Marshall Hall Jr.
Marshall Hall Jr. was born on September 17, 1910, in St. Louis, Missouri to Marshall and Inez (Bethune) Hall. He attended Yale University and was awarded a B.A. degree in 1932. He then spent a year at Cambridge University, where he studied under Phillip Hall, Harold Davenport, and G.H. Hardy. He returned to Yale, where he earned a Ph.D. in 1936, writing a thesis under the direction of Oystein Ore. After a year at the Institute for Advanced Study, he returned to Yale as an instructor until the outbreak of World War II, when he joined Naval Intelligence. There he made significant contributions to the cryptanalysis of both Japanese naval codes and the German Enigma code.
After returning to Yale for a year, he was appointed associate professor at Ohio State in 1946 and was promoted to professor in 1948. He played an important role in the department's growth, including the supervision of six Ph.D. theses. His influence and presence at Ohio State attracted quality young faculty in the fields of group theory and combinatorics.
In 1959 Hall accepted a position at Cal Tech, where he stayed until his retirement in 1981. He then held the position of visiting distinguished professor at Emory University in Atlanta until his death in 1990.
Hall's highly regarded books Theory of Groups and Combinatorial Theory are classics. His mathematical legacy includes over 120 research papers on group theory, coding theory, and design theory. His 1943 paper on projective planes ranks among the most cited papers in mathematics. Several fundamental concepts as well as a sporadic simple group are identified with Hall's name. One of Hall's most celebrated results is his solution to the "Burnside Problem" for exponent 6 -- that is, a finitely generated group in which the order of every element divides 6 must be finite. Hall influenced both John Thompson and Michael Aschbacher, finite group theory's two greatest contributors. It was Hall who suggested Thompson's Ph.D dissertation problem, which led to the solution of Froebenius' conjecture that any fixed-point free automorphism of a group is nilpotent. Hall's Ph.D. students at Cal Tech included Donald Knuth and Robert McEliece.
In his memorial tribute Hans Zassenhaus writes:
The group theoretic collection process of Phillip Hall (no relation) inspired Marshall Hall to the construction of a basis for free Lie rings and higher commutators in free groups ... with great potential for further research ... The book on Combinatorial Theory (1967 and 1986) summarizes his research achievements in combinatorics, in particular his deep results on combinatorial designs, and provides a new chart for an ancient branch of mathematics.
Among the honours Hall received were two Guggenheim Fellowships and membership in the American Academy of Arts and Sciences. Marshall Hall received the honorary Doctor of Science degree from The Ohio State University at the 1988 Autumn Commencement ceremonies, in recognition for his immense contributions to mathematics.