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Marshall Hall showed talent for mathematics at a young age when he constructed a seven-place table of logarithms for the positive integers up to 1000. He entered Yale as an undergraduate, graduating with a B.A. in 1932. He continued graduate studies, spending the year 1932-33 at Cambridge in England.
At Cambridge he was taught by several mathematicians who were to have an important influence on him such as Philip Hall, Harold Davenport and G H Hardy. Hall returned to Yale where he was awarded his doctorate in 1936 for his thesis An Isomorphism Between Linear Recurring Sequences and Algebraic Rings which was supervised by Oystein Ore. After spending the year 1936-37 at Princeton, Hall was to return to Yale.
In 1941 however, he joined Naval Intelligence and was involved, as were many other mathematicians, deciphering coded messages. This work was little known about at the time but it has since emerged how significant this work proved to be. Hall's work in this area remained covered by the Official Secrets Act and when I [EFR] was in a group talking to him in 1981 about such things, he made it clear how seriously he continued to take his signing of the Act.
After World War II, Hall returned to Yale where he continued to teach until 1946. That year he accepted an appointment as an associate professor at Ohio State University. He was promoted to full professor at Ohio and remained there until 1959 when he accepted a post at California Institute of Technology at Pasadena.
During his time at Pasadena, Hall spent leave at Oxford in 1977, at Technion, Haifa in 1980 and at the University at Santa Barbara in 1984. In 1985 he accepted a post at Emory University in Atlanta.
Hall is best known as a group theorist, perhaps because of his famous book Theory of Groups (1959) from which several generations of group theorists have learnt the subject. However he has written many papers of fundamental importance in the subject as well as an extremely important paper in 1943 on projective planes. Perhaps his best known result in group theory is his solution of the Burnside problem for groups of exponent 6. He showed that a finitely generated group in which the order of every element divides 6 must be finite.
As well as the results on finite projective planes, Hall did other work of fundamental importance in the area of combinatorics, in particular on block designs. He wrote another classic text Combinatorial Theory in 1967.
Among the honours Hall received were two Guggenheim Fellowships and membership of the American Academy of Arts and Sciences.
Article by: J J O'Connor and E F Robertson
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