Ethics in mathematics
Ethics in mathematics is a field of applied ethics, the inquiry into ethical aspects of the 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. Many research mathematicians see no ethical implications in their pure research but assumptions made in mathematical approaches can have real consequences [1].
Need for ethics in the mathematics profession
Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with large consequences. 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",[2] and the theory of global warming depends on the reliability of mathematical models of climate. 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 [3], to consider how bias is overseen in automated systems, from algorithms to AI.
Disasters and scandals involving the use of mathematics
These illustrate the major consequences of numerical mistakes and hence the need for ethical care.
- The Club of Rome's 1972 mathematical-model based predictions in The Limits to Growth of widespread collapse of the world system by the end of the century.
- Wrongful conviction of Sally Clark (1999), An English solicitor, Sally Clark, was wrongfully convicted of murdering her two children – each of whom had died due to sudden infant death syndrome – due to a fundamental statistical error in the testimony of an "expert".
The error was further compounded by the "prosecutor's fallacy".[4]
Ethical issues in the mathematical profession
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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. 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 sustain the reputation of the profession and protect society from the impacts of ethical 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 [5].
Ethics in data journalism
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.[6] 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
Much of mathematics as used in applications involves the drawing of conclusions from quantitative data. It is recognised that there are many difficulties in reaching and communicating such conclusions accurately, honestly and with due regard to the uncertainties that remain. It is easy for a statistician to mislead clients whose understanding of data and inference is less developed, so statisticians have professional responsibilities to act fairly.
Mathematical folklore
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[7].
Ethics in pure mathematical research
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 and giving credit, to publish without unreasonable delay, and to correct errors.[8] The European Mathematical Society Ethics Committee also publishes a code of practice relating to the publication, editing and refereeing of research.[9]
It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues.[10] 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.[11]
Teaching ethics in mathematics
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.[12]
See also
- Essentially contested concept
- Ethical calculus
- Misuse of statistics
- Prosecutor's fallacy
- Type I and type II errors
- Type III error
- Unintended consequences
- Big data ethics
Notes
- ^ Chiodo, M. & Bursill-Hall, P. (2018) Four Levels of Ethical Engagement Discussion paper 18/1, Cambridge University Ethics in Mathematics Project
- ^ Felix Salmon, Recipe for disaster: the formula that killed Wall Street", Wired23 Feb 2009.
- ^ Ethics and New Techologies, ICAEW, 2018
- ^ Derbyshire, D., "Misleading statistics were presented as facts in Sally Clark trial", The Telegraph, (12 June 2003).
- ^ Collmann & Matei (Eds.), Ethical Reasoning in Big Data, Basel, CH: Springer, 2016
- ^ McBride, [1], 2017
- ^ van Bendegem, J., Rittberg, C. & Tanswell, F. (2018) Epistemic Injustice in Mathematics, Synthese
- ^ American Mathematical Society Policy Statement on Ethical Guidelines, 2005.
- ^ Code of Practice – European Mathematical Society.
- ^ Reuben Hersh, Mathematics and ethics, The Mathematical Intelligencer 12 (3) (1990), 13–15.
- ^ James Franklin, Ethics of mathematics, Mathematical Intelligencer 13 (1) (1991), 4.
- ^ James Franklin, A “Professional issues and ethics in mathematics” course, Gazette of the Australian Mathematical Society 32 (2005), 98–100.
References
- Aitken, C., Roberts, P. & Jackson, G., Communicating and Interpreting Statistical Evidence in the Administration of Criminal Justice, Practitioner Guide No.1: Fundamentals of Probability and Statistical Evidence in Criminal Proceedings: Guidance for Judges, Lawyers, Forensic Scientists and Expert Witnesses, Royal Statistical Society, 2010.
- Balinski, M., "What is just?", American Mathematical Monthly, Vol.112, No.6, (June-July 2005), pp. 502-511.
- Boylan, M., "Ethical Dimensions of Mathematics Education", Educational Studies in Mathematics, Vol.92, No.3, (July 2016), pp. 395–409.
- Dworkin, G., "A Journal of Mathematical Ethics: A Proposal", The Philosophical Forum, Vol.13, No.4, (Summer 1982), pp. 413–415.
- Ernest, P. "What is Our First Philosophy in Mathematics Education?", For the Learning of Mathematics, Vol.32, No.3, (November 2012), pp. 8–14.
- Ernest, P., "A Dialogue on the Ethics of Mathematics", The Mathematical Intelligencer, Vol.38, No.3, (September 2016), pp. 69–77.
- Ernest, P., "The Ethics of Mathematics: Is Mathematics Harmful?", Ernest, P., (Ed.)The Philosophy of Mathematics Education Today. Switzerland: Springer, 2018, pp 187-216.
- Franklin, J., "On the Parallel Between Mathematics and Morals", Philosophy, Vol.79, No.1, (January 2004), pp. 97–119.
- Henrich, D., "Mathematical Ethics: Values, Valences and Virtue", Philosophy of Mathematics Education Journal, No.29, (July 2015).
- Lesser, L.M. & Nordenhaug, E., "Ethical statistics and statistical ethics: Making an interdisciplinary module", Journal of Statistics Education, Vol.12, No.3, (November 2004), pp. 50–56.
- Levy, D.M. & Peart, S.J., "Inducing Greater Transparency: Towards the Establishment of Ethical Rules for Econometrics", Eastern Economic Journal, Volume 34, Issue 1, (January 2008), pp 103–114.
- Shulman, B. J., "Is there enough poison gas to kill the city?: The teaching of ethics in mathematics classes", The College Mathematics Journal, Vol.33, No.2, (March 2002), pp. 128–125.
- Stinson, D.W., "In Search of Defining Ethics in (Mathematics) Education Research?", Journal of Urban Mathematics Education, Vol.10, No.1, (July 2017), pp. 1–6.
- Strasak, A. M, Zaman, Q, Pfeiffer, K. P., Göbel, G. & Ulmer, H., "Statistical errors in medical research — a review of common pitfalls", Swiss Medical Weekly, (2007), 137: 44–49.
- Vardeman, S.B. & Morris, M.D., "Statistics and Ethics: Some Advice for Young Statisticians", The American Statistician, Vol.57, No.1, (February 2003), pp. 21–6.
- Young, J., "Statistical errors in medical research — a chronic disease?", Swiss Medical Weekly, (2007), 137: 41–43: editorial commentary (and elaboration) on Strasak, et al. by the Swiss Medical Weekly's Statistical Advisor.