**William Feller** was a Croatian-born American mathematician who worked on probability and is best known as the author of a standard work on Statistics.

- His first name was not William.
- William was educated by private tutors as well as attending secondary school at the First Realgymnasium, Zagreb.
- William graduated from the Realgymnasium in June 1923 and entered the University of Zagreb in October of that year.
- However, Vladimir Varicak was the lecturer who influenced Feller most.
- Feller was awarded his first degree in 1925 (after 2 years instead of the usual 4 years) and then went to the University of Göttingen to undertake research.
- At Göttingen, in addition to Courant, Feller was also strongly influenced by David Hilbert.
- This was the year that Feller published his first work on probability theory which was his review of Andrei Nikolaevich Kolmogorov's monograph on probability theory Grundbegriffe der Wahrscheinlichkeitsrechnung Ⓣ(Basic concepts of probability theory.).
- Hitler came to power in Germany in 1933 and there was no way that Feller would accept the requirements placed on academics to sign a Nazi oath.
- Feller went to Copenhagen where he remained until 1934, then he moved to the University of Stockholm where he joined the probability group in the Institute for Insurance Mathematics and Mathematical Statistics headed by Harald Cramér.
- Being a research associate of Cramér was valuable to Feller, as was the fact that he was able to have useful discussions with Marcel Riesz who was also working in Sweden.
- Feller was still in Copenhagen at this time.
- Feller became the first executive editor of Mathematical Reviews which started reviewing articles which appeared from July 1939 and the first issue appeared in January 1940.
- Its successful launch was largely the result of both Neugebauer and Feller's major efforts to get the journal established.
- Feller became an American citizen in 1944, and in the following year accepted a professorship at Cornell University where he became a colleague and friend of Mark Kac who had emigrated to the United States in similar circumstances to Feller.
- Feller's treatise on probability is one of the great masterpieces of mathematics of all time.
- Feller worked on mathematical probability using Kolmogorov's measure theoretic formulation.
- Feller made notable contributions to the mathematical theory of Brownian motion and diffusion processes during the years 1930-1960.
- Some of the first papers reviewed by Mathematical Reviews were written by Feller himself such as Completely monotone functions and sequences (Duke Journal, 1939) and Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung Ⓣ(Fundamentals of Volterra theory of the struggle for existence in a probabilistic treatment) (1939).
- Other papers written by Feller while still at Brown University include: On the time distribution of so-called random events (1940), On the integral equation of renewal theory (1941), On A C Aitken's method of interpolation (1943), The fundamental limit theorems in probability (1945) and Note on the law of large numbers and "fair" games (1945).
- The second last of these papers on the limit theorems is on a topic that Feller kept returning to over many years.
- Feller's most important work was Introduction to Probability Theory and its Applications (1950-71), a two volume work which he frequently revised and improved with new approaches, new examples and new applications.
- The first edition was published in 1950 but Feller began writing it in 1941.
- We are by now so used to Feller's ideas that we tend to forget how much mathematics today goes back to his "recurrent events"; the theory of formal grammars is one outlandish example.
- Such choice of material gives Feller's book a special place among the reference books on the probability theory ...
- By his choice of problems Feller exposes their solutions by 'direct' and especially probabilistic methods.
- This tendency to see probabilistic sense behind their analytical transformations represents the most valuable feature of Feller's book.
- Feller was invited to address the International Congress of Mathematicians in Cambridge, Massachusetts, in 1950.
- Feller delivered the one hour plenary talk Some new connections between probability and classical analysis at the International Congress of Mathematicians held in Edinburgh, Scotland, in 1958.
- Work on the theory of diffusion was a major part of Feller's research at Princeton.
- He also was given the permanent title of visiting professor by Rockefeller University in 1966 and he spent several years there working both with geneticists and mathematicians while on leave from Princeton.
- The expression "proof by intimidation" was coined after Feller's lectures (by Mark Kac).
- During a Feller lecture, the hearer was made to feel privy to some wondrous secret, one that often vanished by magic as he walked out of the classroom at the end of the period.
- Like many great teachers, Feller was a bit of a con man.
- Feller received many honours.
- Feller had been nominated for the National Medal for Science by Oscar Zariski and the case for the award was written by Joseph Doob, Mark Kac and Jerzy Neyman.
- There was a difficult period when Feller was told that he had terminal cancer.
- Feller is also another example of the incredible value that can be derived from immigration.

Born 7 July 1906, Zagreb, Austria-Hungarian Empire (now Croatia). Died 14 January 1970, New York, USA.

View full biography at MacTutor

Origin Croatia, Statistics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive