Ethics in mathematics

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Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics. It deals with the professional responsibilities of mathematicians whose work influences decisions with major consequences, such as in law, finance, the military, and environmental science.

Although many research mathematicians see no ethical implications in their pure research, assumptions made in mathematical approaches can have real consequences.[1] A very instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, but it is easier to see how all branches of mathematics serve to structure and conceptualise solutions to real problems.[2] These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the world view of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices.[3]

Need for ethics in the mathematics profession[edit]

Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with significant consequences.

Issues of accuracy[edit]

For example, complex calculations were needed for the success of the Manhattan Project, while the overextended use of the Gaussian copula formula to price derivatives before the Global Financial Crisis of 2008 has been called "the formula that killed Wall Street",[4] and the theory of global warming depends on the reliability of mathematical models of climate.

Issues of impact[edit]

For the same reason as in medical ethics and engineering ethics, the high impact of the consequences of decisions imposes serious ethical obligations on practitioners to consider the rights and wrongs of their advice and decisions. The potential impact of data and new technology is leading more professions, such as accountancy,[5] to consider how bias is overseen in automated systems, from algorithms to AI.

Disasters and scandals involving the use of mathematics[edit]

These illustrate the major consequences of numerical mistakes and hence the need for ethical care.

Ethical issues in the mathematical profession[edit]

Mathematicians in professional roles in finance and similar work have a particular responsibility to ensure they use the best methods and data to reach the right answer, as the prestige of mathematics is high and others rely on mathematical results which they cannot fully understand.[7][8] Other ethical issues are shared with information economy professionals in general, such as duty of care, confidentiality of information, whistleblowing, and avoiding conflict of interest.

Mathematicians have a professional responsibility to support the ethical use of mathematics in practice, both to sustain the reputation of the profession and to protect society from the impacts of unethical behaviour. For example, mathematics is extensively applied in the use of Big Data in Artificial Intelligence applications, both by mathematicians and non-mathematicians, with complex impacts that are not readily understood or anticipated.[9]

Ethics in data journalism[edit]

Journalism has an established Professional ethics which is affected by mathematical processing and (re-)publication of sources. Reusing information packaged as facts requires checking, and validating, form conceptual confusion to sampling and calculation errors.[10] Other professional issues arise from the potential of automated tools which allow dissemination of publicly available data which has never been collated.

Misuse of statistics[edit]

Applications of mathematics generally involve drawing of conclusions from quantitative data. Due to uncertainties that mathematical models deal with, challenges in drawing and communicating any conclusions, there is a possibility of mathematicians misleading the clients as they are not generally aware of quantitative techniques. To avoid such instance, statisticians codified their ethics in the 1980s in a declaration of the ISI, recognising that there would often be conflicting demands from stakeholders, with ethical decisions a matter of professional judgement.[11]

Mathematical folklore[edit]

Priority and attribution of mathematical discovery are important to professional practice, even as some theorems bear the name of the person making the conjecture rather than finding the proof. Folk theorems, or mathematical folklore cannot be attributed to an individual, and may not have an agreed proof, despite being an accepted result, potentially leading to injustice.[12]

Ethics in pure mathematical research[edit]

The American Mathematical Society publishes a code of ethical guidelines for mathematical researchers. The responsibilities of researchers include being knowledgeable in the field, avoiding plagiarism, giving credit, publishing without unreasonable delay, and correcting errors.[13] The European Mathematical Society Ethics Committee also publishes a code of practice relating to the publication, editing and refereeing of research.[14]

It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues.[15] However, that raises the question of whether and why pure mathematics is ethically worth doing, given that it consumes the lives of many highly intelligent people who could be making more immediately useful contributions.[16]

Parallels between ethics and mathematics[edit]

Ethics and mathematics both appear to rely on reasoning from intuition, unlike empirical sciences which rely fundamentally on observations and experiments. That has been suggested as a reason in support of objectivity or moral realism in ethics, since arguments against objectivity in ethics are paralleled by arguments against objectivity in mathematics, which is generally believed to be false.[17][18]

Justin Clarke-Doane argues to the contrary that although mathematics and ethics are closely parallel, a pluralist attitude should be taken to the truths of both. Just as the parallel postulate is true in Euclidean geometry but false in non-Euclidean geometry, so ethical propositions can be true or false in different systems.[19]

Teaching ethics in mathematics[edit]

Courses in the ethics of mathematics remain rare. The University of New South Wales taught a compulsory course on Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012.[20]

See also[edit]


  1. ^ Chiodo, M. & Bursill-Hall, P. (2018) Four Levels of Ethical Engagement Discussion paper 18/1, Cambridge University Ethics in Mathematics Project
  2. ^ Slightly dirty maths: The richly textured mechanisms of impact Laura R. Meagher Ursula Martin, Research Evaluation (2017) 26 (1): 15-27
  3. ^ O'Neil, C. (2016) Weapons of Math Destruction, Penguin.
  4. ^ Felix Salmon, Recipe for disaster: the formula that killed Wall Street", Wired23 Feb 2009.
  5. ^ Ethics and New Techologies, ICAEW, 2018
  6. ^ Derbyshire, D., "Misleading statistics were presented as facts in Sally Clark trial", The Telegraph, (12 June 2003).
  7. ^ Müller, Dennis; Chiodo, Maurice; Franklin, James (2022). "A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematics". Science and Engineering Ethics. 28 (5): 41. doi:10.1007/s11948-022-00389-y. PMC 9427075. PMID 36042113.
  8. ^ Money Mathematics: Examining Ethics Education in Quantitative Finance
  9. ^ Collmann & Matei (Eds.), Ethical Reasoning in Big Data, Basel, CH: Springer, 2016
  10. ^ McBride, [1], 2017
  11. ^ Jowell, R. (1986) The Codification of Statistical Ethics, J. Official Statist. 2(3): 217-253
  12. ^ van Bendegem, J., Rittberg, C. & Tanswell, F. (2018) Epistemic Injustice in Mathematics, Synthese
  13. ^ American Mathematical Society Policy Statement on Ethical Guidelines, 2005.
  14. ^ Code of Practice – European Mathematical Society.
  15. ^ Hersh, Reuben (1990). "Mathematics and ethics". Mathematical Intelligencer. 12 (3): 13–15. doi:10.1007/BF03024064. S2CID 206832780. Retrieved 30 June 2021.
  16. ^ Franklin, James (1991). "Ethics of mathematics". Mathematical Intelligencer. 13 (1): 4. doi:10.1007/BF03024064. S2CID 206832780. Retrieved 30 June 2021.
  17. ^ Lear, Jonathan (1983). "Ethics, mathematics and relativism". Mind. 92 (365): 38–60. doi:10.1093/mind/XCII.365.38. Retrieved 30 June 2021.
  18. ^ Franklin, James (2021). "'Let no‑one ignorant of geometry…': Mathematical parallels for understanding the objectivity of ethics". Journal of Value Inquiry. 55. doi:10.1007/s10790-021-09831-z. S2CID 235538417. Retrieved 30 June 2021.
  19. ^ Clarke-Doane, Justin (2020). Morality and Mathematics. New York: Oxford University Press. ISBN 9780198823667.
  20. ^ Franklin, James (2005). "A "Professional issues and ethics in mathematics" course" (PDF). Gazette of the Australian Mathematical Society. 32: 98–100. Retrieved 30 June 2021.


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