Marshall Hall Jr. (17 September 1910 – 4 July 1990) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who made significant contributions to

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

and combinatorics.

Career

Hall studied mathematics at

Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

, graduating in 1932. He studied for a year at

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...

under a Henry Fellowship working with

G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

. He returned to Yale to take his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1936 under the supervision of Øystein Ore. He worked in

Naval Intelligence Military intelligence is a military discipline that uses information collection and analysis approaches to provide guidance and direction to assist commanders in their decisions. This aim is achieved by providing an assessment of data from a ...

during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

, including six months in 1944 at

Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years followin ...

, the center of British wartime code breaking. In 1946 he took a position at

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...

. In 1959 he moved to the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

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 Emory University is a private research university in Atlanta, Georgia. Founded in 1836 as "Emory College" by the Methodist Episcopal Church and named in honor of Methodist bishop John Emory, Emory is the second-oldest private institution of ...

in 1985. Hall died in 1990 in

London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...

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 plane In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that d ...

s, which for many years was one of the most cited mathematics research papers.Mathematics Department of

br>Marshall Hall Jr.
via

Wayback Machine The Wayback Machine is a digital archive of the World Wide Web founded by the Internet Archive, a nonprofit based in San Francisco, California. Created in 1996 and launched to the public in 2001, it allows the user to go "back in time" and see ...

In this paper he constructed a family of

non-Desarguesian plane In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is true in all projective ...

s which are known today as

Hall plane In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order ''p''2''n'' for every prime ''p'' and every positive integer ''n'' provided ''p''2''n'' > 4. Algebraic cons ...

s. He also worked on block designs and

coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied ...

. 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 John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, ...

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

Publications

* 1943: "Projective Planes",

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

54(2): 229–77 * 1959: ''The Theory of Groups'', Macmillan **

Wilhelm Magnus Hans Heinrich Wilhelm Magnus known as Wilhelm Magnus (February 5, 1907 in Berlin, Germany – October 15, 1990 in New Rochelle, New York) was a German-American mathematician. He made important contributions in combinatorial group theory, Lie alge ...

(1960
Review: Marshall Hall, Jr. ''Theory of Groups''

Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. I ...

66(3): 144–6. * 1964: (with James K. Senior) ''The Groups of Order 2ⁿ n ≤ 6)'', Macmillan ** Preface: "An exhaustive catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and

lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an orna ...

presentations of each group in the notation the text defines. "Of enduring value to those interested in

finite groups Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

". * 1967: ''Combinatorial Theory'', Blaisdell

Notes

References

* *

External links

* * {{DEFAULTSORT:Hall, Marshall Jr 1910 births 1990 deaths 20th-century American mathematicians Mathematicians from Missouri Scientists from St. Louis Algebraists Group theorists Emory University faculty Combinatorialists California Institute of Technology faculty Ohio State University faculty Yale Graduate School of Arts and Sciences alumni Yale College alumni