¹ Koestler, Arthur, The Act of Creation, Hutchinson, London, 1964, p. 622.Google Scholar

² Crossley, John N., The Emergence of Number, Upside Down A Book Company, Steel's Creek, Australia, 1980, pp. 29–33.Google Scholar

³ Pospisil, Leopold and de Solla Price, Derek J., ‘A survival of Babylonian arithmetic in New Guinea?’, Indian Journal of the History of Science, (1966), 1, pp. 30–33Google Scholar; and ‘Kapauku numeration’, Journal of the Polynesian Society, (1977), 86, 271–272.Google Scholar

⁴ Bowers, Nancy and Lepi, Punda, ‘Kaugel Valley systems of reckoning’, Journal of the Polynesian Society, (1977), 86, (1), pp. 105–116.Google Scholar

⁵ Mariner, William, An Account of the Natives of the Tonga Islands in the South Pacific Ocean. With an original Grammar and Vocabulary of their language. Compiled and arranged from the extensive communications of Mr. William Mariner, several years resident in those islands. By John Martin, M.D. (2 volumes), John Murray, London, 1817, Volume 2, pp. 388–391.Google Scholar Dr John Martin complained pedantically (Volume 2, p. 382) that the Tongans, when speaking their own language, flagrantly ignored the rules (of Latin grammar!) for distinguishing nouns from verbs.

⁶ Leonard, George, He Huinahelu oia ka Helunaau me ka Helukakau, i Huiia, Ka na Misionari mea Pai, Honolulu, 1852Google Scholar, Arithmetic textbook by a Bishop of Hawaii, using dollars and cents on p. 98; Colburn, Warren, He Helunaau ke mea e Maa'i ke Kanaka, Ellsworth, Boston, 1868.Google Scholar Textbook of arithmetic in Hawaiian, by a Bishop of Honolulu; Thomson, James B., Ka Huinahelu Hou; oia hoi ka Arimatika Kulanui, Papa Hoonaauao, Honolulu, 1870.Google Scholar Textbook of arithmetic, in Hawaiian, with dollars and cents used on p. 227. Copies of these three texts are held in the George Grey Collection, in Auckland Public Library.

⁷ (William Colenso) Ko Nga Tepara, He mea ta i te perehi i Paihia, 1835: single sheet with tables for addition (up to 12 + 15) and multiplication (up to 12 x 12), and tables for pounds, shillings and pence. The only known copy was acquired by the Alexander Turnbull Library in 1984.

⁸ Anonymous, Koe Fika Nomiba. Ko hono tolu oe tohi. Koe falakiseni moe Tesimale. Nae Buluji i he Kollij ko Tubou, 1871, p. 64.Google Scholar The George Grey Collection in Auckland Public Library has a copy of that textbook of arithmetic in Rarotongan.

⁹ Anonymous, Ai Vola Ni Fika, Printed by T.D. Hartwell, next the Wesleyan Church, Newton, 1871, p. 29.Google Scholar The George Grey Collection in Auckland Public Library has a copy of that textbook of arithmetic in Fijian. The author explained in the Preface that ‘As this book has been prepared solely for the use of Fijians, the wants and the mental capacity of those tribes alone have been taken into consideration.… It has not been thought advisable to extend this work beyond Vulgar Fractions; for though natives might perhaps be found capable of understanding the more advanced rules, yet neither the national character nor the national prospects for the future give sufficient promise of such knowledge being turned to any practical use; and it is to be feared that the possession of knowledge which cannot be utilised is not only useless, but positively hurtful to savages.’

¹⁰ Warner, Sylvia Townsend, Mr. Fortune's Maggot, Viking Press, New York, 1927.Google Scholar

¹¹ Williams, William, A Dictionary of the New Zealand Language, (1st edn), Press of the Church Missionary Society, Paihia, 1844.Google Scholar

¹² Conant, Levi Leonard, The Number Concept: Its Origin and Development, MacMillan, New York, 1896, pp. 122–123.Google Scholar

¹³ Henrici, Peter, Elements of Numerical Analysis, John Wiley, New York, 1964, p. 291Google Scholar;

Э. И. Березкина ‘О математических методах древних (к историм систем сислений)’, Ист. и Метод. Естест Наук, (1982), вьІп. 29, 31–40.

(Berezkina, È. I., ‘On mathematical methods of the ancients (on the history of number systems)’, (in Russian), History and methodology of the Natural Sciences, (1982), No. 29, pp. 31–40.)Google Scholar

¹⁴ Scholefield, Guy H. (ed.), A Dictionary of New Zealand Biography, (2 vols), Government Printer, Wellington, 1940Google Scholar, article on Frederick William Frankland; an obituary note on Frankland was published in the Bulletin of the American Mathematical Society, (1916), 23, p. 54.Google Scholar I am indebted to the referee for informing me of Frederick William Frankland. (I am also grateful to the referee for the very prompt acceptance of this paper for publication.)

¹⁵ Frankland, Frederick William, ‘On the simplest continuous manifoldness of two dimensions and of finite extent’, Transactions of the New Zealand Institute, (1876), 9, pp. 272–279Google Scholar (reprinted in Proceedings of the London Mathematical Society, (1877), 8, pp. 57–64Google Scholar; and in Nature, (1877), 15, pp. 515–517Google Scholar and Nature, (1880), 22, 170–171)Google Scholar; ‘The non-Euclidean geometry vindicated: a reply to Mr. Skey’, Transactions of the New Zealand Institute, (1885), 18, pp. 58–69.Google Scholar

¹⁶ Gardner, W.J., Colonial Cap and Gown: Studies in the mid-Victorian Universities of Australasia, University of Canterbury, Christchurch, 1979.Google Scholar

¹⁷ Grace A. Lockhart had graduated as Bachelor of Science from Mount Allison University, New Brunswick, in 1875 (Gardner¹⁶, p. 8 1).

¹⁸ Lamb, Horace, A Treatise on the Mathematical Theory of the Motion of Fluids, Cambridge University Press, Cambridge, 1879.Google Scholar The many later editions were entitled Hydrodynamics.

¹⁹ ‘University Plucking Match’, cartoon in Adelaide Punch, 11 January 1879.

²⁰ Potts, R.B., ‘Mathematics at the University of Adelaide 1874–1944’, The Australian Mathematical Society Gazette, (1977), 4, pp. 1–9 and 37–44Google Scholar; Radok, R., A Portrait of Horace Lamb, Mathematics Department, James Cook University, Townsville, 1980Google Scholar; Home, Rod W., ‘The problem of intellectual isolation in scientific life: W.H. Bragg and the Australian scientific community, 1886–1909’, Historical Records of Australian Science, (1984), 6, pp. 19–30CrossRefGoogle Scholar; Moyal, Ann, A Bright and Savage Land: Scientists in Colonial Australia, Collins, Sydney, 1986, pp. 165–166.Google Scholar

²¹ Crowe, Michael J., A History of Vector Analysis, University of Notre Dame Press, Notre Dame, 1967, Ch. 6.Google Scholar

²² McAulay, Alexander, Utility of Quaternions in Physics, MacMillan, London, 1893Google Scholar, and Octonions: a Development of Clifford's Biquaternions, Cambridge University Press, Cambridge, 1898.Google Scholar

²³ Lancaster, Harold Oliver, ‘The departments of mathematics in the University of Sydney’, The Australian Mathematical Society Gazette, (1986), 13, pp. 29–38.Google Scholar

²⁴ Tarnish Bell, Robert John, An Elementary Treatise on Co-ordinate Geometry of Three Dimensions, Bell, London, 1910 (3rd edn 1950).Google Scholar

²⁵ Young Sommerville, Duncan M'Laren, Bibliography of non-Euclidean Geometry, (1st edn) University of St. Andrews Press, 1911Google Scholar (2nd edn, Chelsea, New York, 1970); The Elements of non-Euclidean Geometry, Bell, London, 1914 (Dover edn, New York, 1958)Google Scholar; Analytical Conies, Bell, London, 1924Google Scholar (3rd edn 1933); An Introduction to the Geometry of N Dimensions, Methuen, London, 1925 (Dover edn, New York, 1958)Google Scholar; Analytical Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1934.Google Scholar

²⁶ Forder, Henry George, The Foundations of Euclidean Geometry, Cambridge University Press, Cambridge, 1927Google Scholar (reprinted by Dover, New York, 1958; Rumanian translation fundamentele geometriei euclidiene, Editura Ştiinţifică, Bucureşti, 1970); A School Geometry, Cambridge University Press, Cambridge, 1930 (2nd edn 1938)Google Scholar; Higher Course Geometry, Cambridge University Press, Cambridge, 1931Google Scholar (reprinted 1949 and 1955); The Calculus of Extension, Cambridge University Press, Cambridge, 1941Google Scholar (reprinted by Chelsea Press, New York, 1960); Geometry, Hutchinson, London and Longmans Green, New York, 1950Google Scholar (2nd edn, Hutchinson, London, 1960 and Harper, New York, 1962; Turkish translation Geometri, Millî Eğitim Basimeví, Istanbul, 1968).

²⁷ Butcher, John Charles (ed.), A Spectrum of Mathematics: Essays Presented to H.G. Forder, Auckland University Press and Oxford University Press, Auckland, 1971.Google Scholar

²⁸ Loxton, John H., ‘Celebration of the 80th birthday of Kurt Mahler FRS, FAA’, The Australian Mathematical Society Gazette, (1984), 11, pp. 1–2.Google Scholar In the month following the delivery of this lecture at the Royal Institution, Kurt Mahler died at the Australian National University, on 25 February 1988: cf. Neumann, Bernhard H. and van der Poorten, Alf, ‘Kurt Mahler 1903–1988’, The Australian Mathematical Society Gazette, (1988), 15, pp. 25–27.Google Scholar The Australian National University has set up a Mahler Memorial Fund, whose aims will include the promotion of the theory of numbers among senior high school students and undergraduates.

²⁹ Potts, R.B., ‘Mathematics at the University of Adelaide 1944–1958’, The Australian Mathematical Society Gazette, (1985), 12, pp. 25–30.Google Scholar

³⁰ Newman, Michael F., ‘Hanna Neumann (1914–1971)’, In: Grinstein, Louise S. and Campbell, Paul J. (eds), Women of Mathematics: A Biobibliographic Sourcebook, Greenwood Press, New York, 1987, pp. 156–160Google Scholar; The Selected Papers of Bernhard and Hanna Neumann (6 vols), with commentaries by Bernhard Neumann, have been published in May 1988 by the Charles Babbage Research Centre (University of Manitoba), as a contribution to the Australian Bicentennial celebrations.

³¹ Nield, Donald A., ‘University mathematics in Auckland: a historical essay’, Mathematical Chronicle, (1983), 12, pp. 1–33.Google Scholar

³² Rutherford's first name is often given as Ernest, but his name is spelt Earnest Rutherford on his birth certificate, cf. Hoare, M.E. and Bell, L.G. (eds), In Search of New Zealand's Scientific Heritage (1984), Bulletin 21, The Royal Society of New Zealand, p. 119.Google Scholar

³³ Eve, E.S., Rutherford, Cambridge University Press, Cambridge, 1939.Google Scholar

³⁴ Rutherford, Earnest, ‘The succession of changes in radioactive bodies’, Phil. Trans. Roy. Soc; Series A, (1904), 204, pp. 169–219.CrossRefGoogle Scholar (The Bakerian Lecture for 1904. Reprinted in The Collected Papers of Lord Rutherford (ed. Chadwick, James), George Allen and Unwin, London, Vol. 1, 1962, pp. 671–722).Google Scholar

³⁵ Rutherford, Earnest, ‘The scattering of a and β particles by matter and the structure of the atom’, Phil. Mag; Series 6, (1911), 21, pp. 669–688.CrossRefGoogle Scholar (Reprinted in The Collected Papers of Lord Rutherford ³⁴, vol. 2, 1963, pp. 238–254.)Google Scholar

³⁶ Weatherburn, Charles Ernest, Elementary Vector Analysis with Applications to Geometry and Physics, Bell, London, 1921Google Scholar (revised edition 1956); Advanced Vector Analysis with Applications to Mathematics and Physics, Bell, London, 1924 (and 1957)Google Scholar; Differential Geometry of Three Dimensions, Cambridge University Press, Cambridge, 1927Google Scholar; An Introduction to Riemannian Geometry and the Tensor Calculus, Cambridge University Press, Cambridge, 1938 (and 1942)Google Scholar; A First Course in Mathematical Statistics, Cambridge University Press, 1946 (and 1947).Google Scholar

³⁷ cf. Lancaster.²³

³⁸ John Tee, Garry, ‘Two New Zealand mathematicians’, In: Crossley, John N. (eel.), History of Mathematics: Proceedings of the First Australian Conference, Department of Mathematics, Monash University, Clayton, Victoria, Australia, 1981, pp. 180–199.Google Scholar (L.J. Comrie and A.C. Aitken).

³⁹ Comrie, Leslie John, Modern Babbage Machines, The Office Machinery Users' Association, London, 1933.Google Scholar

⁴⁰ John Comrie, Leslie, ‘Babbage's dream comes true’, Nature, (1946 October 26), 158, pp. 567–569.Google Scholar

⁴¹ Wilkes, Maurice V., ‘How Babbage's dream came true’, Nature, (1975 October 16), 257, pp. 541–544.CrossRefGoogle Scholar

⁴² Randell, Brian (ed.), The Origins of Digital Computers: Selected Papers (3rd edn), Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar (Randell's annotated Bibliography describes c. 850 publications, of which twenty-two are publications by Comrie—more than for any other author (pp. 450–452).)

⁴³ Aitken, Alexander Craig, ‘On Bernoulli's numerical solution of algebraic equations’, Proc. Roy. Soc. Edinb; (1925), 46, pp. 289–305CrossRefGoogle Scholar; ‘On interpolation by iteration of proportional parts, without the use of differences’, Proc. Edinb. Math. Soc; (1931), 3, pp. 56–76Google Scholar, and many other papers.

⁴⁴ Aitken, Alexander Craig, Determinants and Matrices, Oliver and Boyd, Edinburgh, 1939Google Scholar; and Statistical Mathematics, Oliver and Boyd, Edinburgh, 1939.Google Scholar (Both texts have been reprinted in many editions.)

⁴⁵ Smith, Steven B., The Great Mental Calculators, Columbia University Press, New York, 1983, Ch. 31.Google Scholar

⁴⁶ Craig Aitken, Alexander, Gallipoli to the Somme: Recollections of a Neiu Zealand Infantryman, Oxford University Press, Oxford, 1963.Google Scholar

⁴⁷ cf.Tee.³⁸

⁴⁸ cf. Nield.³¹

⁴⁹ cf. Lancaster.²³

⁵⁰ The Proceedings (ed. John N. Crossley³⁸) publish thirteen papers from that conference.

⁵¹ John (sic! for Jock) Hoe, Les systèmes d'équations polynômes dans le Siyuán yùjiàn (1303), Mémoires de l'Institut des Hautcs Ètudes Chinoises, (1977), tome 6, Paris; and Jock Hoe, ‘Zhu Shijie and his Jade Mirror of the Four Unknowns’, In: Crossley,³⁸ pp. 103–134.

⁵² John Tee, Garry, ‘Mathematical science in New Zealand’, Canita Bhāratī, (1987), 9, pp. 1–9.Google Scholar

⁵³ Hawkins, William Francis, The Mathematical Work of John Napier (1550–1617), Ph.D. thesis, University of Auckland, 1982Google Scholar (to be published by University Microfilms International). (Abstract published in Bulletin of the Australian Mathematical Society, (1982), 26, pp. 455–468.)Google Scholar

⁵⁴ Hawkins, William Francis, ‘The first calculating machine (John Napier, 1617)’, The New Zealand Mathematical Society Newsletter, (12 1979), No. 16, Supplement, pp. 1–23.Google Scholar (Reprint in Annals of the History of Computing, (1988), 10, 37–51).Google Scholar

⁵⁵ cf.Tee.⁵²

⁵⁶ Several publications date the award to 13 July 1823—but the medal is inscribed with the date 1824, and the presentation was made by Henry Thomas Colebrooke, who was elected as President of the Society in February 1824.

⁵⁷ John Tee, Garry, ‘The heritage of Charles Babbage in Australasia’, Annals of the History of Computing, (1983), 5, pp. 45–59Google Scholar (reprinted in The World—Te Reo, (08 1983), pp. 5–19)Google Scholar; ‘Charles Babbage (1791–1871) and his New Zealand connections’, In: Hoare, M.E. and Bell, L.G. (eds),³² pp. 81–90Google Scholar (reprinted in The New Zealand Mathematics Magazine, (01 1986), 22, pp. 112–123).Google Scholar

⁵⁸ Hankins, Thomas L., Sir William Rowan Hamilton, The Johns Hopkins University Press, Baltimore and London, 1980, p. 321.Google Scholar

⁵⁹ cf. Tee.⁵² The tombstone on Sydney Margaret Hamilton's grave, in Rosebank Road cemetery in Auckland, tells more about her brother than about herself: cf. Segedin, Marin G., ‘Sir William Rowan Hamilton’, The New Zealand Mathematics Magazine, (1967–1968), 5, pp. 128–131.Google Scholar Hamilton's biographer, Archdeacon Robert Perceval Graves, had arranged for that tombstone to be placed on Sydney's grave (letter from Graves to Sir George Grey, 14 July 1892, Grey Collection, Auckland Public Library, GL-26(2)).

⁶⁰ Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time, printed by Philip Dixon Hardy, Dublin 1835Google Scholar; and Researches Respecting Quaternions, First Series, read 13 11, 1843Google Scholar, printed by M.H. Gill, Dublin, 1847.

⁶¹ John Tee, Garry, ‘Mathematics and ANZAAS’, The New Zealand Mathematical Society Newsletter, (1986), No. 37, p. 34.Google Scholar

⁶² ‘At an ANZAAS Meeting in Adelaide, Schwerdtfeger gave a talk on “The Pfaffian invariant of a skew-symmetric matrix”. The audience consisted of his wife, his two honours students (Wall and Potts), Mrs. Marta Sved, and one unknown, a non-mathematical newspaper reporter, who was intrigued by the mystery of the title of the talk. As one can imagine, the subsequent newspaper article was strange-reading publicity for mathematics at Adelaide!’ [Potts,²⁹ p. 28].

⁶³ Blakers, A.L., ‘The Australian Mathematical Society: foundation and early years’, The Australian Mathematical Society Gazette, (1976), 3, pp. 33–52 and 65–86.Google Scholar

⁶⁴ Sved, Marta, ‘Paul Erdös—portrait of our new Academician’, The Australian Mathematical Society Gazette, (1987), 14, pp. 59–62.Google Scholar

⁶⁵ Kerr, Roy Patrick, ‘Gravitational field of a spinning mass as an example of algebraically special metrics’, Physical Review Letters, (1963 September 1), 11, pp. 237–238.CrossRefGoogle Scholar

⁶⁶ Sheffield, Charles, ‘Killing vector’, In: Vectors, Ace Books, New York, 1979.Google Scholar

⁶⁷ Chandrasekhar, Subrahmanyan, Shakespeare, Newton and Beethoven, or, Patterns of Creativity, The Norma and Edward Ryerson Lecture at the University of Chicago for 1975.Google Scholar