William Feller (1906-1970)

Vilim Feller as a student at the University of Zagreb
with kind permission of prof. Marta Zdenkovic, Zagreb

Darko Zubrinic, 2006
On the occasion of 100 years since the birth of
Vilim (Vili, Willy, Willi, Will, William) Feller
in Zagreb, Croatia (in preparation)

Extended Abstract. William Feller (Zagreb, July 7th, 1906 - New York, January 14th, 1970), outstanding Croatian - American mathematician, born in Croatia as Vilibald Srecko Feller. As a student he changed the name to Vilim. Graduated in mathematics from the University of Zagreb (1925), earned his PhD in Göttingen (1926) under Richard Courant. He prepared a part of his thesis already as a student in Zagreb. Professor in Kiel (1928-1933), Copenhagen (1933-1934), Stockholm, and Lund (1934-1939). In 1938 he married Clara Nielsen. Since 1939 lived in the USA, employed at Universities of Brown, Cornell, and since 1950 at Princeton University as a Eugen Higgins Professor of mathematics. Feller wrote the review of A.N. Kolmogorov's famous book Grundbegriffe der Wahrscheinlichkeitsrechnung for Zentralblatt für Mathematik in 1934. One of initiators of editing Mathematical Reviews (1939), and one of its first executive directors (1944-1945). One of the founders of Probability Theory as a scientific discipline, best known for his two volume monograph An Introduction to Probability Theory and Its Applications, which is considered as one of the finest mathematical text books of the 20th century. It was translated into Russian (with foreword to Volume 1 written by Kolmogorov), Chinese, Spanish, Polish, and Hungarian. Many mathematical notions bear his name: Feller process, Feller transition function, Feller semigroup, Feller's property, Feller Brownian motions, Feller's test for explosions, Lindberg-Feller condition, Feller operator, Feller potential, Feller measures, indefinite Krein-Feller differential operators, and Kolmogorov-Feller equation. At the International Congress of Mathematicians held in 1958 in Edinburgh, Feller delivered a plenary talk "Some new connections between probability and classical analysis." In 1966 he was elected to the international scientific committee which had to choose candidates for the 1966 Fields Medal at the International Congress of Mathematicians in Moscow. Feller had 17 PhD students. Member of several national academies: former Yugoslav (now Croatian) Academy of Sciences and Arts, Royal Danish Academy of Sciences, National Academy of Sciences, USA, American Academy of Arts and Sciences, Boston, and of prestigeous scientific organizations: Royal Statistical Society, London, and The London Mathematical Society (honorary member). Recipient of the 1970 National Medal of Science by the president of the USA. An asteroid was named after him in 1996: 21276 Feller (1996 TF5).

COMPLETE TEXT: WILLIAM FELLER

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It seems to be little known that William Feller wrote a review of the famous book by outstanding Russian mathematician A.N. Kolmogorov (1903-1987), Grundbegriffe der Wahrscheinlichkeitsrechnung [English translation of the book], 1933, in which theoretical foundations of Probability Theory have been laid down:

William Feller: Review of Kolmogorov (1933), Zentralblatt für Mathematik und ihre Grenzegebiete, 7:216, 1934.

It is to be noted that Feller was only 27 years old when this book was published, while Kolmogorov was 30. We need to mention that there exists the KolmogorovFeller Equation in Probability Theory. Also, Kolmogorov wrote Foreword to the second Russian edition of Volume I of Feller's famous book An Introduction to Probability Theory and Its Applications.

Vili Feller with his mother, 1925

Feller defended his habilitation thesis in 1928, and obtained the position of Privat Dozent in Kiel. According to [Croatian Biographical Lexicon] Feller was also a director of the Institute of Applied Mathematics at the University of Kiel. He remained in Kiel until 1933, when he left Germany due to the arrival of Nazism, refusing to sign the Nazi oath. He then continued his carreer in Copenhagen (working at the Mathematical Institute there from 1933 to 1934, where he met also Niels Bohr), and in Stockholm and Lund (from 1934 to 1939; among his colleagues there were Harald Cramér and Marcel Riesz). In 1938 he married Clara Nielsen, who had been his student already in Kiel. In 1939 Feller's emigrated to the USA.

Vilim Feller in 1936, as an established scientist;
with kind permission of prof. Marta Zdenkovic, Zagreb

According to personal information I obtained from Marta and Nikola Zdenkovic in 2006, Zagreb (their grandfather Ferdinand was William Feller's brother), William Feller was on friendly terms with Albert Einstein (1879-1955), despite a difference of almost 30 years. Since 1950, they were both in in Princeton, USA: Einstein at the Institute of Advanced Study and Feller at the Princeton University.

In 1939 Feller became associate professor at Brown University (Providence, Rhode Island), and there he started his work on issuing Mathematical Reviews. In 1944 he became citizen of the USA. In 1945 Feller became a professor at Cornell University. In 1950 he obtained the position of Eugene Higgins Professor of Mathematics at Princeton, where he remained until his death in 1970. During the academic years 1965/66 and 1967/68 he lectured as a visiting professor at the Rockfeller University in New York.

Clara Nielsen, 1937, Feller's student in Kiel (they married in 1938),
with kind permission of prof. Marta Zdenkovic, Zagreb

It is interesting that Feller published two of his scientific works in a Croatian journal, Rad JAZU (JAZU = the then Yugoslav Academy of Sciences and Arts, since 1991 HAZU = Croatian Academy of Sciences and Arts). He wrote both articles in the Croatian language:

• Prilog teoriji mjere u apstraktnim prostorima (Contribution to measure theory in abstract spaces; Bemerkungen zur Masstheorie in abstrakten Räumen), Rad JAZU 249, 1934, 30-45
• O Kolmogoroff - P. Lévyjevu predocivanju beskonacno djeljivih funkcija reparticije (On Kolmogoroff - P. Lévy representation of infinitely divisible distribution functions; Neuer Beweis fur die Kolmogoroff - P. Lévsche Characterisierung der Unbeschränkt teilbaren Verteilungsfunktionen), Rad JAZU, 32, 1939, 1-8.

Under the title of the first article his name is written as follows:

Napisao [written by] Dr. Vilim (W.) Feller

Meanwhile, in 1937 he was elected as corresponding member of JAZU (now Croatian Academy of Sciences and Arts). This is indicated under the title of the second article, where his name is written as

Napisao clan dopisnik [written by corresponding member] Vilim (W) Feller

On July 17th 1953 William Feller delivered a lecture in the building of JAZU, Zagreb, in Croatian language, under the title "Matematicka teorija difuzije" (Mathematical theory of diffusion), see [Mardesic, Some data...].

We provide an excerpt from an article by an American mathematician Michael Golomb, Terror and Exile and a Letter About it by Michael Golomb (A report from Volume 4, #1, of TopCom), which was a part of a special exhibition organized during the International Congress of Mathematicians in Berlin, 1998:

... The List of Expelled Berlin mathematicians contains 53 names. 21 of them found refuge in US, 7 in GB. Next is the List of Emigrants among all German-Speaking Mathematicians. It contains 130 names. It is a surprise to me, and probably also to many readers, that as many as 75 German mathematicians, many of them world-renowned, emigrated to this country in the thirties. I choose from the list names that are universally recognized: Emil Artin, Reinhold Baer, Gustav Bergman, Felix Bernstein, Lipman Bers, Salomon Bochner, Alfred Brauer, Richard Brauer, Herbert Busemann, Richard Courant, Max Dehn, Willy Feller, Kurt Friedrichs, Kurt Goedel, Hans Hamburger, Ernst Hellinger, Eduard Helly, Fritz John, Theodor Karman, Hans Lewy, Karl Loewner, Kurt Mahler, Karl Menger, Richiird von Mises, Otto Neugebauer, Johann von Neumann, Emmy Noether, Wilhelm Prager, Hans Rademacher, Hans Reichenbach, Arthur Rosenthal, Erich Rothe, Hans Samelson, Otto Schilling, Carl L. Siegel, Otto Szasz, Gabriel Szego, Olga Taussky, Abraham Wald, Stefan Warschawsky, Wolfgang Wasow, Hermann Weyl, Max Zorn. The great Albert Einstein, himself an emigrant from Berlin, is not included because he is classified as a Physicist, not a mathematician. By their own work and as teachers of a generation of brilliant young American mathematicians these emigrees from Nazi Germany have made the US the great center of mathematics in the world that it is today. ...

Michael Golomb himself left Germany in 1933, went to the Croatian capital Zagreb, and in 1939 arrived to the USA.

William Feller, photo from [Vladimir Vranic]

Professor Ulrich Krengel from the University of Göttingen wrote the following about Feller's participation at International Mathematical Congresses, [History of Probability and Statistics at the International Congresses of Mathematicians, PS]:

... In Oslo (1936 [International Congress of Mathematicians]), Maurice Frechét devoted a portion of his plenary lecture "Mélanges mathématiques" to topics in probability. In addition to his own work, he discussed progress by Hadamard, Hostinsky, Doeblin and Kolmogorov. He also stressed the fact that by now probability was equally exact as other branches of mathematics, and that many mathematical subjects "integral equations group theory" etc., were used as tools in probability. Another important talk in Oslo was the one given by W. Feller on stochastic processes. He discussed his well known existence and uniqueness theorems for Markov processes with jumps. ...

... In the Conference [International Congress of Mathematicians 1950, Cambridge, Massachussetts] chaired by von Neumann there were three talks related to probability:

• C.E. Shannon: Some topics in information theory
• S.M. Ulam: Random processes and transformations
• W. Feller: Some recent trends in the mathematical theory of diffusion.

Certainly the last of these was a highlight. Feller explained the ties between classical boundary problems for the heat equation and diffusion processes. He also spoke on Ito's theory of stochastic integration. This was possibly the first time that these topics were presented to a broad mathematical public. ...

 

Vilim Feller (on the right) in Zagreb in 1953, in Jurjevska 31a, where he spent his youth,
with Ivo Zdenkovic, father of Marta and Nikola Zdenkovic
(Ivo's wife Eva is the daughter of Ferdinand, Vilim's brother);
with kind permission of prof. Marta Zdenkovic, Zagreb

At the International Congress of Mathematicians (ICM) held in Edinburgh 1958, William Feller delivered one hour plenary talk "Some new connections between probability and classical analysis." For more detailed information see History of Probability and Statistics at the International Congresses of Mathematicians, [PS], by Ulrich Krengel, University of Göttingen, Germany.

Feller was among those who initiated publishing the important Mathematical Reviews journal in 1939, and was one of its first executive editors (1944-1945; the first editors were Otto Neugebauer, 1939-1940 and J.D. Tamarkin, 1940-1944). According to [Annals of Math. Statistics]

... he deserves the gratitude of mathematicians for his six years of effort in establishing the new journal [i.e. Math. Reviews], now the leading review of mathematics in the world.

Clara Nielsen Feller, 1957
with kind permission of prof. Marta Zdenkovic, Zagreb

 

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William Feller's monograph An Introduction to Probability Theory and its Applications, Volumes I and II (the first edition appeared in 1950, when Feller was 44), it had subsequent editions, and was translated into several other languages (Russian, Chinese, Polish, Spanish, and Hungarian). It is considered one of the best mathematical textbooks written in the 20th century. According to Feller's own words, he worked on Volume I for eight years, since 1941 til 1948.

William Feller: An Introduction to Probability Theory and its Applications, Volume one, John Wiley, New York, 1950

A few quotations from the book:

...Probability is a mathematical discipline whose aims are akin to those, for example, of geometry or analytical mechanics. In each field we must be careful to distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, and (c) applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation. [p. 1]

...Nowadays small boys betting and shooting dice, newspapers report on samples of public opinion, and the magic of statistics embraces all phases of life to the extent that young girls anxiously watch the statistics of their chances to get married. [p. 2]

...The history of probability (and of mathematics in general) shows a stimulating interplay of theory and applications: progress in theory opens new fields of applications, and each new application creates new theoretical problems and influences the direction of research. [p. 3]

 

William Feller (1906-1970),
photo by Paul Halmos (1916-2006) from his book
I have a photographic memory (Providence, 1987); Halmos provides also the photo of another outstanding Croatian mathematician - Zvonimir Janko

We provide an excerpt from the review of the 1950 first edition of Feller's book (Volume I), written for Mathematical Reviews by R. Fortet:

Afin d'éviter toute notion mathématique élevée (théorie de la mesure, etc.) et pour que l'ouvrage soit utilisable par des étudiants débutants, l'auteur s'est limité aux questions oů n'interviennent qu'un nombre dénombrable d'éventualités; mais ŕ propos de ces questions simples il aborde les problčmes les plus avancés de calcul des probabilités, dont beaucoup n'avaient pas encore été exposés dans un livre, de sorte que l'ouvrage est également du plus haut interęt pour les spécialistes. Le texte inclut un trčs grand nombre d'exemples ou d'exercises proposés, généralement originaux et remarquablement choisis. ...

From the review of the 1957 second edition of Feller's book (Volume I), written by U. Grenander for Mathematical Reviews:

...As in the first edition the exposition is mathematically rigorous and at the same time elegant and lucid. This fascinating book will remain a standard textbook of mathematical probability for many years to come.

From the review of the 1966 first edition of Feller's book (Part II), written by S. Orey for Mathematical Reviews:

This is the sequel to the popular first volume ... but it is designed so that it can be used independently. The reader of this book need not have any prior knowledge of probability beyond a few basic definitions, say as given in the first chapter of the first volume. Indeed it is the author's aim, admirably realized, to be of interest to a diverse audience, ranging from novice to expert. The book has a rich texture, derived from the wealth of problems treated as applications or illustrations of the theory. The striking aspect is the apparent ease and elegance with which these problems are dispatched, frequently making obsolete the original treatment given in the research literature. ...

Photo from The MacTutor History of Mathematics archive, William Feller

As we have said, Feller worked eight years on preparing Volume I of the first edition of his monograph, issued in 1950 (xii+419 pp).

Feller's book: the second edition fourth printing, of the first volume, released in February 1960. Photo from www.biblio.com .

The second volume appeared sixteen years later, in 1966 (xviii+636 pp). Both volumes comprise altogether 1135 pages. Volume I had two more editions, in 1957 (xv+461 pp) and in 1968 (xviii + 509 pp). Both of them were substantially improved with respect to previous editions.

In the Preface to the Volume II of his book, published in 1966, Feller wrote the following:

[speaking about the unexpected success of Volume I] ... The book seems even to acquire new friends. The fact that laymen are not deterred by passages which proved difficult to students of mathematics shows that the level of difficulty cannot be measured objectively; it depends on the type of information one seeks and the details one is prepared to skip. The traveler often has the choice between climbing a peak or using a cable car. ...

Here are the data about the latest editions of both Volumes (from MathSciNet), which comprise altogether 1178 pp:

Feller, William: An Introduction to Probability Theory and Its Applications. Vol. I. Third edition John Wiley & Sons, Inc., New York-London-Sydney 1968 xviii+509 pp.

Feller, William: An Introduction to Probability Theory and Its Applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp.

The second edition of Volume II was issued in 1971, soon after Feller's death in the Memorial Hospital in New York, January 14, 1970, at the age of 63. His wife Clara wrote on p. xi of the book the following lines:

THE MANUSCRIPT HAD BEEN FINISHED AT THE TIME OF THE AUTHOR'S DEATH, but no proofs had been received. I am grateful to the publisher for providing a proofreader to compare the print against the manuscript and for compiling the index. J. Goldman, A. Grunbaum, H. McKean, L. Pitt, and A. Pittenger divided the book among themselves to check on the mathematics. Every mathematician knows what an incredible amount of work that entails. I express my deep gratitude to these men and extend my heartfelt thanks for their labor of love.

May 1970, Clara N. Feller

 

As we have said, his books have been translated into Russian, Chinese, Polish, Spanish and Hungarian. The first Russian translation of Volume I appeared just a year after the appearance of the book in 1950! And also the first Russian translation of Volume II appeared just a year after the appearance of the book in 1966! Moreover, Feller himself provided corrections of the English 1966 edition for the 1967 Russian edition of Volume II! Here is more detailed information based on Mathematical Reviews:

Russian editions

Feller, V. Vvedenie v teoriyu veroyatnostei i eë prilozeniya. (Diskretnye raspredeleniya.) (Russian) [An introduction to probability theory and its applications. (Discrete distributions.)] Izdat. Inostrannoj Literatury, Moscow, 1951. 427 pp.

Feller, V.: Vvedenie v teoriyu veroyatnostej i ee prilozheniya. Tom 1. (Russian) [An introduction to probability theory and its applications. Vol. 1] Translated from the English by R. L. Dobrusin, A. A. Juskevic and S. A. Molcanov. Edited by E. B. Dynkin, with an introduction by A. N. Kolmogorov. Second edition, reprinted Izdat. ``Mir'', Moscow 1964 and 1967 (reprinted 1964 edition). 498 pp.

Feller, V.: Vvedenie v teoriyu veroyatnostej i ee prilozheniya. Tom 2. (Russian) [An introduction to probability theory and its applications. Vol. 2] Translated from the English by Ju. V. Prohorov Izdat. ``Mir'', Moscow 1967 752 pp.

Feller, V.: Vvedenie v teoriyu veroyatnostej i ee prilozheniya. Tom 1. (Russian) [An introduction to probability theory and its applications. Vol. 1] Translated from the third English edition and with a preface by Yu. V. Prokhorov. Second edition. With a preface by A. N. Kolmogorov. ``Mir'', Moscow, 1984. 528 pp.

Feller, V.: Vvedenie v teoriyu veroyatnostej i ee prilozheniya. Tom 2. (Russian) [An introduction to probability theory and its applications. Vol. 2] Translated from the second English edition and with a preface by Yu. V. Prokhorov. Second edition. ``Mir'', Moscow, 1984. 752 pp.

 

From the Introduction to the second Russian edition to Fellers book (Volume I, Moscow 1964), written by A.N. Kolmogorov:

The first edition of Feller's book already obtained a widespread approval in the USSR. Now we bring to the reader's attention the translation of the second English edition, improved and added to by the author in many details. ... It is precisely this choice of material which enables Feller's book to occupy an independent place in the literature on probability theory. ... ... By the choice of problems Feller brings to light their solving by "direct", and specifically probabilistic means. This tendency to see behind analytical transformations their "probabilistic" sense, belongs to the most valuable features of Feller's book. Deserving our attention is also the author's effort in the book in clearly illustrating the character of effects of probabilistic laws on carefully chosen examples . In many cases the author manages to introduce the reader into really interesting questions of comparation between statistical data and probabilistic theory of events. ... (translated from Russian by D.Z.)

Yu. V. Prokhorov in his introduction to the first Russian edition of Volume II wrote the following:

... Professor Feller, having learned about the prepartion of the second volume, kindly sent us a list of many necessary corrections, that were included into the text. I am very grateful to him for his kindness. ... (translated form Russian by D.Z.)

Spanish edition

Feller, William: Introducción a la teoría de probabilidades y sus aplicaciones, v. I (504 p.); [version espańola, Salvador Morales Vaca, Salvador, traductor], México : Limusa-Wiley, 1973

Feller, William: Introducción a la teoría de probabilidades y sus aplicaciones, v. II (738 p.) [version espańola, Sergio Fernandez Everest], México [etc.] : Limusa, 1985

Polish edition

Feller, William: Wstep do rachunku prawdopodobienstwa. Tom I. (Polish) [Introduction to probability theory. Vol. I] Translated from the second English language edition. Third revised edition (!). Panstwowe Wydawnictwo Naukowe, Warsaw, 1977. 420 pp. First edition in 1966.

Feller, William: Wstep do rachunku prawdopodobienstwa. Tom II. (Polish) [Introduction to probability theory. Vol. II] Translated from the English. Second revised edition (!). Panstwowe Wydawnictwo Naukowe, Warsaw, 1978. 587 pp.

 

Chinese edition

Feller, William K'ai-lü-lun chi ch'i yin-yung. Ts'e I. (Chinese) [Probability theory and its applications. Vol. I] Translated from the English by Hu Ti-ho and Lin Hsiang-ching Science Press, Peking 1964. xii+253 pp.

Photo from Book.ChinaUnix.net

Hungarian edition

William Feller: Bevezetés a valószínuségszámításba és alkalmazásaiba, Muszaki Kiadó, Budapest, 1978.

Many thanks to Professor Jozsef Pelikan
from the University of Budapest for his kind help

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William Feller with his students; photo by J.R. Goldman, USA

Feller's scientific interests in mathematics were very broad. He contributed to calculus, geometry, and functional analysis. About half of his papers are in the field of probability theory.

According to Mathematical Reviews, Feller's works are cited 1320 times by 1649 authors. The first part of his book is cited 390 times, and the second part 712 times. It should be noted that Math Reviews is reviewing math articles starting with the year 1939, so that Feller's very productive scientific work before that (that is, between 1926 and 1939) is not evidenced there. His most cited article (37 times) is

Feller, William: The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math. (2) 55, (1952). 468-519. (Reviewer: K. Yosida),

Besides two volumes of his famous book Feller wrote 104 scientific papers, see the complete list in the memorial issue of [Annals of Math. Statistics].

Many mathematical notions bear his name:

Feller process strong Feller process Feller chain Feller transition function Feller semigroup Feller generator Feller's property strong Feller's property Feller operator Feller kernel Dirichlet-Feller operator Trotter-Feller operator Feller potential Riesz-Feller potential Kato-Feller potential Kato-Feller class Kato-Feller norm Kato-Feller property Feller Brownian motions Feller's test for explosions Lindberg-Feller condition Erdös-Feller-Pollard theorem Feller measures Markov-Feller operators indefinite Krein-Feller differential operators Kolmogorov-Feller equation

 

William Feller has the Erdös number equal to 1 (one): he has a joint paper with Paul Erdös written in 1949 (and with Pollard). Erdös wrote more than 1500 papers, and had 509 coauthors!

In 1966 Feller had a great honour to become a member of the international scientific committee which had to elect candidates for the 1966 Fields Medal. The committee consisted of Georges de Rham (chair), Harold Davenport, Max Deuring, Willi Feller, Michael Al. Lavrentiev, Jean-Pierre Serre, Donald C. Spencer, and René Thom, see here. Recipients of the Fields Medal at the 1966 International Congress of Mathematicians in Moscow were Michael Francis Atiyah, Alexander Grothendieck, and Stephen Smale.

Feller is the author or coauthor of two more books:

• Willy Feller: Über die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Berlin : Springer, 1929 (when he was teaching in Kiel, Germany)
• Jacob David Tamarkin, Willy Feller (Brown University, Graduate School): Partial differential equations, Providence, R.I., 1941

According to the Mathematical Geneaology Project (with his name indicated as Willi K. Feller), William Feller was thesis advisor to 17 students in the period of 1941 to 1969, and he has as many as 609 descendants. Marta and Nikola Zdenkovic, Zagreb, informed me in 2006 that they do not know the meaning of initial "K." appearing in Feller's name in the Math Geneaology Project, and expressed their doubts about it. Here are the names of Feller's PhD students:

 

Patrick Billingsley,Princeton University,1955 William Cleveland (second advisor),Yale University,1969 George Forsythe,Brown University,1941 David Freedman,Princeton University,1960 Jay Goldman,Princeton University,1965 Mario Juncosa,Cornell University,1949 Wilfred Kincaid,Brown University,1946 Frank Knight,Princeton University,1959 Robert Kurtz,Princeton University,1967 Henry McKean, Jr.,Princeton University,1955 Loren Pitt,Princeton University,1967 George Seifert,Cornell University,1950 Lawrence Shepp,Princeton University,1961 Martin Silverstein,Princeton University,1965 Hale Trotter,Princeton University,1956 Maria Weber,Cornell University,1949 Benjamin Weiss, Princeton University, 1965

 

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William Feller; photo from [Croatian Biographical Lexicon]

Feller was a member of the Croatian Academy of Sciences and Arts in Zagreb (the then JAZU) since 1937, that is, at the age of 31. He was also a member of the Royal Danish Academy of Sciences, and the Royal Statistical Society in London. Shortly before his death he was elected as an honorary memebr of the London Mathematical Society. He was also a governor of the New Jersey section of the Mathematical Association of America (1958-1961, [PDF]), and a president of the Institute of Mathematical Statistics in 1947.

National Medal of Science, conferred to William Feller in the White House
by president Richard Nixon in 1970 (posthumously)

Feller was a member of the National Academy of Sciences (USA, since 1960) and of the American Academy of Arts and Sciences, Boston, since 1958 (Career description: Mathematician; Educator). He was awarded the National Medal of Science of the USA in 1969 (Discipline: Mathematics and Computer Science). The National Medal of Science award was established by the U.S. Congress as a Presidential award. It was conferred in 1970 by president Richard Nixon to Feller's wife Clara during the official ceremony held in the White House, a month after Feller's death at the age of 63. This prestigeous medal has been conferred to him for

• his important contributions to pure and applied mathematics,
• his efforts to make probability theory accessible to broad audience,
• his pioneering work in establishing Mathematical Reviews.

 

Some mathematicians dedicated their scientific works to the memory of William Feller, for example by his PhD student H.P. McKean:

H. P. McKean. Geometry of differential space: Dedicated to the memory of Will Feller. The Annals of Probability, 1:197 -- 206, 1973.

He was in touch with his relatives in Zagreb, as well as with his colleagues at the University of Zagreb. During the post WWII period Feller visited Zagreb on three occasions: in 1953, 1956 and in 1958. He helped professor Sibe Mardesic from Zagreb, at that time a young scientist, to spend the academic years 1957/58 and 1958/59 at the Institute for Advanced Study in Princeton, see [here]. S. Mardesic was introduced to Feller in person by Zeljko Markovic in his office, when Feller visited Department of Mathematics, PMF, Zagreb, in 1956. According to [Vranic, p. 352], "...not only that Vilim Feller did not hide his Croatian descent, but he was also proud of it."

J. Dieudonné, a well known French mathematician, and a member of the Bourbaki group, in his book A panorama of pure mathematics - As seen by N. Bourbaki (Academic Press, New York, London, 1982), indicated that the main ideas of probability theory are related to the names of:

J. Bernoulli (1654-1705), A. de Moivre (1667-1754), P. Laplace (1749-1827), D. Poisson (1781-1840), P. Chebisev (1821-1894), A. Markov (1856-1922), E. Borel (1871-1956), N. Wiener (1894-1959), P. Lévy (1886-1971), A. Kolmogorov (1903-1987), A. Hincin (1894-1959), W. Feller (1906-1970), J. Doob (1910-2004), and G. Hunt (b. 1916).

William Feller in 1964; photo from The MacTutor History of Mathematics archive;
the source is probably [Halmos]

It is amusing that the name of the street in Princeton where William Feller lived since 1950 until his death was

RANDOM ROAD

If you go here http://maps.google.com/ and type "Random Road" "Princeton, New Jersey" you will go right to the short road where Prof. Feller and his wife lived. It's just off Nassau St., the main street in Princeton. (Was the name of the street given in honour of Feller? D.Z.)

Many thanks to Mr Paul C. Kettler, Norway, a former student of professor Feller, for this wonderful information (2006). Here is another lovely detail from Feller's lectures, described by Mr Kettler:

Feller's favorite number was "17," employed over and over in his talks whenever a natural number was in order, and the low integers one, two, and three, were not evident choices. This was in expressions such as, "Consider the sum of 17 random variables," etc. This use of "17" was a standing joke, which he loved as much as anybody else.

One other anecdote by Mr. Kettler:

Feller and Salomon Bochner each had corner offices on the first floor of the old Fine Hall (now Jones, the Psychology Department.) As there was a central auditorium-style classroom on the floor, offices and smaller classrooms were to the outside of a rectangular hallway around the floor. Bochner's office was in the near right corner as you entered the building, and Feller's was at the next corner continuing. Frequently the two of them, precipitated by a quick phone call from one to the other, would meet in the hall, then march around (always counter-clockwise) several times in very animated discussion. Sometimes they would retire to one or the other's office for more talk, but usually they would not. After three circuits or so they would have exhausted their comments to each other, and would retire back to their offices. It was really a funny, and frequent, sight.

Besides his native Croatian, William Feller spoke also German, English, French, Latin, Hebrew, and very probably Swedish as well (recall that he spent five years in Sweden, from 1934 till 1939). According to the information I obtained from Mr. Nikola Zdenkovic in 2006, his hobby was translating old texts from Sanskrit.

Professor Feller was a member of editorial boards of two prestigeous journals: Transactions of the American Mathematical Society and the Annals of Mathematical Statistics.

William Feller's vivid lecturing, photo by J.R. Goldman, USA
(from the cover of an internal magazine of IBM)

From an introductory article written by the editorial board of [Annals of Math. Statistics] on the occasion of death of William Feller in 1970, we cite the following:

... His expository lectures and articles have done a great deal to spread the knowledge and recognition of probability throughout the world. His books catch the flavor of his mathematics, though only his presence could convey the full enthusiasm of his lectures. The jacket cover of the third edition of Volume I bears this appreciation from Gian-Carlo Rota of MIT: "... one of the great events in mathematics of this century. Together with Weber's Algebra and Artin's Geometric Algebra this is the finest text book in mathematics in this century. It is a delight to read and it will be immensly useful to scientists in all fields."

In the same issue of the [Annals of Math. Statistics] we can find the following dedication on the separate page:

By action of the Council of the Institute of Mathematical Statistics, the 1970 volume of the Annals of Mathematical Statistics is dedicated to the memory of

WILLIAM FELLER

William Feller, probably in 1940s, when he worked on establishing Math. Reviews;
photo from [Proceedings of the Sixth Berkeley Symposium on Mathematical Statisics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory]

Mark Kac in his very interesting article [William Feller, In Memoriam], wrote the following lines:

William Feller, one of the most original, accomplished, and colorful mathematicians of our times, died after a long illness on 14 January, 1970. The entrie mathematical community mourns his death but at this sympositum his loss will be felt more deeply, for all of us here have been influenced both by his work and by his person. ...

Volume I, or to be precise, An Introduction to Probability and its Applications, Volume I, is a book with few peers in scientific literature. It is a treatise and a textbook, a masterpiece of exposition and a credo of methodology of sweeping panorama of a subject and a collection of examplary jewels. No wonder it has appealed to an audience so wide as to border on the incredible, ...

Feller was a man of enormous vitality. Not even in the last stages of his illness was his zest for life visibly lessened. ...

Outside of mathematics and science Feller was especially interested in ancient history - and in this fascinating field his knowledge and competence bordered on the professional. ...

Joseph Doob, a renowned American mathematician, wrote about Feller the following, see his article [William Feller and twentieth century probability]:

... No other book even remotely resembles it in its combination of the purest mathematics together with a dazzling virtuosity of techniques and applications, all written in a style which displays the enthusiasm of the author. This style has made the book unexpectedly popular with nonspecialists, just as its elegance and breadth, not to mention its originality, has made it an inspiration for specialists.

... Those who knew him personally remember Feller best for his gusto, the pleasure with which he met life, and the excitement with which he drew on his endless fund of anecdotes about life and its absurdities, particularly the absurdities involving mathematics and mathematicians. To listen to his lecture was a unique experience, for no one else could lecture with such intense excitement. No one could generate in himself as well as in his auditors so much intense excitement. In losing him, the world of mathematics has lost one of its strongest personalities as well as one of its strongest researchers.

In the same obituary Joseph Doob wrote the following:

Feller (1906-1970) made original and profound contributions to probability theory over a period (from 1935 till his death) over which it was transformed from a poor relation to a central branch of mathematics.

 

Vilim Feller, photo from [Vranic]

 

Vilim Feller in 1907 (?), Zagreb;
with kind permission of prof. Marta Zdenkovic, Zagreb

...


COMPLETE TEXT: WILLIAM FELLER


Formated for CROWN by Prof.Dr. Darko Žubrinić
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