Marshall Hall (mathematician)

Marshall Hall, Jr.
Marshall Hall, Jr.
Born	(1910-09-17)17 September 1910 St Louis, Missouri, U.S.
Died	4 July 1990(1990-07-04) (aged 79) London, UK
Residence	U.S.
Nationality	American
Fields	Mathematician
Institutions	Yale University Ohio State University California Institute of Technology Emory University
Alma mater	Cambridge University Yale University
Doctoral advisor	Øystein Ore
Doctoral students	Robert Calderbank Donald Knuth Robert McEliece E. T. Parker
Known for	Group theory, Combinatorics

Marshall Hall, Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics.^[1]

Career

He studied mathematics at Yale, graduating in 1932. He studied for a year at Cambridge University under a Henry Fellowship working with G. H. Hardy.^[2] He returned to Yale to take his Ph.D. in 1936 under the supervision of Øystein Ore.^[3]

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 The 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.

Contributions

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.^[4] In this paper he constructed a family of non-Desarguesian projective 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 J. Wiley & Sons.

He proposed Hall's conjecture on the differences between perfect squares and perfect cubes, which remains an open problem as of 2015.

Publications

• Hall, Jr., Marshall (1943), "Projective planes", Transactions of the American Mathematical Society, American Mathematical Society, 54 (2): 229–277, doi:10.2307/1990331, ISSN 0002-9947, JSTOR 1990331, MR 0008892 
• Hall, Jr., Marshall (1959), Theory of Groups, Macmillan, LCCN 59005035, MR 103215 . Review by Wilhelm Magnus published in Bull. Amer. Math. Soc. Volume 66, Number 3 (1960), 144-146 and available at http://projecteuclid.org/euclid.bams/1183523505
• Hall, Jr., Marshall; Senior, James K. (1964), The Groups of Order 2n (n ≤ 6), Macmillan, LCCN 64016861, MR 168631 . An exhaustive catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and lattice presentations of each group in the notation the text defines. "Of enduring value to those interested in finite groups" (from the preface).
• Hall, Jr., Marshall (1967), Combinatorial Theory, Blaisdell Publishing, LCCN 67011108, MR 224481 

Notes

References

• Hall, Jr., Marshall (1989), "Mathematical Biography: Marshall Hall Jr.", in Duran, Peter; Askey, Richard; Merzbach, Uta C., A Century of mathematics in America, vol 1 (PDF), Providence, RI: American Mathematical Society, pp. 367–374, ISBN 0-8218-0124-4 
• Obituary at Ohio State University
• Zassenhaus, Hans (1990), "Marshall Hall, Jr.: 1910–1990", Notices of the American Mathematical Society, 37 (8): 1033, ISSN 0002-9920, MR 1071446 

External links

• O'Connor, John J.; Robertson, Edmund F., "Marshall Hall jr", MacTutor History of Mathematics archive, University of St Andrews .
• Marshall Hall at the Mathematics Genealogy Project