Eric Charles Milner
Encyclopedia
Eric Charles Milner, FRSC
(May 17, 1928–July 20, 1997) was a mathematician
who worked mainly in combinatorial
set theory
.
starting in 1946, where he competed as a featherweight
boxer
. He graduated in 1949 as the best mathematics student in his year, and received a masters degree in 1950 under the supervision of Richard Rado
and Charles Coulson
. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the Straits Trading Company
in Singapore
assaying
tin
. Soon thereafter he joined the mathematics faculty at the University of Malaya
in Singapore, where Alexander Oppenheim
and Richard K. Guy
were already working. In 1958, Milner took a sabbatical at the University of Reading
, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the University of London
in 1963. He joined his former Singapore colleagues Guy and Peter Lancaster as a professor at the University of Calgary
in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada
.
In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children. Estelle died of cancer in 1975, and in 1979 Milner remarried Elizabeth Forsyth Borthwick, with whom he had another son.
to Singapore and by meeting András Hajnal
while on sabbatical in Reading.
He generalized Chang
's ordinal partition theorem (expressed in the arrow notation for Ramsey theory
) ωω→(ωω,3)2 to ωω→(ωω,k)2 for arbitrary finite k He is also known for the Milner–Rado paradox
.
Royal Society of Canada
The Royal Society of Canada , may also operate under the more descriptive name RSC: The Academies of Arts, Humanities and Sciences of Canada , is the oldest association of scientists and scholars in Canada...
(May 17, 1928–July 20, 1997) was a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who worked mainly in combinatorial
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
.
Biography
A former London street urchin, Milner attended King's College LondonKing's College London
King's College London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. King's has a claim to being the third oldest university in England, having been founded by King George IV and the Duke of Wellington in 1829, and...
starting in 1946, where he competed as a featherweight
Featherweight
Featherweight is a weight class division in the sport of boxing. There are similarly named divisions under several Mixed Martial Arts organizations and in Greco-Roman wrestling.-Professional boxing:...
boxer
Boxing
Boxing, also called pugilism, is a combat sport in which two people fight each other using their fists. Boxing is supervised by a referee over a series of between one to three minute intervals called rounds...
. He graduated in 1949 as the best mathematics student in his year, and received a masters degree in 1950 under the supervision of Richard Rado
Richard Rado
Richard Rado FRS was a Jewish German mathematician. He earned two Ph.D.s: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to...
and Charles Coulson
Charles Coulson
Charles Alfred Coulson FRS was an applied mathematician, theoretical chemist and religious author.His major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity...
. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the Straits Trading Company
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....
in Singapore
Singapore
Singapore , officially the Republic of Singapore, is a Southeast Asian city-state off the southern tip of the Malay Peninsula, north of the equator. An island country made up of 63 islands, it is separated from Malaysia by the Straits of Johor to its north and from Indonesia's Riau Islands by the...
assaying
Metallurgical assay
A metallurgical assay is a compositional analysis of an ore, metal, or alloy.Some assay methods are suitable for raw materials; others are more appropriate for finished goods. Raw precious metals are assayed by an assay office...
tin
Tin
Tin is a chemical element with the symbol Sn and atomic number 50. It is a main group metal in group 14 of the periodic table. Tin shows chemical similarity to both neighboring group 14 elements, germanium and lead and has two possible oxidation states, +2 and the slightly more stable +4...
. Soon thereafter he joined the mathematics faculty at the University of Malaya
University of Malaya
The University of Malaya is located on a campus near the centre of Kuala Lumpur, and is the oldest university in Malaysia. It was founded in 1905 as a public-funded tertiary institution...
in Singapore, where Alexander Oppenheim
Alexander Oppenheim
Sir Alexander Oppenheim, OBE FRSE Knight Bachelor PMN was a British mathematician and philanthropist. In mathematics, his most notable contribution is his Oppenheim conjecture...
and Richard K. Guy
Richard K. Guy
Richard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
were already working. In 1958, Milner took a sabbatical at the University of Reading
University of Reading
The University of Reading is a university in the English town of Reading, Berkshire. The University was established in 1892 as University College, Reading and received its Royal Charter in 1926. It is based on several campuses in, and around, the town of Reading.The University has a long tradition...
, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
in 1963. He joined his former Singapore colleagues Guy and Peter Lancaster as a professor at the University of Calgary
University of Calgary
The University of Calgary is a public research university located in Calgary, Alberta, Canada. Founded in 1966 the U of C is composed of 14 faculties and more than 85 research institutes and centres.More than 25,000 undergraduate and 5,500 graduate students are currently...
in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada
Royal Society of Canada
The Royal Society of Canada , may also operate under the more descriptive name RSC: The Academies of Arts, Humanities and Sciences of Canada , is the oldest association of scientists and scholars in Canada...
.
In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children. Estelle died of cancer in 1975, and in 1979 Milner remarried Elizabeth Forsyth Borthwick, with whom he had another son.
Research
Milner's interest in set theory was sparked by visits of Paul ErdősPaul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
to Singapore and by meeting András Hajnal
András Hajnal
András Hajnal is an emeritus 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, in Hungary....
while on sabbatical in Reading.
He generalized Chang
Chen Chung Chang
Chen Chung Chang is a mathematician who works 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 theory. Chang's conjecture is named after him...
's ordinal partition theorem (expressed in the arrow notation for Ramsey theory
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...
) ωω→(ωω,3)2 to ωω→(ωω,k)2 for arbitrary finite k He is also known for the Milner–Rado paradox
Milner–Rado paradox
In set theory, a branch of mathematics, the Milner – Rado paradox, found by , states that every ordinal number α less than the successor κ+ of some cardinal number κ can be written as the union of sets X1,X2,... where Xn is of order type at most κn for n a positive integer....
.