William Feller
Encyclopedia
William Feller born Vilibald Srećko Feller (July 7, 1906 – January 14, 1970), was a Croatia
n-American
mathematician
specializing in probability theory
.
to Ida Oemichen-Perc, a Croatian-Austrian
Catholic, and Eugen Victor Feller, who was born to a Polish
Jew named David Feller and an Austrian
Catholic named Elsa Holzer. 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—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. 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.
position at the University of Kiel
beginning in 1928. Because he refused to sign a Nazi oath, he fled the Nazis
and went to Copenhagen
, Denmark
in 1933. He also lectured in Sweden
(Stockholm
and Lund
). 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.
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
. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota
. 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 chain
s and differential equation
s, where his theory of generators of one-parameter semigroups of stochastic process
es gave rise to the theory of "Feller operators".
es, Feller's explosion test, Feller–Brown movement, and the Lindberg–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
.
Feller was born, raised, and educated in Croatia
. After he emigrated, Feller continued to write and when possible to visit his Croatian relatives. He visited and lectured at the University of Zagreb
. He held academic posts in Boston
, Zagreb
, London
, Copenhagen
, and Cornell University
. Fleeing from Nazi persecution, Feller spent much of the 1930s and World War II in Sweden, where he taught at Lund University
and Stockholm University
.
Croatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...
n-American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
.
Early life and education
Feller was born in ZagrebZagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
to Ida Oemichen-Perc, a Croatian-Austrian
Austrians
Austrians are a nation and ethnic group, consisting of the population of the Republic of Austria and its historical predecessor states who share a common Austrian culture and Austrian descent....
Catholic, and Eugen Victor Feller, who was born to a Polish
Poles
thumb|right|180px|The state flag of [[Poland]] as used by Polish government and diplomatic authoritiesThe Polish people, or Poles , are a nation indigenous to Poland. They are united by the Polish language, which belongs to the historical Lechitic subgroup of West Slavic languages of Central Europe...
Jew named David Feller and an Austrian
Austrians
Austrians are a nation and ethnic group, consisting of the population of the Republic of Austria and its historical predecessor states who share a common Austrian culture and Austrian descent....
Catholic named Elsa Holzer. Eugen was a famous chemist and created Elsa fluid named after his mother. According to Gian-Carlo Rota
Gian-Carlo Rota
Gian-Carlo Rota was an Italian-born American mathematician and philosopher.-Life:Rota was born in Vigevano, Italy...
, Feller's father's surname was a "Slavic tongue twister", which William changed at the age of twenty—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. In his school documentation, the small municipality of Donja Stubica
Donja Stubica
Donja Stubica is a town in Croatia, about 40 km northeast of Zagreb on the northern slope of Medvednica. The total population is 5,727, with 2,202 people in Donja Stubica itself , with a total area of 44.6 km²...
in Zagorje
Zagorje
Hrvatsko Zagorje is a region in northern Croatia.Zagorje may also refer to:*Zagorje ob Savi, a town and a municipality in Slovenia*NK Zagorje, a Slovenian football club-See also:...
is mentioned. This is the birthplace of his father, who was an apothecary
Apothecary
Apothecary is a historical name for a medical professional who formulates and dispenses materia medica to physicians, surgeons and patients — a role now served by a pharmacist and some caregivers....
and owner of a company producing hygienic utensils and cosmetics
Cosmetics
Cosmetics are substances used to enhance the appearance or odor of the human body. Cosmetics include skin-care creams, lotions, powders, perfumes, lipsticks, fingernail and toe nail polish, eye and facial makeup, towelettes, permanent waves, colored contact lenses, hair colors, hair sprays and...
.
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
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
where he gained the doctoral
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
degree in 1926
under the supervision of Richard Courant
Richard Courant
Richard Courant was a German American mathematician.- Life :Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there...
, with his work Über algebraisch rektifizierbare transzendente Kurven.
Work
Feller held a docentDocent
Docent is a title at some European universities to denote a specific academic appointment within a set structure of academic ranks below professor . Docent is also used at some universities generically for a person who has the right to teach...
position at the University of Kiel
Kiel
Kiel is the capital and most populous city in the northern German state of Schleswig-Holstein, with a population of 238,049 .Kiel is approximately north of Hamburg. Due to its geographic location in the north of Germany, the southeast of the Jutland peninsula, and the southwestern shore of the...
beginning in 1928. Because he refused to sign a Nazi oath, he fled the Nazis
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
and went to Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
in 1933. He also lectured in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
(Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...
and Lund
Lund
-Main sights:During the 12th and 13th centuries, when the town was the seat of the archbishop, many churches and monasteries were built. At its peak, Lund had 27 churches, but most of them were demolished as result of the Reformation in 1536. Several medieval buildings remain, including Lund...
). Finally, in 1939 he arrived in the U.S.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
where he became a citizen in 1944 and was on the faculty at Brown
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
and Cornell
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
. In 1950 he became a professor at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
The works of Feller are contained in 104 papers and two books on a variety of topics such as mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, theory of measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
, functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, and differential equations.
Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
as a branch of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
and the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota
Gian-Carlo Rota
Gian-Carlo Rota was an Italian-born American mathematician and philosopher.-Life:Rota was born in Vigevano, Italy...
. 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 chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
s and differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, where his theory of generators of one-parameter semigroups of stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es gave rise to the theory of "Feller operators".
Results
Numerous topics relating to probability are named after him, including Feller processFeller process
In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process.-Definitions:Let X be a locally compact topological space with a countable base...
es, Feller's explosion test, Feller–Brown movement, and the Lindberg–Feller theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
. Feller
made fundamental contributions to renewal theory
Renewal theory
Renewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times. Applications include calculating the expected time for a monkey who is randomly tapping at a keyboard to type the word Macbeth and comparing the long-term benefits of different...
, Tauberian theorems, random walks, diffusion processes, and the law of the iterated logarithm
Law of the iterated logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Y. Khinchin . Another statement was given by A.N...
. Feller was among those early editors who launched the journal Mathematical Reviews
Mathematical Reviews
Mathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
.
Feller was born, raised, and educated in Croatia
Croatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...
. After he emigrated, Feller continued to write and when possible to visit his Croatian relatives. He visited and lectured at the University of Zagreb
University of Zagreb
The University of Zagreb is the biggest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of Southeastern Europe...
. He held academic posts in Boston
Boston
Boston is the capital of and largest city in Massachusetts, and is one of the oldest cities in the United States. The largest city in New England, Boston is regarded as the unofficial "Capital of New England" for its economic and cultural impact on the entire New England region. The city proper had...
, Zagreb
Zagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
, London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
, and Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
. Fleeing from Nazi persecution, Feller spent much of the 1930s and World War II in Sweden, where he taught at Lund University
Lund University
Lund University , located in the city of Lund in the province of Scania, Sweden, is one of northern Europe's most prestigious universities and one of Scandinavia's largest institutions for education and research, frequently ranked among the world's top 100 universities...
and Stockholm University
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
.
