The Ethics of Mathematics: Is Mathematics Harmful?

  • Paul ErnestEmail author
Part of the ICME-13 Monographs book series (ICME13Mo)


In this chapter I challenge the idea that mathematics is an unqualified force for good. Instead I show the harm that learning mathematics can inadvertently cause unless it is taught and applied carefully. I acknowledge that mathematics is a widespread force for good but make the novel case that there is significant collateral damage caused by learning mathematics. I describe three ways in which mathematics causes collateral damage. First, the nature of pure of mathematics itself leads to styles of thinking that can be damaging when applied beyond mathematics to social and human issues. Second the applications of mathematics in society can be deleterious to our humanity unless very carefully monitored and checked. Third, the personal impact of learning mathematics on learners’ thinking and life chances can be negative for a minority of less successful students, as well as potentially harmful for successful students. I end with a recommendation for the inclusion of the philosophy and ethics of mathematics alongside its teaching all stages from school to university, to attempt to reduce or obviate the harm caused; the collateral damage of learning mathematics.


Critical mathematics education Ethics Collateral damage Harm Instrumentalism Philosophy of mathematics 


  1. Adorno, R., Frenkel-Brunswik, E., Levinson, D., & Sanford, R. (1950). The authoritarian personality. New York: Harper.Google Scholar
  2. American Mathematical Society. (2005). Ethical guidelines. Accessed May 1, 2015.
  3. Arendt, H. (1963). Eichmann in Jerusalem: A report on the banality of evil. London: Faber and Faber.Google Scholar
  4. Bakan, J. (2004). The corporation. London: Constable.Google Scholar
  5. Banerjee, P. A. (2016). A systematic review of factors linked to poor academic performance of disadvantaged students in science and maths in schools. Cogent Education, 3(1). Accessed October 9, 2017.
  6. Baron-Cohen, S. (2003). The essential difference: Men, women and the extreme male brain. London: Penguin Books.Google Scholar
  7. Belbase, S. (2010). Images, anxieties and attitudes toward mathematics. Laramie, Wyoming: College of Education, University of Wyoming. Accessed July 29, 2017.
  8. Bell, E. T. (1952). Mathematics queen and servant of science. London: G. Bell and Sons.Google Scholar
  9. Berkeley, G. (1710). The principles of human knowledge. Reprinted 1962 in Fontana Library. Glasgow: W. Collins.Google Scholar
  10. Bird, S. J. (2014). Social responsibility and research ethics: Not either/or but both. Accessed May 1, 2015.
  11. Blunden, A. (Ed.). (n.d.). Encyclopedia of marxism. Glossary of terms, instrumental reason and communicative reason. Accessed March 12, 2009.
  12. Bohman, J. (2005). Critical theory. Stanford encyclopedia of philosophy. Accessed May 5, 2015.
  13. Bourdieu, P. (1986). The forms of capital. In J. G. Richardson (Ed.), Handbook of theory and research for the sociology of education (pp. 241–258). New York: Greenwood press.Google Scholar
  14. Buerk, D. (1982). An experience with some able women who avoid mathematics. For the Learning of Mathematics, 3(2), 19–24.Google Scholar
  15. Bunge, M. (1977). Towards a technoethics. Monist, 60(1), 96–107.CrossRefGoogle Scholar
  16. Burnyeat, M. F. (2000). Plato on why mathematics is good for the soul. Proceedings of the British Academy, 103. Accessed September 15, 2013.
  17. Burton, L. (Ed.). (1990). Gender and mathematics education: An international perspective. London: Cassell and UNESCO.Google Scholar
  18. Burton, L. (1995). Moving towards a feminist epistemology of mathematics. In P. Rogers & G. Kaiser (Eds.), Equity in mathematics education (pp. 209–225). London: Taylor and Francis.Google Scholar
  19. Buxton, L. (1981). Do you panic about maths? Coping with maths anxiety. London: Heinemann Educational Books.Google Scholar
  20. Cockcroft, W. H. (Chair). (1982). Mathematics counts (Report of the Committee of Inquiry on the Teaching of Mathematics). London: Her Majesty’s Stationery Office.Google Scholar
  21. Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: Social class, sex and problem-solving. London: Open University Press.Google Scholar
  22. Corradetti, C. (n.d.). The Frankfurt school and critical theory. The internet encyclopedia of philosophy. Accessed May 5, 2015.
  23. Cournand, A. (1977). The code of the scientist and its relationship to ethics. Science, 198(4318), 699–705.CrossRefGoogle Scholar
  24. D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44–48.Google Scholar
  25. D’Ambrosio, U. (1998). Mathematics and peace: Our responsibilities. Zentralblatt für Didaktik der Mathematik, 30(3), 67–73.CrossRefGoogle Scholar
  26. Davis, C. (1988). A Hippocratic oath for mathematicians? In C. Keitel (Ed.), Mathematics, education and society (pp. 44–47). Paris: UNESCO.Google Scholar
  27. Davis, P. J. (2007). Applied mathematics as social contract. Philosophy of Mathematics Education Journal (22). Accessed May 2, 2015.
  28. Dreyfus, H. L. (2004). Heidegger on gaining a free relation to technology. In D. M. Kaplan (Ed.), Readings in the philosophy of technology (pp. 53–62). Summit, Pennsylvania: Rowman and Littlefield.Google Scholar
  29. Ernest, P. (1991). The philosophy of mathematics education. London: Routledge.Google Scholar
  30. Ernest, P. (1995). Values, gender and images of mathematics: A philosophical perspective. International Journal of Mathematics Education, Science and Technology, 26(3), 449–462.CrossRefGoogle Scholar
  31. Ernest, P. (1996). A bibliography of mathematics education. Exeter: University of Exeter School of Education. Accessed May 3, 2015.
  32. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany, New York: State University of New York Press.Google Scholar
  33. Ernest, P. (2007). Values and the social responsibility of mathematics. Philosophy of Mathematics Education Journal (22). Retrieved May 1, 2015 from
  34. Ernest, P. (2008). Epistemology plus values equals classroom image of mathematics. The Philosophy of Mathematics Education Journal (23). Accessed August 3, 2017.
  35. Ernest, P. (2011). Mathematics and special educational needs. Saarbrucken, Germany: Lambert Academic Publishing.Google Scholar
  36. Ernest, P. (2012). What is our first philosophy in mathematics education? For the Learning of Mathematics, 32(3), 8–14.Google Scholar
  37. Ernest, P. (2013). The psychology of mathematics. Amazon Digital Services, Inc.: Kindle edition.Google Scholar
  38. Ernest, P. (2015). The problem of certainty in mathematics. Educational Studies in Mathematics, 90(3), 1–15.Google Scholar
  39. Ernest, P. (2016a). Values and mathematics: Overt and covert. Culture and Dialogue, 4(1), 48–82 (Special issue Culture, Science and Dialogue, Guest editor: M. Ovens).Google Scholar
  40. Ernest, P. (2016b). A dialogue on the ethics of mathematics. The Mathematical Intelligencer, 38(3), 69–77.CrossRefGoogle Scholar
  41. Ernest, P., Sriraman, B., & Ernest, N. (Eds.). (2016). Critical mathematics education: Theory, praxis and reality. Charlotte, NC, USA: Information Age Publishing.Google Scholar
  42. European Union. (n.d.). Consolidated version of the treaty on European Union title I: Common provisions, Article 3. Accessed April 20, 2015.
  43. Evers, K. (2001). Standards for ethics and responsibility in science. Accessed May 1, 2015.
  44. Forgasz, H. J., Becker, J. R., Lee, K., & Steinthorsdottir, O. (Eds.). (2010). International perspectives on gender and mathematics education. Charlotte, N. C., USA: Information Age Publishing.Google Scholar
  45. Frankenstein, M. (1990). Re-learning mathematics. London: Free Association Books.Google Scholar
  46. Frazer, M. J., & Kornhauser, A. (1986). Ethics and social responsibility in science education. The Netherlands: Elsevier Ltd.CrossRefGoogle Scholar
  47. Fromm, E. (1978). To have or to be?. London: Jonathon Cape.Google Scholar
  48. Gilligan, C. (1982). In a different voice. Cambridge, Massachusetts: Harvard University Press.Google Scholar
  49. Ginott, H. G. (1972). Teacher and child: A book for parents and teachers. London: Macmillan.Google Scholar
  50. Gladwell, M. (2008). Outliers. New York, USA: Little, Brown and Company.Google Scholar
  51. Gowers, W. T. (n.d.). The importance of mathematics. Accessed May 5, 2015.
  52. Hardy, G. H. (1941). A mathematician’s apology. Cambridge: Cambridge University Press.Google Scholar
  53. Haynes, J. D. (2008). Calculative thinking and essential thinking in Heidegger’s phenomenology. Accessed May 3, 2015.
  54. Hersh, R. (1990). Mathematics and ethics. The Mathematical Intelligencer, 12(3), 13–15.CrossRefGoogle Scholar
  55. Hersh, R. (1997). What is mathematics, really?. London: Jonathon Cape.Google Scholar
  56. Hersh, R. (2007). Ethics for mathematicians. Philosophy of Mathematics Education Journal (22). Accessed May 1, 2015.
  57. Howe, M. J. A. (1990). The origins of exceptional abilities. Oxford: Blackwell.Google Scholar
  58. Høyrup, J. (1980). Influences of institutionalized mathematics teaching on the development and organisation of mathematical thought in the pre-modern period. In J. Fauvel & J. Gray (Eds.), (1987). The history of mathematics: A reader (pp. 43–45). London: Macmillan.Google Scholar
  59. Høyrup, J. (1994). In measure, number, and weight. New York, USA: SUNY Press.Google Scholar
  60. Isaacson, Z. (1989). Of course you could be an engineer, dear, but wouldn’t you rather be a nurse or teacher or secretary? In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 188–194). London: Falmer Press.Google Scholar
  61. Johnson, T. (2015). Finance and mathematics: Where is the ethical malaise? Accessed August 3, 2017.
  62. Jonas, H. (1985). The imperative of responsibility: In search of an ethics for the technological age. Chicago, USA: The University of Chicago.Google Scholar
  63. Kant, I. (1993). Grounding for the metaphysics of morals (3rd ed.). (J. W. Ellington, Trans.). Indianapolis and Cambridge, USA: Hackett.Google Scholar
  64. Kelman, H. C. (1973). Violence without moral restraint: Reflections on the dehumanization of victims and victimizers. Journal of Social Issues, 29(4), 25–62.CrossRefGoogle Scholar
  65. Khan, R. N. (1988). Science, scientists and society: Public attitudes towards science and technology. Impacts of Science on Society, 1(3&4), 257–271.Google Scholar
  66. King, R. (1982). Multiple realities and their reproduction in infants’ classrooms. In C. Richards (Ed.), New directions in primary education (pp. 237–246). Lewes, Sussex: Falmer Press.Google Scholar
  67. Lenk, H. (1983). Notes on extended responsibility and increased technological power. In P. T. Durbin & F. Rapp (Eds.), Philosophy and technology (pp. 195–210). Dordrecht, Holland: D. Reidel Publishing Company.CrossRefGoogle Scholar
  68. Levinas, E. (1978). Otherwise than being or beyond essence (A. Lingis, Trans.). Dordrecht and Boston, MA, USA: Kluwer Academic Publishers.Google Scholar
  69. Luppicini, R. (2008). The emerging field of technoethics. In R. Luppicini & R. Adell (Eds.), Handbook of research on technoethics (pp. 1–18). Hershey, PA, USA: Idea Group Publishing.Google Scholar
  70. Marcuse, H. (1964). One dimensional man. London: Routledge and Kegan Paul.Google Scholar
  71. Maslow, A. H. (1954). Motivation and personality. New York: Harper.Google Scholar
  72. Maxwell, J. (1989). Mathephobia. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 221–226). London: Falmer Press.Google Scholar
  73. Mellin-Olsen, S. (1987). The politics of mathematics education. Dordrecht: Reidel.Google Scholar
  74. Mendick, H. (2006). Masculinities in mathematics. Maidenhead, UK: Open University Press.Google Scholar
  75. Milgram, S. (1974). Obedience to authority: An experimental view. New York, USA: Harper.Google Scholar
  76. Miller, A. (1983). For your own good: Hidden cruelty in child-rearing and the roots of violence. New York, USA: Farrar Straus Giroux.Google Scholar
  77. Moor, J. (2005). Why we need better ethics for emerging technologies. Ethics and Information Technology, 7(3), 111–119.CrossRefGoogle Scholar
  78. Mukhopadhyay, S., & Greer, B. (Eds.). (2015). Proceedings of the Eighth International Mathematics Education and Society Conference (Draft Volumes 1–3), June 21–26, 2015. Oregon, United States: Portland State University. Accessed May 1, 2015.
  79. Niss, M. (1994). Mathematics in society. In R. Biehler, R. W. Scholz, R. Straesser, & B. Winkelmann (Eds.), The didactics of mathematics as a scientific discipline (pp. 367–378). Dordrecht: Kluwer.Google Scholar
  80. Picker, S. H., & Berry, J. (2000). Investigating pupils’ images of mathematicians. Educational Studies in Mathematics, 43(1), 65–94.CrossRefGoogle Scholar
  81. Pinker, S. (2012). The better angels of our nature. New York, USA: Penguin Books.Google Scholar
  82. Powell, A. B., & Frankenstein, M. (Eds.). (1997). Ethnomathematics: Challenging eurocentrism in mathematics education. Albany, New York, USA: SUNY Press.Google Scholar
  83. Radical Statistics Group. (n.d.). About us. Accessed August 3, 2017.
  84. Rogers, P., & Kaiser, G. (Eds.). (1995). Equity in mathematics education. London: Falmer Press.Google Scholar
  85. Rotblat, J. (1995). Remember your humanity. Nobel Peace Prize Lecture. Accessed April 23, 2015.
  86. Rotman, B. (1993). Ad infinitum the ghost in turing’s machine: Taking god out of mathematics and putting the body back in. Stanford, California, USA: Stanford University Press.Google Scholar
  87. Russell, B. (1919). Mysticism and logic: And other essays. Longman: London.Google Scholar
  88. Russell, B., & Einstein, A. (1955). The Russell-Einstein manifesto. Accessed April 23, 2015.
  89. Ruthven, K. (1987). Ability stereotyping in mathematics. Educational Studies in Mathematics, 18(3), 243–253.CrossRefGoogle Scholar
  90. Sakharov, A. (1981). The responsibility of scientists. Nature, 291(5812), 184–185.CrossRefGoogle Scholar
  91. Schecter, D. (2010). The critique of instrumental reason from Weber to Habermas. London: Bloomsbury Academic.Google Scholar
  92. Sells, L. W. (1973). High school mathematics as the critical filter in the job market. In Proceedings of the Conference on Minority Graduate Education (pp. 37–49). Berkeley, USA: University of California.Google Scholar
  93. Sells, L. W. (1978). Mathematics—Critical filter. The Science Teacher, 45(2), 28–29.Google Scholar
  94. Shelley, N. (1995). Mathematics: Beyond good and evil. In P. Rogers & G. Kaiser (Eds.), Equity in mathematics education (pp. 248–266). London: Taylor and Francis.Google Scholar
  95. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching (77), 20–26.Google Scholar
  96. Skovsmose, O. (1988). Mathematics as a part of technology. Educational Studies in Mathematics, 19(1), 23–41.CrossRefGoogle Scholar
  97. Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht, Holland: Kluwer.CrossRefGoogle Scholar
  98. Small, B. H. (2011). Ethical relationships between science and society: Understanding the social responsibility of scientists (Unpublished Doctor of Philosophy Thesis). University of Waikato, New Zealand. Accessed April 23, 2015.
  99. Stanic, G. M. A. (1989). Social inequality, cultural discontinuity, and equity in school mathematics. Peabody Journal of Education, 66(2), 57–71.CrossRefGoogle Scholar
  100. UNESCO. (1999). World Conference on Science—Science Agenda Framework for Action. Budapest, Hungary, 26 June–1 July 1999. Accessed May 1, 2015.
  101. UNESCO. (n.d.). Ethics of science and technology. Accessed May 1, 2015.
  102. Vygotsky, L. S. (1978). In M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds.). Mind in society: The development of the higher psychological processes. Cambridge, Massachusetts, USA: Harvard University Press.Google Scholar
  103. Walkerdine, V. (1988). The mastery of reason. London: Routledge.Google Scholar
  104. Walkerdine, V. (1998). Counting girls out (2nd ed.). London: Falmer Press.Google Scholar
  105. Weinberg, A. (1978). The obligations of citizenship in the republic of science. Minerva, 16(1–3), 1978.Google Scholar
  106. Weiner, B. (1972). Attribution theory, achievement motivation and the educational process. Review of Educational Research, 42(2), 203–215.CrossRefGoogle Scholar
  107. Wikipedia. (n.d., a). Anti-globalization movement. Wikipedia. Accessed April 20, 2015.
  108. Wikipedia. (n.d., b). Occupy movement. Wikipedia. Accessed April 20, 2015.
  109. Wilde, O. (1907). The writings of Oscar Wilde (Uniform Edition, Vol. 10, p. 116). New York: A. R. Keller & Co. Inc.Google Scholar
  110. Zevenbergen, R. (1998). Language, mathematics and social disadvantage: A Bourdieuian analysis of cultural capital in mathematics education. Accessed May 3, 2015.
  111. Ziman, J. (1998). Why must scientists become more ethically sensitive than they used to be. Science, 282, 1813–1814.CrossRefGoogle Scholar
  112. Ziman, J. (2001). Getting scientists to think about what they are doing. Science and Engineering Ethics, 7(2), 165–176.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Graduate School of EducationUniversity of ExeterExeterUK

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