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Ethics in mathematics is an emerging field of
applied ethics Applied ethics is the practical aspect of morality, moral considerations. It is ethics with respect to real-world actions and their moral considerations in private and public life, the professions, health, technology, law, and leadership. For ex ...
, the inquiry into ethical aspects of the practice and applications of
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
. It deals with the professional responsibilities of
mathematicians A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One ...
whose work influences decisions with major consequences, such as in law, finance, the military, and environmental science. When understood in its socio-economic context, the development of mathematical works can lead to ethical questions ranging from the handling and manipulation of big data to questions of responsible mathematisation and falsification of models, explainable and safe mathematics, as well as many issues related to communication and documentation. The usefulness of a Hippocratic oath for mathematicians is an issue of ongoing debate among scholars. As an emerging field of applied ethics, many of its foundations are still highly debated. The discourse remains in flux. Especially the notion that mathematics can do harm remains controversial. The ethical questions surrounding the practice of mathematics can be connected to issues of
dual-use In politics, diplomacy and export control, dual-use items refer to goods, software and technology that can be used for both civilian and military applications.
. An instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, yet it might be easier to see how all branches of mathematics serve to structure and conceptualize 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 worldview of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices. As mathematicians can enter the workforce of industrialised nations in many places that are no longer limited to teaching and academia, scholars have made the argument that it is necessary to add ethical training into the mathematical curricula at universities. The philosophical positions on the relationship between mathematics and ethics are varied. Some philosophers (e.g.
Plato Plato ( ; Greek language, Greek: , ; born  BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...
) see both mathematics and ethics as rational and similar, while others (e.g.
Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. ...
) see ethics as irrational and different from mathematics. Possible tensions between applying mathematics in a social context and its ethics can already be observed in Plato's
Republic A republic, based on the Latin phrase ''res publica'' ('public affair' or 'people's affair'), is a State (polity), state in which Power (social and political), political power rests with the public (people), typically through their Representat ...
(Book VIII) where the use of mathematics to produce better guardians plays a critical role in its collapse.


Need for ethics in the mathematics profession

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


Issues of accuracy

For example, complex calculations were needed for the success of the
Manhattan Project The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada. From 1942 to 1946, the ...
, while the overextended use of the
Gaussian copula In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval  , 1 Copulas are used to describe / model the ...
formula to price derivatives before the
2008 financial crisis The 2008 financial crisis, also known as the global financial crisis (GFC), was a major worldwide financial crisis centered in the United States. The causes of the 2008 crisis included excessive speculation on housing values by both homeowners ...
has been called "the formula that killed Wall Street", and the theory of global warming depends on the reliability of mathematical models of climate.


Issues of impact

For the same reason as in
medical ethics Medical ethics is an applied branch of ethics which analyzes the practice of clinical medicine and related scientific research. Medical ethics is based on a set of values that professionals can refer to in the case of any confusion or conflict. T ...
and
engineering ethics Engineering ethics is the field concerned with the system of moral principles that apply to the practice of engineering. The field examines and sets the obligations by engineers to society, to their clients, and to the profession. As a scholarly ...
, 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. Due to its large impact and its necessity in the modern industrialised world, mathematics has been labelled as a new
factor of production In economics, factors of production, resources, or inputs are what is used in the production process to produce output—that is, goods and services. The utilised amounts of the various inputs determine the quantity of output according to the rela ...
by some scholars. Mathematics is a fundamental driver of today's economies and plays an everyday role in the decision making in
capitalist Capitalism is an economic system based on the private ownership of the means of production and their use for the purpose of obtaining profit. This socioeconomic system has developed historically through several stages and is defined by ...
markets. When studied in its socio-economic context, the debates surrounding the ethical use of mathematics often go under different names, e.g. some people speak of the ethics of quantification. These discourses are often disjoint from those directly affecting or driven by parts of the mathematical community.


Disasters involving the use of mathematics

These illustrate the major consequences of numerical mistakes and hence the need for ethical care. * The
Club of Rome The Club of Rome is a nonprofit, informal organization of intellectuals and business leaders whose goal is a critical discussion of pressing list of global issues, global issues. The Club of Rome was founded in 1968 at Accademia dei Lincei in R ...
's 1972 mathematical-model-based predictions in ''
The Limits to Growth ''The Limits to Growth'' (''LTG'') is a 1972 report that discussed the possibility of exponential Economic growth, economic and population growth with finite supply of resources, studied by computer simulation. The study used the World3 computer ...
'' of widespread collapse of the world system by the end of the 21st century. * The 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 Sudden infant death syndrome (SIDS), sometimes known as cot death or crib death, is the sudden unexplained death of a child of less than one year of age. Diagnosis requires that the death remain unexplained even after a thorough autopsy and ...
– 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 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 behavior. For example, mathematics is extensively applied in the use of
Big Data Big data primarily refers to data sets that are too large or complex to be dealt with by traditional data processing, data-processing application software, software. Data with many entries (rows) offer greater statistical power, while data with ...
in
Artificial Intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...
applications, both by mathematicians and non-mathematicians, with complex impacts that are not readily understood or anticipated.


Ethics in data journalism

Journalism Journalism is the production and distribution of reports on the interaction of events, facts, ideas, and people that are the "news of the day" and that informs society to at least some degree of accuracy. The word, a noun, applies to the journ ...
has established
Professional ethics Professional ethics encompass the personal and corporate standards of behavior expected of professionals. The word professionalism originally applied to vows of a religious order. By no later than the year 1675, the term had seen secular appli ...
which is affected by mathematical processing and (re-)publication of sources. Reusing information packaged as facts require checking, and validating, from conceptual confusion to sampling and calculation errors. Other professional issues arise from the potential of automated tools which allow the dissemination of publicly available data which has never been collated.


Misuse of statistics

Applications of mathematics generally involve drawing conclusions from quantitative data. Due to uncertainties that mathematical models deal with, and 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 instances, statisticians codified their ethics in the 1980s in a declaration of the ISI, recognizing that there would often be conflicting demands from stakeholders, with ethical decisions a matter of professional judgment.


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 In common mathematical parlance, a mathematical result is called folklore if it is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists. More specifically, folk mathematics, or ...
cannot be attributed to an individual, and may not have an agreed proof, despite being an accepted result, potentially leading to injustice.


Ethics in pure mathematical research

The
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
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. The
European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The curren ...
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. The study of ethical challenges in pure mathematics is deeply connected to the philosophy of mathematical practice. Arguments against the ethical neutrality of pure mathematical work often builds on the social constitution, i.e. the socio-cultural context of the research and the many decisions involved in mathematical proofs. The problem of
epistemic injustice Epistemic injustice is injustice related to knowledge. It includes exclusion and silencing; systematic distortion or misrepresentation of one's meanings or contributions; undervaluing of one's status or standing in communicative practices; unfai ...
in mathematical research is actively discussed in this context.


Parallels between ethics and mathematics

Ethics and mathematics both appear to rely on reasoning from
intuition Intuition is the ability to acquire knowledge without recourse to conscious reasoning or needing an explanation. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledg ...
, unlike empirical sciences which rely fundamentally on observations and experiments. That has been suggested as a reason in support of objectivity or
moral realism Moral realism (also ethical realism) is the position that ethical sentences express propositions that refer to objective features of the world (that is, features independent of subjective opinion), some of which may be true to the extent that t ...
in ethics, since arguments against objectivity in ethics are paralleled by arguments against objectivity in mathematics, which is generally believed to be false. 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 In geometry, the parallel postulate is the fifth postulate in Euclid's ''Elements'' and a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior ...
is true in
Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...
but false in
non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
, so ethical propositions can be true or false in different systems.


Teaching ethics in mathematics

Courses in the ethics of mathematics remain rare. The
University of New South Wales The University of New South Wales (UNSW) is a public research university based in Sydney, New South Wales, Australia. It was established in 1949. The university comprises seven faculties, through which it offers bachelor's, master's and docto ...
taught a compulsory course on Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012. In 2023, the
ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...
taught an optional seminar on ethics in mathematics and a non-examinable seminar also exists at the
University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
. A mini-seminar has also been taught at
Swarthmore College Swarthmore College ( , ) is a Private college, private Liberal arts colleges in the United States, liberal arts college in Swarthmore, Pennsylvania, United States. Founded in 1864, with its first classes held in 1869, Swarthmore is one of the e ...
. Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice." Similar approaches can also be found in the teaching of ethics to computer science students, where the term "embedded ethics" has established itself for the integration of ethics teaching into the curriculum. These programmes are currently explored at
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
,
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
and other places.


See also

* * * * * * * * * Ethics of quantification - Ethics of quantification *
Ethics of artificial intelligence The ethics of artificial intelligence covers a broad range of topics within AI that are considered to have particular ethical stakes. This includes algorithmic biases, Fairness (machine learning), fairness, automated decision-making, accountabili ...
- Ethics of artificial intelligence and machine learning * Critical mathematics pedagogy - Pedagogical approach behind some of the courses on ethics in mathematics and mathematics for social justice


Notes


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
.
Alayont, F. (2022), "A Case for Ethics in the Mathematics Major Curriculum", ''Journal of Humanistic Mathematics'', Vol.12, No.2, (July 2022), pp.160-177.
* 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.
Buell C, Piercey V. (2022), "Special Issue Ethics in Mathematics: Foreword", ''Journal of Humanistic Mathematics'', Vol.12, No.2, (July 2022), pp.3-6.
* Dubbs, Christopher (2020), "Whose Ethics? Toward Clarifying ''Ethics'' in Mathematics Education Research", ''Journal of Philosophy of Education'', Vo.54, No.3, (June 2020), pp.521-540. * 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)
* Kambartel, Friedrich (1972), "Ethik und Mathematik", pp.489–503 in Riedel, Manfred (ed.), ''Rehabilitierung Der Praktischen Philosophie, Band I: Geschichte, Probleme, Aufgaben'', Freiburg im Breisgau: Rombach Verlag. * Kambartel, Freidrich (trans. Gervasi, J.A. & Rentsch, T.) (1984), "Ethics and Mathematics", pp.49-61 in Christensen, D.E. (ed.), ''Contemporary German Philosophy, Volume 4'', University Park, PA: Pennsylvania State University Press.
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

Miller A.N. (2022). "A Mini-seminar: Teaching Ethics in Mathematics in an Hour a Week", ''Journal of Humanistic Mathematics''. ''12''(2): 178-203.

Nickel G. (2022), "Ethics and Mathematics Some Observations Fifty Years Later", ''Journal of Humanistic Mathematics'', Vol.12, No.2, (July 2022), pp.7-27.
*
Spindler, R. (2022), "Foundational Mathematical Beliefs and Ethics in Mathematical Practice and Education", ''Journal of Humanistic Mathematics'', Vol.12, No.2, (July 2022), pp.49-71.

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. {{refend


External links


Cambridge University Ethics in Mathematics Society

American Mathematical Society: Policy Statement on Ethical Guidelines

Royal Statistical Society: Statistics and the Law
Ethics of science and technology Philosophy of statistics Philosophy of mathematics Ethics and statistics Business ethics Professional ethics