Marshall Hall (mathematician) should not be confused with Philip Hall.
| Marshall Hall Jr. | |
| Birth Date: | 17 September 1910 |
| Birth Place: | St Louis, Missouri, U.S. |
| Nationality: | American |
| Death Place: | London, England |
| Field: | Abstract algebra |
| Work Institution: | Yale University Ohio State University California Institute of Technology Emory University |
| Alma Mater: | Cambridge University Yale University |
| Thesis Title: | An isomorphism between linear recurring sequences and algebraic rings |
| Thesis Year: | 1936 |
| Doctoral Advisor: | Øystein Ore |
| Doctoral Students: | Robert Calderbank Donald Knuth Robert McEliece E. T. Parker |
| Known For: | Group theory Combinatorics Hall's conjecture Hall multiplier Hall plane Hall-Janko group Planar ternary ring |
Marshall Hall Jr. (17 September 1910 - 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics.[1]
Hall studied mathematics at Yale University, graduating in 1932. He studied for a year at Cambridge University under a Henry Fellowship working with G. H. Hardy. He returned to Yale to take his Ph.D. in 1936 under the supervision of Øystein Ore.[2]
He worked in Naval Intelligence during World War II, including six months in 1944 at Bletchley Park, the center of British wartime code breaking. In 1946 he took a position at Ohio State University. In 1959 he moved to the California Institute of Technology where, in 1973, he was named the first IBM Professor at Caltech, the first named chair in mathematics. After retiring from Caltech in 1981, he accepted a post at Emory University in 1985.
Hall died in 1990 in London on his way to a conference to mark his 80th birthday.
He wrote a number of papers of fundamental importance in group theory, including his solution of Burnside's problem for groups of exponent 6, showing that a finitely generated group in which the order of every element divides 6 must be finite.
His work in combinatorics includes an important paper of 1943 on projective planes, which for many years was one of the most cited mathematics research papers.[3] In this paper he constructed a family of non-Desarguesian planes which are known today as Hall planes. He also worked on block designs and coding theory.
His classic book on group theory was well received when it came out and is still useful today. His book Combinatorial Theory came out in a second edition in 1986, published by John Wiley & Sons.
He proposed Hall's conjecture on the differences between perfect squares and perfect cubes, which remains an open problem as of 2015.
Hall's work[4] on continued fractions showed that the Lagrange spectrum includes all numbers greater than 6. This interval is known as Hall's Ray. The lower limit of Hall’s ray was established by Freiman in 1975.