Thomas Gerald Room
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Thomas Gerald Room FRS FAA (10 November 1902 – 2 April 1986) was an
Australian Australian(s) may refer to: Australia * Australia, a country * Australians, citizens of the Commonwealth of Australia ** European Australians ** Anglo-Celtic Australians, Australians descended principally from British colonists ** Aboriginal Aus ...
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 is best known for Room squares. He was a Foundation
Fellow of the Australian Academy of Science The Fellowship of the Australian Academy of Science is made up of about 500 Australian scientists. Scientists judged by their peers to have made an exceptional contribution to knowledge in their field may be elected to Fellowship of the Academy ...
. . Also published in ''Historical Records of Australian Science'' 7 (1): 109–122, . An abridged version i
online at the web site of the Australian Academy of Science
First published in ''Australian Dictionary of Biography'', Volume 18, (MUP), 2012. Room was born in London and educated at
St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...
he moved to Sydney, Australia, in 1935. During the Second World War he worked for the Australian government to decrypt coded Japanese communications. After the war Room became dean of the faculty of science at the
University of Sydney The University of Sydney (USYD) is a public university, public research university in Sydney, Australia. Founded in 1850, it is the oldest university in both Australia and Oceania. One of Australia's six sandstone universities, it was one of the ...
and later worked in the US and England.


Biography

Thomas Room was born on 10 November 1902, near
London London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...
,
England England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...
. He studied mathematics in
St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...
, and was a wrangler in 1923. He continued at Cambridge as a graduate student, and was elected as a fellow in 1925, but instead took a position at the
University of Liverpool The University of Liverpool (abbreviated UOL) is a Public university, public research university in Liverpool, England. Founded in 1881 as University College Liverpool, Victoria University (United Kingdom), Victoria University, it received Ro ...
. He returned to Cambridge in 1927, at which time he completed his PhD, with a thesis supervised by
H. F. Baker Henry Frederick Baker Royal Society, FRS Royal Society of Edinburgh, FRSE (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations ...
. Room remained at Cambridge until 1935, when he moved to the
University of Sydney The University of Sydney (USYD) is a public university, public research university in Sydney, Australia. Founded in 1850, it is the oldest university in both Australia and Oceania. One of Australia's six sandstone universities, it was one of the ...
, where he accepted the position of Chair of the Mathematics Department, a position he held until his retirement in 1968. During
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
he worked for the Australian government, helping to
decrypt In cryptography, encryption (more specifically, encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the information, known as plai ...
Japanese communications. In January 1940, with the encouragement of the Australian Army, he, together with some colleagues at the University of Sydney, began to study Japanese codes. The others were the mathematician Richard Lyons and the classicists
Arthur Dale Trendall Arthur Dale Trendall, (28 March 1909 – 13 November 1995) was a New Zealand art historian and classical archaeologist whose work on identifying the work of individual artists on Greek ceramic vessels at Apulia and other sites earned him i ...
and Athanasius Treweek. By this time Room had already begun learning Japanese under Margaret Ethel Lake (1883-?) at the University of Sydney. In May 1941 Room and Treweek attended a meeting at the Victoria Barracks in Melbourne with the Director of Naval Intelligence of the
Royal Australian Navy The Royal Australian Navy (RAN) is the navy, naval branch of the Australian Defence Force (ADF). The professional head of the RAN is Chief of Navy (Australia), Chief of Navy (CN) Vice admiral (Australia), Vice Admiral Mark Hammond (admiral), Ma ...
, several Australian Army intelligence officers and
Eric Nave Captain Eric Nave (18 March 1899 – 23 June 1993) was an Australian cryptographer and intelligence officer in the Royal Australian Navy (RAN) and Royal Navy, noted for his work with joint Allied intelligence units during World War II. He serv ...
, an expert Japanese cryptographer with the Royal Australian Navy. As a result it was agreed that Room's group, with the agreement of the University of Sydney, would move in August 1941 to work under Nave at the Special Intelligence Bureau in Melbourne. On 1 September 1941, Room was sent to the
Far East Combined Bureau The Far East Combined Bureau, an outstation of the British Government Code and Cypher School, was set up in Hong Kong in March 1935, to monitor Japanese, and also Chinese and Russian (Soviet) intelligence and radio traffic. Later it moved to Sing ...
in Singapore to study the codebreaking techniques used there. After the outbreak of war they were working for
FRUMEL Fleet Radio Unit, Melbourne (FRUMEL) was a United States–Australian–British signals intelligence unit, founded in Melbourne, Australia, during World War II. It was one of two major Allied signals intelligence units called Fleet Radio Units in ...
(Fleet Radio Unit Melbourne), a joint American-Australian intelligence unit, but when Lieutenant Rudolph Fabian took over command of FRUMEL and particularly when, in October 1942, FRUMEL was placed under direct control of the US Navy, civilians such as the member of Room's group were found surplus to requirements and returned to their academic posts. After the war, Room served as dean of the faculty of science at the University of Sydney from 1952 to 1956 and again from 1960 to 1965. He also held visiting positions at the
University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...
in 1948, and the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
and
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
in 1957.Hirschfeld, J. W. P.; Wall, G. E. (1987). "Thomas Gerald Room. 10 November 1902 – 2 April 1986". ''Biographical Memoirs of Fellows of the Royal Society'' 33: 574. doi:10.1098/rsbm.1987.0020. JSTOR 769963.. Also published in ''Historical Records of Australian Science'' 7 (1): 109–122, doi:10.1071/HR9870710109. An abridged version is online at the web site of the Australian Academy of Science. He retired from Sydney in 1968 but took short-term positions afterwards at
Westfield College Westfield College was a small college situated in Hampstead, London, from 1882 to 1989. It was the first college to aim to educate women for University of London degrees from its opening. The college originally admitted only women as students and ...
in London and the
Open University The Open University (OU) is a Public university, public research university and the largest university in the United Kingdom by List of universities in the United Kingdom by enrolment, number of students. The majority of the OU's undergraduate ...
before returning to Australia in 1974. He died on 2 April 1986. Room married Jessica Bannerman, whom he met in Sydney, in 1937; they had one son and two daughters.


Research

Room's PhD work concerned generalizations of the Schläfli double six, a
configuration Configuration or configurations may refer to: Computing * Computer configuration or system configuration * Configuration file, a software file used to configure the initial settings for a computer program * Configurator, also known as choice board ...
formed by the 27 lines on a cubic
algebraic surface In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of di ...
. In 1938 he published the book ''The geometry of determinantal loci'' through the
Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...
. Nearly 500 pages long, the book combines methods of
synthetic geometry Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulates ...
and
algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
to study higher-dimensional generalizations of
quartic surface In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An ''affine'' quartic surface ...
s and
cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than ...
s. It describes many infinite families of
algebraic varieties Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. ...
, and individual varieties in these families, following a unifying principle that nearly all loci arising in algebraic geometry can be expressed as the solution to an equation involving the
determinant In mathematics, the determinant is a Scalar (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the ...
of an appropriate
matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ...
.Review of ''The geometry of determinantal loci'' by Virgil Snyder (1939), ''Bulletin of the AMS'' 45: 499–501, . In the postwar period, Room shifted the focus of his work to
Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real number ...
and
spinor In geometry and physics, spinors (pronounced "spinner" IPA ) are elements of a complex numbers, complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infi ...
groups A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...
. Later, in the 1960s, he also began investigating
finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...
, and wrote a textbook on the foundations of geometry. Room invented Room squares in a brief note published in 1955. A Room square is an ''n'' × ''n'' grid in which some of the cells are filled by sets of two of the numbers from 0 to ''n'' in such a way that each number appears once in each row or column and each two-element set occupies exactly one cell of the grid. Although Room squares had previously been studied by
Robert Richard Anstice Robert Richard Anstice (1813–1853) was an English clergyman and mathematician who wrote two remarkable papers on combinatorics, published the same year he died in the Cambridge and Dublin Mathematical Journal. He pioneered the use of primiti ...
, Anstice's work had become forgotten and Room squares were named after Room. In his initial work on the subject, Room showed that, for a Room square to exist, ''n'' must be odd and cannot equal 3 or 5. It was later shown by W. D. Wallis in 1973 that these are necessary and sufficient conditions: every other odd value of ''n'' has an associated Room square. The nonexistence of a Room square for ''n'' = 5 and its existence for ''n'' = 7 can both be explained in terms of configurations in
projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...
. Despite retiring in 1968, Room remained active mathematically for several more years, and published the book ''Miniquaternion geometry: An introduction to the study of projective planes'' in 1971 with his student Philip B. Kirkpatrick.


Awards and honours

In 1941, Room won the
Thomas Ranken Lyle Medal The Thomas Ranken Lyle Medal is awarded at most every two years by the Australian Academy of Science to a mathematician or physicist for his or her outstanding research accomplishments.
of the Australian National Research Council and was elected as a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
. He was one of the Foundation Fellows of the
Australian Academy of Science The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The academy is modelled after the Royal Soci ...
, chartered in 1954. From 1960 to 1962, he served as president of the
Australian Mathematical Society The Australian Mathematical Society (AustMS) was founded in 1956 and is the national society of the mathematics profession in Australia. One of the society's listed purposes is to promote the cause of mathematics in the community by representing ...
and he later became the first editor of its journal. The T. G. Room award of the Mathematical Association of New South Wales, awarded to the student with the best score in the NSW Higher School Certificate Mathematics Extension 2 examination, is named in Room's honour.The T G Room Award
, Mathematical Association of New South Wales. Retrieved 1 June 2010.


References

{{DEFAULTSORT:Room, Thomas Gerald 1902 births 1986 deaths 20th-century Australian mathematicians Academic staff of the University of Sydney Fellows of the Australian Academy of Science Alumni of St John's College, Cambridge Fellows of the Royal Society Australian cryptographers British emigrants to Australia