**Eugene Lukacs** was born into a Jewish family. The family lived in Vienna where Eugene's father worked in a bank. However Eugene was born in his grandmother's house in Szombathely, then moved to Vienna a few weeks later and he was educated in that city. After primary and the Realgymnasium secondary school, Lukacs entered the Technical University in Vienna in 1925 where he studied mechanical engineering. However, he soon transferred to the University of Vienna to study mathematics. Among his teachers at the University of Vienna were H Hahn, E Helly, W Meyer, L Vietoris and W Wirtinger.

After taking his first degree, Lukacs continued to study at Vienna for his doctorate. His doctoral dissertation on a geometry topic was supervised by W Meyer and, in 1930, he was awarded his doctorate. He continued to study, taking an actuarial degree in 1931.

By May 1931 Austria was close to financial and economic disaster. This was no time to get an academic position in a university, so Lukacs took a post as a secondary school teacher in Vienna. However, the poor economic state and the rise of the National Socialists in Germany, resulted in considerable support being given to the Nazis in Austria. By spring 1933 Adolf Hitler was in power in Germany, and Nazi propaganda for the incorporation of Austria was greatly increased. Austria turned to Italy for help. All this was bad news for Lukacs, particularly since he was Jewish.

Lukacs left school teaching in 1933 and took up a position as an actuary at an insurance company, having E Helly, another of Jewish origin, amongst his colleagues in the insurance company. The political situation in Austria continued to deteriorate. A civil war followed with four days of fighting. All political parties were abolished except the Fatherland Front but, in July 1934, a group of Nazis attempted to seize power but they were compelled to surrender, and their leaders were executed. Hitler and Mussolini allied themselves in 1936 and Austria became totally isolated. During this time Lukacs had married Elizabeth Weisz. They had met at the University of Vienna in 1927 while they were both studying mathematics and physics.

In 1937 Lukacs left the insurance company. He also taught mathematics at the Volkshochschule Wien Volksheim but his position was becoming increasingly difficult. In March 1938, German troops, accompanied by Hitler himself, entered Austria. Austria was absorbed into Germany and the Nazis arrested the leaders of the Austrian political parties. Many Austrians, especially those of Jewish origin, went into exile and Lukacs and his wife decided that they had to take this route. Elizabeth Lukacs left for the United States late in 1938 while Eugene left some time later, reaching the United States in February 1939.

While at the University of Vienna, Lukacs had met Wald who was also a Hungarian Jew. Wald had reached the United States in 1938 and now the two made contact. Wald was working on statistics and probability and he persuaded Lukacs to take an interest in this topic too. The job position in the United States was extremely bad, since this was the time following the great depression. However Elizabeth Lukacs found a post teaching at Garrison High School in Baltimore and she encouraged Eugene to apply for a position at Friends High School in Baltimore. He was appointed to teach Latin and advanced mathematics but, after a short time he moved to another college. He taught physics and mathematics at several colleges before being appointed to Our Lady of Cincinnati College in 1945.

In 1942 Lukacs had made an important contribution to mathematical statistics by introducing, for the first time, the method of differential equations in characteristic function theory. He used this method to solve problems of characterisation of distributions. The method allowed him to invesitgate the independence of the sample mean and sample variance in certain cases.

After moving to Cincinnati, Lukacs worked with Szász who had held a post there from 1936. The two worked on probability and wrote a number of joint papers. He continued at Our Lady of Cincinnati College until 1953, although he spent some leave working as a mathematical statistician at the National Bureau of Standards in Washington, D.C. In 1953 Lukacs Eugene joined the Office of Naval Research and he later became the Head of its Statistics.

Lukacs moved again, this time in 1955 to the Catholic University of America where, in 1959, he set up the Statistical Laboratory becoming its director. It became an important research establishment, visited by many mathematicians including Harald Cramer, Jerzy Neyman, Alfred Renyi, Paul Lévy, R A Fisher, Mark Kac, Yu Linnik, Paul Erdős, Jacob Wolfowitz, William Cochran and William Feller.

Lukacs retired in 1972, and went first to Bowling Green where he remained for four years. After holding visiting posts back in Europe, in particular his home university of Vienna and at Erlangen, he returned to his home in Washington D.C. in 1978. One of his most important books *Developments in Characteristic Function Theory* was published in 1983, eleven years after he retired.

Perhaps his most famous work was *Characteristic Functions* (1960) which studied the properties of characteristic functions and their applications. Other topics to which Lukacs made major contributions include characterisations of distributions, stability of characterisation results and functional equations.

In [3] Lukacs's many visiting appointments are listed:-

Eugene liked to travel. This led him to spend time teaching or lecturing as visiting professor at the Sorbonne(1961-62, 1965-66), the Swiss Federal Institute, Zürich(1961-62), the Institute of Technology, Vienna(1965-66, 1970, 1975-77), the University of Hull(1971), the University of Sheffield(1974-75), the University of Erlangen(1977-78), the University of Brussels(1961-62)and the University of Athens(1961-62).

Lukacs's hobbies and interests included stamp and coin collecting, hiking, bird watching, photography and, as stated above, travelling. One of his favourite places was the Mathematics Research Institute at Oberwolfach in southern Germany. He spent part of his holiday at his cottage in the Viennese Woods almost every summer.

In [3] his attitude is described:-

Eugene was a constant source of encouragement to his colleagues and students. He showed a great deal of interest in their work and was always available for consultation. He promptly responded to countless queries that he received from all over the world, mostly on questions concerning characteristic functions.

We shall miss Eugene greatly, not only for his contributions to probability and statistics but also as a colleague, a friend and as a human being of integrity.

Lukacs undertook many editorial duties. He was an associate editor of the *Journal of the American Statistical Association* (1951-55, 1961-63), the *Annals of Mathematical Statistics* (1958-64,1968-70), and the *Journal of Multivariate Analysis* (1970-83). Jointly with Z W Birnbaum, he was the founding editor of the *Academic Press Series in Probability and Mathematical Statistics* (1962-85).

He received many honors such as being elected a fellow of the Institute of Mathematical Statistics in 1957, a fellow of the American Statistical Association in 1969, and a fellow of the American Association for Advancement of Science in 1958. He was elected to the Austrian Academy of Sciences in 1973.

**Article by:** *J J O'Connor* and *E F Robertson*

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