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. Many research mathematicians see no ethical implications in their pure research but assumptions made in mathematical approaches can have real consequences . 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 . 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 .
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. The potential impact of data and new technology is leading more professions, such as accountancy , to consider how bias is overseen in automated systems, from algorithms to AI.
These illustrate the major consequences of numerical mistakes and hence the need for ethical care.
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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 .
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. Other professional issues arise from the potential of automated tools which allow dissemination of publicly available data which has never been collated.
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. In the 1980s statisticians codified their ethics in a declaration of the ISI, recognising that there would often be conflicting demands from stakeholders, with ethical decisions a matter of professional judgement .
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.
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.
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.