Thomas Gerald Room

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Thomas Gerald Room FRS FAA (10 November 1902 – 2 April 1986) was an Australian mathematician who is best known for Room squares. He was a Foundation Fellow of the Australian Academy of Science.[1][2]


Thomas Room was born on 10 November 1902, near London, 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.[1] He returned to Cambridge in 1927, at which time he completed his Ph.D., with a thesis supervised by H. F. Baker.[1][3] Room remained at Cambridge until 1935, when he moved to the University of Sydney.[1][4] During World War II he worked for the Australian government, helping to decrypt Japanese communications.[1] 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.[1] He also held visiting positions at the University of Washington in 1948, and the Institute for Advanced Study and Princeton University in 1957.[1][5][6] 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.[1][7]


Room's Ph.D. work concerned generalizations of the Schläfli double six, a configuration formed by the 27 lines on a cubic algebraic surface.[1][3]

In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press.[1] Nearly 500 pages long, the book combines methods of synthetic geometry and algebraic geometry to study higher-dimensional generalizations of quartic surfaces and cubic surfaces. 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.[1][8]

In the postwar period, Room shifted the focus of his work to Clifford algebra and spinor groups.[1] Later, in the 1960s, he also began investigating finite geometry, and wrote a textbook on the foundations of geometry.[1]

Room invented Room squares in a brief note published in 1955.[9] 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,[10] 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.[1]

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.[1]

Awards and honours[edit]

In 1941, Room won the Thomas Ranken Lyle Medal of the Australian National Research Council and was elected as a Fellow of the Royal Society.[1][11][12] He was one of the Foundation Fellows of the Australian Academy of Science, chartered in 1954.[1][2] From 1960 to 1962, he served as president of the Australian Mathematical Society and he later became the first editor of its journal.[1]

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.[1][13]


  1. ^ a b c d e f g h i j k l m n o p q r s 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.
  2. ^ a b John Mack. "Room, Thomas Gerald (1902–1986)". Australian Dictionary of Biography. National Centre of Biography, Australian National University.  First published in Australian Dictionary of Biography, Volume 18, (MUP), 2012.
  3. ^ a b Thomas Gerald Room at the Mathematics Genealogy Project
  4. ^ "The University. Chair of Mathematics. Professor T. G. Room", Sydney Morning Herald, 21 December 1934 .
  5. ^ "Princeton Appoints 17 Guest Professors", New York Times, 4 September 1957 .
  6. ^ "Institute Names 128 For Research; Scholars Will Do Advanced Study On Historical Topics And In Mathematics", New York Times, 15 September 1957 .
  7. ^ "Professor and Bride Dodge Rice", Sydney Morning Herald, 8 November 1937 .
  8. ^ Review of The geometry of determinantal loci by Virgil Snyder (1939), Bulletin of the AMS 45: 499–501, doi:10.1090/S0002-9904-1939-07011-0.
  9. ^ Room, T. G. (1955), "A new type of magic square", Mathematical Gazette, 39: 307 .
  10. ^ O'Connor, John J.; Robertson, Edmund F., "Robert Anstice", MacTutor History of Mathematics archive, University of St Andrews ..
  11. ^ "Lyle Medals Awarded", Sydney Morning Herald, 10 July 1941 .
  12. ^ Thomas Ranken Lyle Medal, Australian Academy of Science, retrieved 6 June 2010.
  13. ^ The T G Room Award, Mathematical Association of New South Wales, retrieved 1 June 2010.