Mathematical  Culture and Thought

Mathematical Culture and Thought

The Rise of British Analysis in the Early 20th Century‎: ‎ The Role of G.H‎. ‎Hardy and the London Mathematical Society

Document Type : Translation

Authors
Department of Mathematics‎, ‎University of Bojnord‎, ‎Iran
Abstract
It has often been observed that the early years of the 20th century witnessed a significant and noticeable rise in‎
‎both the quantity and quality of British analysis‎. ‎Invariably in these accounts‎, ‎the name of G.H‎. ‎Hardy (1877–1947)‎
‎features most prominently as the driving force behind this development‎. ‎But how accurate is this interpretation?‎
‎This paper attempts to reevaluate Hardy’s influence on the British mathematical research community and its‎
‎analysis during the early 20th century‎, ‎with particular reference to his relationship with the London Mathematical‎
‎Society.
Keywords
Subjects

Rice‎, ‎A‎. ‎C.‎, ‎Wilson‎, ‎R‎. ‎J.‎, ‎The rise of British analysis in the early 20th century‎:‎ the role of G.H‎. ‎Hardy and the London Mathematical Society‎, Historia Math., 30 (2003)‎, ‎173-194.

[1]    Albers, D., Alexanderson, G. L., Reid, C., International Mathematical Congresses: An Illustrated History 1893-1986, Springer-Verlag, New York, 1987.
[2]    Ausejo, E., Hormigón, M., eds., Messengers of Mathematics: European Mathematical Journals (1800-1946), Siglo XXI de España Editores, Zaragoza, 1993.
[3]    Barrow-Green, J., International congresses of mathematicians from Zürich 1897 to Cambridge 1912, Math. Intelligencer, 16 (1994), 38-41.
[4]    Becher, H.W., William Whewell and Cambridge mathematics, Hist. Stud. Phys. Sci., 11 (1980), 1-48.
[5]    Biermann, K. R., Die Mathematik und ihre Dozenten an der Berliner Universität 1810-1933, Akademie Verlag, Berlin, 1988.
[6]    Bollobás, B., ed., Littlewood’s Miscellany, Cambridge Univ. Press, Cambridge, UK, 1986.
[7]    Brigaglia, A., The Circolo matematico di Palermo and its Rendiconti: the contribution of the Italian mathematical community to the diffusion of international mathematical journals 1884-1914, in [2] 71-93.
[8]    Burkill, J. C., Hardy, Godfrey Harold, in Dictionary of Scientific Biography, vol. 6, C. C. Gillispie, ed., New York, 1972, 113-114.
[9]    Burkill, J. C., John Edensor Littlewood, Biograph. Mem. Fellows Roy. Soc., 28 (1978), 323-336.
[10]    Burnside, W., On the theory of groups of finite order, Proc. London Math. Soc., 7 (1909), no. 2, 1-7.
[11]    Collingwood, E. F., A century of the London Mathematical Society, J. London Math. Soc., 41 (1966), 577-594.
[12]    Dauben, J. W., Mathematicians and World War I: The international diplomacy of G.H. Hardy and Gösta Mittag-Leffler as reflected in their personal correspondence, Historia Math., 7 (1980), 261288.
[13]    Despeaux, S. E., International mathematical contributions to British scientific journals, 1800-1900, in [37], 61-87.
[14]    Fauvel, J., 800 years of mathematical traditions, in [16], 1-27.
[15]    Fauvel, J., James Joseph Sylvester, in [16], 219-239.
[16]    Fauvel, J., Flood, R., Wilson, R., eds., Oxford Figures: 800 Years of the Mathematical Sciences, Oxford Univ. Press, Oxford, 2000.
[17]    Fletcher, C. R., Refugee mathematicians: A German crisis and a British response, 1933-1936, Historia Math., 13 (1986), 13-27.
[18]    Grattan-Guinness, I., A mathematical union: William Henry and Grace Chisholm Young, Ann. Sci., 29 (1972), 105-186.
[19]    Grattan-Guinness, I., Russell and G. H. Hardy: A study of their relationship, Russell: The Journal of the Bertrand Russell Archives (N. S.), 11 (1991-1992), 165-179.
[20]    Grattan-Guinness, I., The emergence of mathematical analysis and its foundational progress, 17801880, in From the Calculus to Set Theory, 1630–1910, I. Grattan-Guinness, ed., Duckworth, London, 1980, 94-148.
[21]    Grattan-Guinness, I., The interest of G. H. Hardy, F. R. S., in the philosophy and the history of mathematics, Notes and Records Roy. Soc. London, 55 (2001), 411-424.
[22]    Griffin, N., Lewis, A. C., Bertrand Russell’s mathematical education, Notes and Records Roy. Soc. London, 44 (1990), 51-71.
[23]    Hardy, G. H., A Course of Pure Mathematics, Cambridge Univ. Press, Cambridge, UK, 1908.
[24]    Hardy, G. H., A Mathematician’s Apology, Cambridge Univ. Press, Cambridge, UK, 1940.
[25]    Hardy, G. H., Divergent Series, Clarendon, Oxford, 1949.
[26]    Hardy, G. H., Prolegomena to a chapter on inequalities, J. London Math. Soc., 4 (1929), 61-78.
[27]    Hardy, G. H., William Henry Young., J. London Math. Soc., 17 (1942), 218-237.
[28]    Hardy, G. H., Littlewood, J. E., A new solution of Waring’s problem, Göttinger Nachrichten, (1920), 33-54.
[29]    Heilbronn, H. A., On the class number in imaginary quadratic fields, Quart. J. Math., 5 (1934), 150-160.
[30]    Hobson, E. W., Love, A. E. H., eds., Proceedings of the Fifth International Congress of Mathematicians (Cambridge, 22-28 August 1912), Cambridge Univ. Press, Cambridge, UK, 1913.
[31]    Larmor, J., Address by the retiring president, Proc. London Math. Soc., 16 (1918), no. 2, 1-7.
[32]    Lehto, O., Mathematics Without Borders: A History of the International Mathematical Union, Springer-Verlag, New York, 1998.
[33]    Morrell, J., Science at Oxford 1914–1939: Transforming an Arts University, Clarendon, Oxford, 1997.
[34]    Neville, E. H., Andrew Russell Forsyth, J. London Math. Soc., 17 (1942), 237-256.
[35]    Parshall, K. H., How we got where we are: an international overview in national contexts (18751900), Notices Amer. Math. Soc., 43 (1996), no. 3, 287-296.
[36]    Parshall, K. H., Mathematics in national contexts (1875-1900): an international overview, in Proc. Internat. Congr. Math.(August 3-11, 1994), Birkhäuser Verlag, Zürich, 1995, 1581-1589.
[37]    Parshall, K. H., Rice, A. C., eds., Mathematics Unbound: The Emergence of an International Mathematical Research Community, 1800-1945, American Mathematical Society, Providence, RI, London Mathematical Society, London, 2002.
[38]    Parshall, K. H., Rice, A. C., The emergence ofan international mathematical research community, 1800-1945; an overview and an agenda, in [37]
[39]    Parshall, K. H., Rowe, D. E., The Emergence of the American Mathematical Research Community 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore, American Mathematical Society, Providence, RI, London Mathematical Society, London, 1994.
[40]    Rankin, R., G. H. Hardy as I knew him, Gaz. Australian Math. Soc., 25 (1998), 73-81.
[41]    Rayner, M.E., 2000. The twentieth century, in [14], 241-255.
[42]    Reid, C., Courant in Göttingen and New York, Springer-Verlag, New York, 1976.
[43]    Rice, A. C., Wilson, R. J., From national to international society: the London Mathematical Society, 1867–1900, Historia Math., 25 (1998), 185-217.
[44]    Rice, A. C., Wilson, R. J., Gardner, J. H., From student club to national society: the founding of the London Mathematical Society in 1865, Historia Math., 22 (1995), 402-421.
[45]    Rider, R., Alarm and opportunity: emigration of mathematicians and physicists to Britain and the United States, 1933–1945, Hist. Stud. Phys. Sci., 15 (1984), 107-176.
[46]    Russell, B., The Autobiography of Bertrand Russell, vol. 1, George Allen and Unwin, London, 1967.
[47]    Schubring, G., Pure and applied mathematics in divergent institutional settings in Germany: the role and impact of Felix Klein, in The History of Modern Mathematics, vol. 2., D. E. Rowe, J. McCleary, eds., Academic Press, Boston, 1989, 171-220.
[48]    Segal, S. L., War, refugees, and the creation of an international mathematical community, in [37], 359-380.
[49]    Siegmund-Schultze, R., Mathematiker auf der Flucht vor Hitler: Quellen und Studien zur Emigration einer Wissenschaft, Vieweg, Braunschweig/Wiesbaden, 1998.
[50]    Siegmund-Schultze, R., The effects of Nazi rule on the international participation of German mathematicians: an overview and two case studies, in [37], 335-357.
[51]    Snow, C. P., Foreword, in Hardy, G. H., A Mathematician’s Apology, Cambridge Univ. Press, Cambridge, UK, 1967.
[52]    Titchmarsh, E. C., Godfrey Harold Hardy, Obituary Notices of Fellows of the Royal Society, 6 (1949), 447–458.
[53]    Whittaker, E. T., Andrew Russell Forsyth, Obituary Notices of Fellows of the Royal Society, 4 (1942), 209–227.
[54]    Wilson, R. J., Hardy and Littlewood, in Cambridge Scientific Minds, P. Harman, S. Mitton, eds., Cambridge Univ. Press, Cambridge, UK, 2002, 202-219.
Volume 44, Issue 2 - Serial Number 77
October 2025
Pages 235-262

  • Receive Date 12 September 2022
  • Revise Date 09 January 2023
  • Accept Date 10 January 2023
  • Publish Date 23 September 2025