Thomas Gerald Room
Encyclopedia
Thomas Gerald Room was an Australian mathematician
who is best known for Room square
s.
, England
. He studied mathematics in St John's College, Cambridge
, 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
. He returned to Cambridge in 1927, at which time he completed his Ph.D., with a thesis supervised by H. F. Baker
. Room remained at Cambridge until 1935, when he moved to the University of Sydney
. During World War II
he worked for the Australian government, helping to decrypt Japanese communications. After the war, Room returned to the University of Sydney, where he was dean of the faculty of science from 1952 to 1956 and again from 1960 to 1965. He also held visiting positions at the University of Washington
in 1948, and the Institute for Advanced Study
and Princeton University
in 1957. He retired from Sydney in 1968 but took short-term positions afterwards at Westfield College
in London and the Open University
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.
formed by the 27 lines on a cubic algebraic curve
.
In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press
. Nearly 500 pages long, the book combines methods of synthetic geometry
and algebraic geometry
to study higher-dimensional generalizations of quartic surface
s and cubic surface
s. It describes many infinite families of algebraic varieties
, 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
of an appropriate matrix
.
In the postwar period, Room shifted the focus of his work to Clifford algebra
and spinor
groups
. Later, in the 1960s, he also began investigating finite geometry
, and wrote a textbook on the foundations of geometry.
Room invented Room square
s 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 Anstice, 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
.
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.
of the Australian National Research Council and was elected as a Fellow of the Royal Society. He was one of the founding fellows of the Australian Academy of Science
, chartered in 1954. From 1960 to 1962, he served as president of the Australian Mathematical Society
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 examination, is named in Room's honour.
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 is best known for Room square
Room square
A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:# Each cell of the array is either empty or contains an unordered pair from the set of symbols...
s.
Biography
Thomas Room was born on 10 November 1902, near LondonLondon
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. He studied mathematics in St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
, 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
University of Liverpool
The University of Liverpool is a teaching and research university in the city of Liverpool, England. It is a member of the Russell Group of large research-intensive universities and the N8 Group for research collaboration. Founded in 1881 , it is also one of the six original "red brick" civic...
. He returned to Cambridge in 1927, at which time he completed his Ph.D., with a thesis supervised by H. F. Baker
H. F. Baker
Henry Frederick Baker was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations , and Lie groups....
. Room remained at Cambridge until 1935, when he moved to the University of Sydney
University of Sydney
The University of Sydney is a public university located in Sydney, New South Wales. The main campus spreads across the suburbs of Camperdown and Darlington on the southwestern outskirts of the Sydney CBD. Founded in 1850, it is the oldest university in Australia and Oceania...
. During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
he worked for the Australian government, helping to decrypt Japanese communications. After the war, Room returned to the University of Sydney, where he was dean of the faculty of science from 1952 to 1956 and again from 1960 to 1965. He also held visiting positions at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...
in 1948, and the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
and Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1957. He retired from Sydney in 1968 but took short-term positions afterwards at Westfield College
Westfield College
Westfield College was a small college situated in Kidderpore Avenue, Hampstead, London, and was a constituent college of the University of London from 1882 to 1989. The college originally admitted only women as students and became coeducational in 1964. In 1989, Westfield College merged with Queen...
in London and the Open University
Open University
The Open University is a distance learning and research university founded by Royal Charter in the United Kingdom...
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 Ph.D. work concerned generalizations of the Schläfli double six, a configurationConfiguration (geometry)
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.Although certain specific...
formed by the 27 lines on a cubic algebraic curve
Algebraic curve
In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...
.
In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press
Cambridge University Press
Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
. Nearly 500 pages long, the book combines methods of synthetic geometry
Synthetic geometry
Synthetic or axiomatic geometry is the branch of geometry which makes use of axioms, theorems and logical arguments to draw conclusions, as opposed to analytic and algebraic geometries which use analysis and algebra to perform geometric computations and solve problems.-Logical synthesis:The process...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
to study higher-dimensional generalizations of quartic surface
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...
s and cubic surface
Cubic surface
A cubic surface is a projective variety studied in algebraic geometry. It is an algebraic surface in three-dimensional projective space defined by a single polynomial which is homogeneous of degree 3...
s. It describes many infinite families of algebraic varieties
Algebraic variety
In mathematics, an algebraic variety is the set of solutions of a system of polynomial equations. Algebraic varieties are one of the central objects of study in algebraic geometry...
, and individual varieties in these families, following a unifying principle that nearly all loci
Locus (mathematics)
In geometry, a locus is a collection of points which share a property. For example a circle may be defined as the locus of points in a plane at a fixed distance from a given point....
arising in algebraic geometry can be expressed as the solution to an equation involving the determinant
Determinant
In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...
of an appropriate matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
.
In the postwar period, Room shifted the focus of his work to Clifford algebra
Clifford algebra
In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal...
and spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
groups
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
. Later, in the 1960s, he also began investigating finite geometry
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact as many points as there are real numbers...
, and wrote a textbook on the foundations of geometry.
Room invented Room square
Room square
A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:# Each cell of the array is either empty or contains an unordered pair from the set of symbols...
s 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 Anstice, 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
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
.
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 MedalThomas 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. It is named after Thomas Ranken Lyle, an Irish mathematical physicist who became a professor at the University of...
of the Australian National Research Council and was elected as a Fellow of the Royal Society. He was one of the founding fellows of the Australian Academy of Science
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 Society and operates under a Royal Charter; as such it is...
, chartered in 1954. From 1960 to 1962, he served as president of the Australian Mathematical Society
Australian Mathematical Society
The Australian Mathematical Society 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 the interests of the profession to government. The Society...
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 examination, is named in Room's honour.