Eric Charles Milner, FRSC (May 17, 1928 – July 20, 1997) was a

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, mathematical structure, structure, space, Mathematica ...

who worked mainly in

combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ap ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

Biography

Born into a South East London working-class family, Milner was sent to a

Reading Reading is the process of taking in the sense or meaning of Letter (alphabet), letters, symbols, etc., especially by Visual perception, sight or Somatosensory system, touch. For educators and researchers, reading is a multifaceted process invo ...

boarding school for the war but, hating it, ran away and roamed the streets of London. Eventually, another school was found for him; Milner attended King's College London starting in 1946, where he competed as a

featherweight Featherweight is a weight class in the combat sports of boxing, kickboxing, mixed martial arts, and Greco-Roman wrestling. Boxing Professional boxing History A featherweight boxer weighs in at a limit of . In the early days of the division, this ...

boxer Boxer most commonly refers to: *Boxer (boxing), a competitor in the sport of boxing *Boxer (dog), a breed of dog Boxer or boxers may also refer to: Animal kingdom *Boxer crab * Boxer shrimp, a small group of decapod crustaceans * Boxer snipe eel, ...

. He graduated in 1949 as the best mathematics student in his year, and received a master's degree in 1950 under the supervision of

Richard Rado Richard Rado FRS (28 April 1906 – 23 December 1989) was a German-born British mathematician whose research concerned combinatorics and graph theory. He was Jewish and left Germany to escape Nazi persecution. He earned two PhDs: in 1933 from th ...

and

Charles Coulson Charles Alfred Coulson (13 December 1910 – 7 January 1974) was a British applied mathematician and theoretical chemist. Coulson's major scientific work was as a pioneer of the application of the quantum theory of valency to problems of mo ...

. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the

Straits Trading Company The Straits Trading Company Limited is a Singapore-based corporation with operations in Singapore and Malaysia, as well as various localities in Asia and Australia. Founded in 1887, the company was the result of a partnership for tin smelting be ...

Singapore Singapore (), officially the Republic of Singapore, is a sovereign island country and city-state in maritime Southeast Asia. It lies about one degree of latitude () north of the equator, off the southern tip of the Malay Peninsula, borde ...

assaying

tin Tin is a chemical element with the symbol Sn (from la, stannum) and atomic number 50. Tin is a silvery-coloured metal. Tin is soft enough to be cut with little force and a bar of tin can be bent by hand with little effort. When bent, ...

. Soon thereafter he joined the mathematics faculty at the

University of Malaya The University of Malaya ( ms, Universiti Malaya, UM; abbreviated as UM or informally the Malayan University) is a public research university located in Kuala Lumpur, Malaysia. It is the oldest and highest ranking Malaysian institution of highe ...

in Singapore, where Alexander Oppenheim and

Richard K. Guy Richard Kenneth Guy (30 September 1916 – 9 March 2020) was a British mathematician. He was a professor in the Department of Mathematics at the University of Calgary. He is known for his work in number theory, geometry, recreational mathemat ...

were already working. In 1958, Milner took a sabbatical at the

University of Reading The University of Reading is a public university in Reading, Berkshire, England. It was founded in 1892 as University College, Reading, a University of Oxford extension college. The institution received the power to grant its own degrees in 192 ...

, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degre ...

in 1963. He joined his former Singapore colleagues Guy and

Peter Lancaster Peter Lancaster (born 14 November 1929) is a British-Canadian mathematician. He is professor emeritus at the University of Calgary, where he has worked since 1962. His research focuses on matrix analysis and related fields, motivated by proble ...

as a professor at the

University of Calgary The University of Calgary (U of C or UCalgary) is a public research university located in Calgary, Alberta, Canada. The University of Calgary started in 1944 as the Calgary branch of the University of Alberta, founded in 1908, prior to being inst ...

in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became a Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada.. In 1974 he was a Plenary Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Vancouver Vancouver ( ) is a major city in western Canada, located in the Lower Mainland region of British Columbia. As the most populous city in the province, the 2021 Canadian census recorded 662,248 people in the city, up from 631,486 in 2016. Th ...

.Milner, E. C
"Transversal theory."
In ''Proceedings of the International Congress of Mathematicians, Vancouver, BC'', vol. 1, pp. 155–169. 1974. In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children who were Paul Milner, Mark Milner, Suzanne Milner, and Simon Milner. Estelle died of cancer in 1975, and in 1979 Milner married Elizabeth Forsyth Borthwick, with whom he had his son Robert Milner.

Research

Milner's interest in set theory was sparked by visits of Paul Erdős to Singapore and by meeting

András Hajnal András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,

while on sabbatical in Reading. He generalized

Chen Chung Chang Chen Chung Chang (Chinese: 张晨钟) was a mathematician who worked in model theory. He obtained his PhD from Berkeley in 1955 on "Cardinal and Ordinal Factorization of Relation Types" under Alfred Tarski. He wrote the standard text on model t ...

's ordinal partition theorem (expressed in the arrow notation for

Ramsey theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask ...

) ω^ω→(ω^ω,3)² to ω^ω→(ω^ω,''k'')² for arbitrary finite ''k''. He is also known for the

Milner–Rado paradox In set theory, a branch of mathematics, the Milner – Rado paradox, found by , states that every ordinal number \alpha less than the successor \kappa^ of some cardinal number \kappa can be written as the union of sets X_1, X_2,... where X_n is ...

. He has 15 joint papers with Paul Erdős.

Selected works

* * *

References

External links

Eric Milner award

University of Calgary Eric Milner Colloquium
* {{DEFAULTSORT:Milner, Eric Charles 1928 births 1997 deaths Alumni of King's College London Set theorists 20th-century Canadian mathematicians Fellows of the Royal Society of Canada Academic staff of the University of Calgary 20th-century English mathematicians