktor Feller Eugen Viktor Feller (26 January 1871 – 15 November 1936) was a Croatian pharmacist, entrepreneur and pioneer of the industrial drug production in Croatia. Feller was born in 1871, in Lwów region, which after the partition of Poland was at the ...

, son of a Polish-Jewish father (David Feller) and an Austrian mother (Elsa Holzer). Eugen Feller was a famous chemist and created ''Elsa fluid'' named after his mother. According to

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, proba ...

, Eugen Feller's surname was a "Slavic tongue twister", which William changed at the age of twenty. This claim appears to be false. His forename, Vilibald, was chosen by his Catholic mother for the saint day of his birthday.

Work

Feller held a docent position at the University of

Kiel Kiel () is the capital and most populous city in the northern German state of Schleswig-Holstein, with a population of 246,243 (2021). Kiel lies approximately north of Hamburg. Due to its geographic location in the southeast of the Jutland ...

beginning in 1928. Because he refused to sign a Nazi oath, he fled the

Nazis Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in N ...

and went to

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

, Denmark in 1933. He also lectured in Sweden ( Stockholm and Lund). As a refugee in Sweden, Feller reported being troubled by increasing fascism at the universities. He reported that the mathematician

Torsten Carleman Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, Stockholm), born Tage Gillis Torsten Carleman, was a Sweden, Swedish mathematician, known for his results in classical analysis and its applications. As the direct ...

would offer his opinion that Jews and foreigners should be

executed Capital punishment, also known as the death penalty, is the state-sanctioned practice of deliberately killing a person as a punishment for an actual or supposed crime, usually following an authorized, rule-governed process to conclude that t ...

. Finally, in 1939 he arrived in the

U.S. The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

where he became a citizen in 1944 and was on the faculty at

Brown Brown is a color. It can be considered a composite color, but it is mainly a darker shade of orange. In the CMYK color model used in printing or painting, brown is usually made by combining the colors orange and black. In the RGB color model us ...

and Cornell. In 1950 he became a professor at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

. The works of Feller are contained in 104 papers and two books on a variety of topics such as

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, theory of measurement,

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, and differential equations in addition to his work in

mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...

and probability. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of

as a branch of

in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while

was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by

. 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 equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s, 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 In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber. The original examples are Abel's theorem showing tha ...

, 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); 2nd edn. (1957) * ''An Introduction to Probability Theory and its Applications, Volume II, 2nd edition'' (1971)

Recognition

Feller was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

in 1958, the United States National Academy of Sciences in 1960, and the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

in 1966. Feller won the

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

in 1969. He was president of the

Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts o ...

. In 1949, he was named a

Fellow of the American Statistical Association Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its highest honorary grade of membership. The number of new fellows per year is limited ...

. He was elected to the National Academy of Sciences in 1980.

References

External links

*
A biographical memoir
by Murray Rosenblatt
Croatian Giants of Science - in Croatian
*

Contains a section on Feller at Princeton.
Feller Matriculation Form giving personal details
{{DEFAULTSORT:Feller, William 1906 births 1970 deaths 20th-century American mathematicians 20th-century Croatian people Croatian mathematicians Presidents of the Institute of Mathematical Statistics 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 Scientists from Zagreb Yugoslav emigrants to the United States Members of the United States National Academy of Sciences Fellows of the American Statistical Association Members of the American Philosophical Society