Gordon Bamford Preston (28 April 1925 – 14 April 2015) was an English mathematician best known for his work on

semigroup In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...

s. He received his

D.Phil. 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 mathematics in 1954 from

Magdalen College, Oxford Magdalen College (, ) is a constituent college of the University of Oxford. It was founded in 1458 by William of Waynflete. Today, it is the fourth wealthiest college, with a financial endowment of £332.1 million as of 2019 and one of the s ...

. He was born in

Workington Workington is a coastal town and civil parish at the mouth of the River Derwent on the west coast in the Allerdale borough of Cumbria, England. The town was historically in Cumberland. At the 2011 census it had a population of 25,207. Loca ...

and brought up in

Carlisle Carlisle ( , ; from xcb, Caer Luel) is a city that lies within the Northern England, Northern English county of Cumbria, south of the Anglo-Scottish border, Scottish border at the confluence of the rivers River Eden, Cumbria, Eden, River C ...

. 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 opposin ...

, he left his undergraduate studies at Oxford University for

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 following ...

, to help crack German codes with a small group of mathematicians, which included

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...

. At Bletchley Park he persuaded

Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...

(who thought that the women would not care for the "intellectual effort") to authorise talks to the

Wrens Wrens are a family of brown passerine birds in the predominantly New World family Troglodytidae. The family includes 88 species divided into 19 genera. Only the Eurasian wren occurs in the Old World, where, in Anglophone regions, it is comm ...

to explain their work mathematically, and the talks were very popular. After graduation, he was a teacher at

Westminster School (God Gives the Increase) , established = Earliest records date from the 14th century, refounded in 1560 , type = Public school Independent day and boarding school , religion = Church of England , head_label = Hea ...

, London and then The Royal Military College of Science. In 1954 he wrote three highly influential papers in the

Journal of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

, laying the foundations of

inverse semigroup In group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy'', i.e. a regular semig ...

theory. Before Preston and

Alfred H. Clifford Alfred Hoblitzelle Clifford (July 11, 1908 – December 27, 1992) was an American mathematician born in St. Louis, Missouri who is known for Clifford theory and for his work on semigroups. He did his undergraduate studies at Yale and his PhD at ...

's book, ''The Algebraic Theory of Semigroups'' (Vol 1 1961) (Vol 2 1967) and the Russian, Evgenii S. Lyapin's, ''Semigroups'' (1960) there was no systematic treatment of semigroups. ''The Algebraic Theory of Semigroups'' was hailed as an excellent achievement that greatly influenced the future development of the subject. In 1963, Preston moved to Australia to take up the chair of mathematics at

Monash University Monash University () is a public research university based in Melbourne, Victoria, Australia. Named for prominent World War I general Sir John Monash, it was founded in 1958 and is the second oldest university in the state. The university has a ...

Melbourne Melbourne ( ; Boonwurrung/Woiwurrung: ''Narrm'' or ''Naarm'') is the capital and most populous city of the Australian state of Victoria, and the second-most populous city in both Australia and Oceania. Its name generally refers to a met ...

. Preston was an important contributor to algebraic semigroup theory and a respected head of school during his various Monash appointments from 1963 until his retirement in 1990. He subsequently spent six months each year in both Oxford, UK, and Melbourne, Australia, dying on 14 April 2015 in Oxford at age 89.

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* {{DEFAULTSORT:Preston, Gordon 1925 births 2015 deaths 20th-century English mathematicians 21st-century English mathematicians Alumni of Magdalen College, Oxford Monash University faculty Bletchley Park people People educated at Carlisle Grammar School People from Carlisle, Cumbria People from Workington