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A History of Mathematics in South Africa: Modern Milestones

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Notes

  1. The Bantu-speaking people comprise the following main groups: Nguni, Sotho, Venda, and Tsonga. The Xhosa tribe is part of the Nguni group [2, p. 17].

  2. The decision to establish the observatory was made in 1820. It took several years for the project to be realized [14, p. 9].

  3. The observatory was administered by the admiralties from the time of its establishment until 1965.

  4. According to Pieter Maritz, the year was 1658. His source is Jan van Riebeeck’s diary, the entry dated April 17, 1658 [39, p. 4].

  5. The level of requisite mathematical knowledge is not known.

  6. Between 1848 and 1859, four institutions were established: Diocesan College in Rondebosch; Theological Seminary in Stellenbosch; St. Andrew’s in Grahamstown; Grey Institute in Port Elizabeth. The list titled The Foundation of Some Scientific Institutions and Societies in South Africa provides the chronology. See [48, pp. 70–71].

  7. It would take over a century for the conjecture to be resolved. In 1976, Kenneth Appel and Wolfgang Haken obtained a proof that required extensive computer calculation. For more on what is now known as the four color theorem, see [64].

  8. In addition, he took up the editorship of the Daily News [36, p. 67].

  9. The class size varied, but it was usually below one hundred until the 1890s.

  10. Kruger had left for Europe and never returned. He died in Switzerland.

  11. He expressed his views on February 27, 1904, at the degree ceremony of the University of the Cape of Good Hope.

  12. In Johannesburg, there were approximately \(51\,000\) Chinese immigrant workers engaged in mining. There were \(18\,00\)0 Whites and \(94\,000\) Africans. See [2, p. 95].

  13. The gymnasium was founded in 1866.

  14. BAAS is now known as the British Science Association.

  15. Dona Strauss specializes in topology and functional analysis. Her doctoral thesis became one of the original sources of pointless topology.

  16. Interview with Dona Strauss on November 11, 2019, in Pretoria.

  17. He also studied Afrikaans, Greek, and Hebrew at the university [40, p. 424].

  18. Gill retired in 1906 and moved to London. He served as president of the Royal Astronomical Society from 1909 to 1911.

  19. The research journal Quaestiones Mathematicae is published by SAMS. It holds an annual congress and facilitates South African mathematicians engaging with activities of the International Mathematical Union (IMU) and the African Mathematical Union (AMU).

  20. They proved the following theorem: for each prime p, there is a metabelian p-group G with trivial center such that every proper subgroup of G is nilpotent and subnormal. Such a p-group would later be called the Heineken–Mohamed-type group [18].

  21. Mohamed remained an advocate of the abolishment of apartheid education. Because he encouraged his Black staff to join in protest and delivered a speech against racial discrimination in 1976, he was detained and put in prison, and he then lost his university position. After he was released in 1977, he accepted an associate professorship at the University of the Witwatersrand, but was again arrested, this time for high treason, in February 1985. Thanks to the collective pleas from about three hundred group theorists inside and outside South Africa, Mohamed was released in June 1986. After the abolishment of the apartheid laws, Mohamed was elected as an African National Congress Member of Parliament. He served for three terms and retired in 2009 [41].

  22. Nongxa’s boarding school, Freemantle Boys High School, in Lady Frere, offered only biology classes. There was no mathematics or physical sciences [62, pp. 170–171].

  23. Nongxa was sixteen when he switched schools. He had to spend an extra year at his new school to catch up, and he obtained a junior certificate in mathematics. He was planning to study medicine, but the dean of science persuaded him to continue his study of mathematics [62, p. 170].

  24. The number of publications by mathematicians in South Africa on MathSciNet, for example, has been growing steadily.

  25. In 2015, the percentage of instructional staff members working in mathematics at universities in South Africa who are South African citizens was 77.8% [44].

References

  1. Carter Bays and Richard H. Hudson. A new bound for the smallest \(x\) with \(\pi (x) >{\rm li}(x)\). Mathematics of Computation 69:231 (2000), 1285–1296.

  2. Roger B. Beck. The History of South Africa. Wesport: Greenwood Press, 2000.

    Google Scholar 

  3. Veronica Belling. Recovering the Lives of South African Jewish Women During the Migration Years, c1880–1939. PhD dissertation, University of Cape Town, 2018.

  4. Maurice Boucher. A brief history of the South African university system. Paper presented at the Conference of the South African Association for the Advancement of Education, Pretoria, January 25, 1973.

  5. Maurice Boucher. Spes in Arduis: A History of the University of South Africa. Pretoria: University of South Africa, 1973.

    Google Scholar 

  6. Jane Carruthers. Henry Selby Hele-Shaw LLD, DSc, EngD, FRS, WhSch (1854–1941): engineer, inventor and educationist. South African Journal of Science 106:1–2 (2019), 34–39.

    Google Scholar 

  7. Centre International de Rencontres Mathématuques. Interview at CIRM: Peter Sarnak. YouTube video, December 14, 2016, available at https://www.youtube.com/watch?v=IsCUlZahQMc, accessed October 15, 2020.

  8. Kuok Fai Chao and Roger Plymen. A new bound for the smallest \(x\) with \(\pi (x) > \rm Li(x)\). International Journal of Number Theory 6:3 (2010), 681–690. https://doi.org/10.1142/S1793042110003125.

  9. Colonial Secretary’s Ministerial Division. Report of the University of the Cape of Good Hope for the year ended 31st December 1906. Paper presented to both houses of Parliament by command of His Excellency the Governor [Sir Walter Hely-Hutchinson], 1907.

  10. Mary R. S. Creese with Thomas M. Creese. Ladies in the Laboratory III: South African, Australian, New Zealand, and Canadian Women in Science. Lanham: Scarecrow Press, 2010.

  11. Kathy Driver. Mathematical sciences. In The State of Science in South Africa, edited by Roseanne Diab and Wieland Gevers, pp. 69–81. Pretoria: Academy of Science of South Africa, 2009.

    Google Scholar 

  12. Roger C. Entringer and Henda C. Swart. Spanning cycles of nearly cubic graphs. Journal of Combinatorial Theory 29:3 (1980), 303–309.

    Article  MathSciNet  Google Scholar 

  13. Faculty of Science. Annual Report. Stellensbosch: Stellenbosch University, 2012. Available at http://www.sun.ac.za/english/faculty/science/Documents/SUScience2012.pdf.

  14. Ian S. Glass. The Royal Observatory at the Cape of Good Hope: History and Heritage. Cape Town: Mons Mensa, 2015.

    Google Scholar 

  15. A. V. Hall. A history of the Royal Society of South Africa. In A History of Scientific Endeavour in South Africa: A Collection of Essays Published on the Occasion of the Centenary of the Royal Society of South Africa, edited by Alexander Claude Brown, pp. 474–487. Cape Town: The Royal Society of South Africa and the University of Cape Town, 1977.

    Google Scholar 

  16. Jakob K. E. Halm. Further considerations relating to the systematic motions of the stars. Monthly Notices of the Royal Astronomical Society 71:8 (1911), 610–639.

    Article  Google Scholar 

  17. Godfrey H. Hardy. The Indian mathematician Ramanujan. American Mathematical Monthly 44:3 (1937), 137–155.

    Article  MathSciNet  Google Scholar 

  18. Hermann Heineken and Ismail J. Mohamed. A group with trivial centre satisfying the normalizer condition. Journal of Algebra 10 (1968), 368–376.

    Article  MathSciNet  Google Scholar 

  19. Christine Keitel. Reflections on mathematical education research in South Africa. In Researching Mathematics Education in South Africa: Perspectives, Practices and Possibilities, edited by Renuka Vithal, Jill Adler, and Christine Keitel, pp. 329–345. Cape Town: Human Sciences Research Council Press, 2005.

    Google Scholar 

  20. John Knopfmacher: a life in mathematics. Available at https://www.wits.ac.za/maths/associated-structures/john-knopfmacher-home-page/john-knopfmacher---a-life-in-mathematics/, accessed November 15, 2019.

  21. John Knopfmacher. A note on perfect numbers. Mathematical Gazette 44 (1960), 45.

    Article  MathSciNet  Google Scholar 

  22. John Knopfmacher. Universal envelopes for non-associative algebras. Quarterly Journal of Mathematics Oxford Second Series 13 (1962), 264–282.

    Article  MathSciNet  Google Scholar 

  23. John Knopfmacher. On Chern classes of representations of finite groups. Bulletin of the American Mathematical Society 71 (1965), 568–571.

    Article  MathSciNet  Google Scholar 

  24. John Knopfmacher. Extensions in varieties of groups and algebras. Acta Mathematica 115 (1966), 17–50.

    Article  MathSciNet  Google Scholar 

  25. John Knopfmacher. Arithmetical properties of finite rings and algebras and analytic number theory. Bulletin of the American Mathematical Society 76 (1970), 830–883.

    Article  MathSciNet  Google Scholar 

  26. John Knopfmacher. Finite modules and algebras over Dedekind domains and analytic number theory. Bulletin of the American Mathematical Society 78 (1972), 193–196.

    Article  MathSciNet  Google Scholar 

  27. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, I. Journal für die Reine und Angewandte Mathematik 252 (1972), 16–43.

    MathSciNet  MATH  Google Scholar 

  28. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, II. Journal für die Reine und Angewandte Mathematik 254 (1972), 74–99.

    MATH  Google Scholar 

  29. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, III. Journal für die Reine und Angewandte Mathematik 259 (1973), 157–170.

    MATH  Google Scholar 

  30. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, VI. Journal für die Reine und Angewandte Mathematik 270 (1974), 97–114.

    MATH  Google Scholar 

  31. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, V. Journal für die Reine und Angewandte Mathematik 271 (1974), 95–121.

    MATH  Google Scholar 

  32. John Knopfmacher. Arithmetical properties of finite rings and algebras, and analytic number theory, VI. Journal für die Reine und Angewandte Mathematik 277 (1975), 45–62.

    MATH  Google Scholar 

  33. John Edensor Littlewood. Sur la distribution des nombres premiers. Comptes Rendus 158 (1914), 1869–1872.

  34. David N. Livingstone. Debating Darwin at the Cape. Journal of Historical Geography 52 (2016), 1–15.

    Article  MathSciNet  Google Scholar 

  35. Doran Lubinsky. John Knopfmacher: a mathematical biography. Quaestiones Mathematicae 24:3 (2001), 261–262.

    Article  MathSciNet  Google Scholar 

  36. Pieter Maritz and Sonja Mouton. Francis Guthrie: a colourful life. Mathematical Intelligencer 34:3 (2012), 67–75.

    Article  MathSciNet  Google Scholar 

  37. Pieter Maritz. Mathematics in and for Africa. In A Particular Frame of Mind: Faculty of Science Stellenbosch University, 1918–2018. Stellenbosch: Stellenbosch University Faculty of Science (2018), 129–135.

  38. Pieter Maritz. Mathematics, 1874. In A Particular Frame of Mind: Faculty of Science Stellenbosch University, 1918–2018. Stellenbosch: Stellenbosch University Faculty of Science (2018), 6–11.

  39. Pieter Maritz. Sir Thomas Muir, 1844–1934. Linear Algebra and Its Applications 411 (2005), 3–67.

    Article  MathSciNet  Google Scholar 

  40. David P. Mason. Arthur Bleksley: pioneer of science awareness in South Africa. South African Journal of Science 104 (2008), 423–427.

    Google Scholar 

  41. Mac Tutor. Ismail Jacobus Mohamed. Available at http://mathshistory.st-andrews.ac.uk/Biographies/Mohamed.html, accessed July 9, 2020.

  42. Ismail J. Mohamed. On series of subgroups related to groups of automorphisms. Proceedings of the London Mathematical Society 3:13 (1963), 711–723.

    Article  MathSciNet  Google Scholar 

  43. Ismail J. Mohamed. On the class of the stability group of a subgroup chain. Journal of the London Mathematical Society 39 (1964), 109–114.

    Article  MathSciNet  Google Scholar 

  44. Johann Mouton, Isabel Basson, Jaco Blanckenberg, Nelius Boshoff, Kyle Ford, Mariana Joubert, Lynn Lorenzen, Herman Redelinghuys, Milandré van Lill, and Marthie van Niekerk. A Scientometric Assessment of Statistics in South Africa. Available at https://www.iccssa.org.za/wp-content/uploads/2019/09/Final-Report-Statistics-in-South-Africa-March-2019.pdf, accessed July 9, 2020.

  45. Thomas Muir. The Theory of Determinants in the Historical Order of Development. Parts I and II. London: Macmillan, 1906 and 1911.

  46. Thomas Muir. A Treatise on the Theory of Determinants. Revised and enlarged by William H. Metzler. New York: Dover, 1960.

  47. Bruce K. Murray. Wits: The “Open” Years: A History of the University of the Witwatersrand, Johannesburg, 1939–1959. Johannesburg: Witwatersrand University Press, 1997.

  48. Meiring S. Naudé and Alexander C. Brown. The growth of scientific institutions in South Africa. In A History of Scientific Endeavour in South Africa: A Collection of Essays Published on the Occasion of the Centenary of the Royal Society of South Africa, edited by Alexander Claude Brown, pp. 60–85. Cape Town: The Royal Society of South Africa and the University of Cape Town, 1977.

    Google Scholar 

  49. J. J. O’Connor and E. F. Robertson. MacTutor History of Mathematics. St Andrews: The University of St Andrews, 2000.

  50. William Ritchie. The History of the South African College: 1829–1918. Cape Town: T. Maskew Miller, 1918.

    Google Scholar 

  51. School of Mining Engineering. Annual Report. Johannesburg: University of the Witwatersrand, 2014.

  52. Lawrence H. Shirley. History of mathematics in Africa: a section of the Second Pan-African Congress of Mathematicians of the African Mathematical Union. Report on Meetings (1986), 293, available at https://core.ac.uk/download/pdf/82601616.pdf, accessed July 9, 2020.

  53. South African Mathematical Society (SAMS). Available at http://sams.ac.za.www78.cpt1.host-h.net/history-increasemath-sams/, accessed July 30, 2021.

  54. South African Mathematical Society (SAMS). Stand on discrimination. Available at http://sams.ac.za.www78.cpt1.host-h.net/history-increasemath-sams/, accessed July 30, 2021.

  55. Stanley Skewes. On the difference \(\pi (x) - {\rm Li}(x)\), (I). Journal of the London Mathematical Society 8 (1933), 277–283.

  56. Stanley Skewes. On the difference \(\pi (x) - {\rm Li} (x)\), (II). Proceedings of the London Mathematical Society 5:17 (1955), 48–70.

  57. Bertha Solomon. Time Remembered: The Story of a Fight. Cape Town: Howard Timmins, 1968.

    Google Scholar 

  58. \(\text{S}_2 \text{ A}_3\): biographical database of Southern African Science. Available at http://www.s2a3.org.za/bio/Biograph_final.php?serial=634, accessed January 4, 2021.

  59. Herman J. J. Te Riele. On the sign of the difference \(\pi (x) - {\rm Li} (x)\). Mathematics of Computation 48 (1987), 323–328.

  60. H. W. Turnbull. Sir Thomas Muir, 1844–1934. Royal Society (1935), 179–184, https://doi.org/10.1098/rsbm.1934.0002.

  61. H. W. Turnbull. Thomas Muir. Journal of the London Mathematical Society 10 (1935), 76–80.

    Article  Google Scholar 

  62. Christopher L. Vaughan. On the Shoulder of Oldenburg: A Biography of the Academic Rating System in South Africa. Pretoria: National Research Foundation, 2015.

    Google Scholar 

  63. H. Paul Williams. Stanley Skewes and the Skewes number. LSE Research Online. Available at http://eprints.lse.ac.uk/31662/, accessed July 9, 2020.

  64. Robin Wilson. Four Colors Suffice: How the Map Problem Was Solved. Princeton: Princeton University Press, 2003.

    MATH  Google Scholar 

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Acknowledgments

This project was supported by the Visiting Professor Programme at the University of Pretoria, which enabled the second author to host the first author in 2019. We are grateful to the members of the Department of Mathematics and Applied Mathematics at the University of Pretoria for giving us the opportunity to carry out our project. Both authors traveled to interview David Mason, Pieter Maritz, and Kenneth Hughes and learned about the timeline, the key events, and the people who contributed to the development of mathematics in South Africa. We are grateful to David Erwin and John Webb for providing us with scanned copies of Skewes’s documents that were left at the University of Cape Town. David Erwin, Peter Dunsby, and members of the Department of Mathematics and Applied Mathematics at the University of Cape Town also gave us much insight when we visited them in May 2019. Lloyd B. Hill provided support and information on the research regarding the education system in South Africa. We also thank Jacek Banasiak, Kathy Driver, Kerstin Jordan, Loyiso Nongxa, and Dona Strauss for providing information and giving us helpful suggestions. We are thankful to David Erwin, Miek Messerschmidt, Jens Funke, Florian Luca, Pieter Maritz, David Mason, and Pieter Moree for reading earlier drafts and giving us detailed comments at various stages. We greatly appreciate Christopher Hollings, Bernard Lightman, and Juliet Gillies for their feedback and editorial assistance and are thankful for the anonymous readers and their comments, and we are grateful to David Kramer, the managing editor of this journal, for his careful reading of this article. We are fortunate to have been guided by many scholars, and our research is deeply indebted to their kindness, though any errors are solely ours.

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  1. University of Oxford, Oxford , UK

    Tomoko L. Kitagawa

  2. University of Pretoria, Pretoria, South Africa

    Eder Kikianty

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Appendix

Appendix

The Centre for Higher Education Transformation, a nongovernmental organization that monitors higher education, classified selected universities in South Africa into three categories. The “red” cluster indicates a research-intensive institute; the “blue” cluster indicates universities that provide technical training; the “green” cluster covers both:

  • Red Cluster

    • University of the Witwatersrand

    • Stellenbosch University

    • University of Cape Town

    • University of Pretoria

    • Rhodes University

  • Green Cluster

    • University of the Free State

    • University of KwaZulu-Natal

    • North-West University

    • University of Fort Hare

    • University of Limpopo

    • University of Western Cape

    • University of Johannesburg

    • Nelson Mandela Metropolitan University

    • University of Zululand

  • Black Cluster

    • Vaal University of Technology

    • Central University of Technology

    • Durban University of Technology

    • Mangosuthu University of Technology

    • Tshwane University of Technology

    • Cape Peninsula University of Technology

    • University of Venda

    • Walter Sisulu University

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Kitagawa, T.L., Kikianty, E. A History of Mathematics in South Africa: Modern Milestones. Math Intelligencer 43, 33–47 (2021). https://doi.org/10.1007/s00283-021-10068-8

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