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.
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", 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.
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".
Ethical issues in the mathematical profession
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.
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.
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. The European Mathematical Society Ethics Committee also publishes a code of practice relating to the publication, editing and refereeing of research.
It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues. 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.
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.
- Essentially contested concept
- Ethical calculus
- Misuse of statistics
- Prosecutor's fallacy
- Type I and type II errors
- Type III error
- Unintended consequences
- Felix Salmon, Recipe for disaster: the formula that killed Wall Street", Wired23 Feb 2009.
- Derbyshire, D., "Misleading statistics were presented as facts in Sally Clark trial", The Telegraph, (12 June 2003).
- American Mathematical Society Policy Statement on Ethical Guidelines, 2005.
- Code of Practice – European Mathematical Society.
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- 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.