Ethics in mathematics

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. ^[1] 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. ^[2] 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. ^[3]

Contents

• Need for ethics in the mathematics profession
• Issues of accuracy
• Issues of impact
• Disasters involving the use of mathematics
• Ethical issues in the mathematical profession
• Ethics in data journalism
• Misuse of statistics
• Mathematical folklore
• Ethics in pure mathematical research
• Parallels between ethics and mathematics
• Teaching ethics in mathematics
• See also
• Notes
• References
• External links

The ethical questions surrounding the practice of mathematics can be connected to issues of dual-use. ^[4] 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. ^[5] These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. ^[6] 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. ^[7] 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. ^[8]

The philosophical positions on the relationship between mathematics and ethics are varied. ^[9] Some philosophers (e.g. Plato) see both mathematics and ethics as rational and similar, while others (e.g. Rudolf Carnap) see ethics as irrational and different from mathematics. ^[10] Possible tensions between applying mathematics in a social context and its ethics can already be observed in Plato's Republic (Book VIII) where the use of mathematics to produce better guardians plays a critical role in its collapse. ^[11]

Need for ethics in the mathematics profession

Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with significant consequences. ^[12]

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's 1972 mathematical-model-based predictions in The Limits to Growth 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 – due to a fundamental statistical error in the testimony of an "expert". The error was further compounded by the "prosecutor's fallacy". ^[19]

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 in Artificial Intelligence applications, both by mathematicians and non-mathematicians, with complex impacts that are not readily understood or anticipated. ^[20]

Ethics in data journalism

Journalism has established Professional ethics 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. ^[21] 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. ^[22]

Mathematical folklore

Priority and attribution of mathematical discovery are important to professional practice, ^[23] 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. ^[24]

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, giving credit, publishing without unreasonable delay, and correcting errors. ^[25] The European Mathematical Society Ethics Committee also publishes a code of practice relating to the publication, editing and refereeing of research. ^[26]

It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues. ^[27] 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. ^[28]

The study of ethical challenges in pure mathematics is deeply connected to the philosophy of mathematical practice. ^[29] 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. ^[30] The problem of epistemic injustice in mathematical research is actively discussed in this context. ^[31]

Parallels between ethics and mathematics

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. ^{[32] [33]}

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. ^[34]

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. ^[35] In 2023, the ETH Zurich taught an optional seminar on ethics in mathematics ^[36] and a non-examinable seminar also exists at the University of Cambridge. ^[37] A mini-seminar has also been taught at Swarthmore College. ^[38]

Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice." ^[39]

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. ^[40] These programmes are currently explored at Harvard University, ^[41] Stanford University ^[42] and other places.

See also

• Essentially contested concept  – A theory that proposes that some concepts will never have a single, widely agreed-upon instantiation
• Ethical calculus  – Application of mathematics to calculate issues in ethics
• Misuse of statistics  – Use of statistical arguments to assert falsehoods
• Prosecutor's fallacy  – Error in thinking which involves under-valuing base rate informationPages displaying short descriptions of redirect targets
• Type I and type II errors  – Concepts from statistical hypothesis testing
• Type III error  – Term in statistical hypothesis testing
• Unintended consequences  – Unforeseen outcomes of an action
• Big data ethics  – Ethics of mass data analytics
• Ethics of quantification - Ethics of quantification
• Ethics of artificial intelligence - 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

Related Research Articles

In ethics, casuistry is a process of reasoning that seeks to resolve moral problems by extracting or extending abstract rules from a particular case, and reapplying those rules to new instances. This method occurs in applied ethics and jurisprudence. The term is also used pejoratively to criticise the use of clever but unsound reasoning, especially in relation to moral questions. It has been defined as follows:

Study of cases of conscience and a method of solving conflicts of obligations by applying general principles of ethics, religion, and moral theology to particular and concrete cases of human conduct. This frequently demands an extensive knowledge of natural law and equity, civil law, ecclesiastical precepts, and an exceptional skill in interpreting these various norms of conduct....

Ethics or moral philosophy is the philosophical study of moral phenomena. It investigates normative questions about what people ought to do or which behavior is morally right. It is usually divided into three major fields: normative ethics, applied ethics, and metaethics.

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.

The Latin maxim ignoramus et ignorabimus, meaning "we do not know and will not know", represents the idea that scientific knowledge is limited. It was popularized by Emil du Bois-Reymond, a German physiologist, in his 1872 address "Über die Grenzen des Naturerkennens".

Computer ethics is a part of practical philosophy concerned with how computing professionals should make decisions regarding professional and social conduct.

Medical humanities is an interdisciplinary field of medicine which includes the humanities, social science and the arts and their application to medical education and practice.

The ethics of care is a normative ethical theory that holds that moral action centers on interpersonal relationships and care or benevolence as a virtue. EoC is one of a cluster of normative ethical theories that were developed by some feminists and environmentalists since the 1980s. While consequentialist and deontological ethical theories emphasize generalizable standards and impartiality, ethics of care emphasize the importance of response to the individual. The distinction between the general and the individual is reflected in their different moral questions: "what is just?" versus "how to respond?" Carol Gilligan, who is considered the originator of the ethics of care, criticized the application of generalized standards as "morally problematic, since it breeds moral blindness or indifference".

Information ethics has been defined as "the branch of ethics that focuses on the relationship between the creation, organization, dissemination, and use of information, and the ethical standards and moral codes governing human conduct in society". It examines the morality that comes from information as a resource, a product, or as a target. It provides a critical framework for considering moral issues concerning informational privacy, moral agency, new environmental issues, problems arising from the life-cycle of information. It is very vital to understand that librarians, archivists, information professionals among others, really understand the importance of knowing how to disseminate proper information as well as being responsible with their actions when addressing information.

James Franklin is an Australian philosopher, mathematician and historian of ideas.

Plus Magazine is an online popular mathematics magazine run under the Millennium Mathematics Project at the University of Cambridge.

Pragmatic ethics is a theory of normative philosophical ethics and meta-ethics. Ethical pragmatists such as John Dewey believe that some societies have progressed morally in much the way they have attained progress in science. Scientists can pursue inquiry into the truth of a hypothesis and accept the hypothesis, in the sense that they act as though the hypothesis were true; nonetheless, they think that future generations can advance science, and thus future generations can refine or replace their accepted hypotheses. Similarly, ethical pragmatists think that norms, principles, and moral criteria are likely to be improved as a result of inquiry.

Juliana González Valenzuela is a Mexican philosopher.

Simon Rogerson is lifetime Professor Emeritus in Computer Ethics at the Centre for Computing and Social Responsibility (CCSR), De Montfort University. He was the founder and editor for 19 volumes of the Journal of Information, Communication and Ethics in Society. He has had two careers; first as a technical software developer and then in academia as reformer. He was the founding Director of CCSR, launching it in 1995 at the first ETHICOMP conference which he conceived and co-directed until 2013. He became Europe's first Professor in Computer Ethics in 1998. His most important research focuses on providing rigorously grounded practical tools and guidance to computing practitioners. For his leadership and research achievements in the computer and information ethics interdisciplinary field he was awarded the fifth IFIP-WG9.2 Namur Award in 2000 and the SIGCAS Making a Difference Award in 2005.

Isaac Elishakoff is a Distinguished Research Professor in the Ocean and Mechanical Engineering Department in the Florida Atlantic University, Boca Raton, Florida. He is a figure in the area of mechanics. He has made several contributions in the areas of random vibrations, solid mechanics of composite material, semi-inverse problems of vibrations and stability, functionally graded material structures, and nanotechnology.

Amy Shell-Gellasch is a mathematician, historian of mathematics, and book author. She has written or edited the books

Elena Anne Corie Marchisotto is a mathematician, mathematics educator, and historian of mathematics. She is a professor emeritus of mathematics at California State University, Northridge.

Dutch philosophy is a broad branch of philosophy that discusses the contributions of Dutch philosophers to the discourse of Western philosophy and Renaissance philosophy. The philosophy, as its own entity, arose in the 16th and 17th centuries through the philosophical studies of Desiderius Erasmus and Baruch Spinoza. The adoption of the humanistic perspective by Erasmus, despite his Christian background, and rational but theocentric perspective expounded by Spinoza, supported each of these philosopher's works. In general, the philosophy revolved around acknowledging the reality of human self-determination and rational thought rather than focusing on traditional ideals of fatalism and virtue raised in Christianity. The roots of philosophical frameworks like the mind-body dualism and monism debate can also be traced to Dutch philosophy, which is attributed to 17th century philosopher René Descartes. Descartes was both a mathematician and philosopher during the Dutch Golden Age, despite being from the Kingdom of France. Modern Dutch philosophers like D.H. Th. Vollenhoven provided critical analyses on the dichotomy between dualism and monism.

Math on Trial: How Numbers Get Used and Abused in the Courtroom is a book on mathematical and statistical reasoning in legal argumentation, for a popular audience. It was written by American mathematician Leila Schneps and her daughter, French mathematics educator Coralie Colmez, and published in 2013 by Basic Books.

Erna Beth Seecamp Yackel was an American college professor and math educator. She was a member of the faculty at Purdue University Northwest from 1984 to 2004.

Mathematics for social justice is a pedagogical approach to mathematics education that seeks to incorporate lessons from critical mathematics pedagogy and similar educational philosophies into the teaching of mathematics at schools and colleges. The approach tries to empower students on their way to developing a positive mathematics identity and becoming active, numerically literate citizens who can navigate and participate in society. Mathematics for social justice puts particular emphasis on overcoming social inequalities. Its proponents, for example, Bob Moses, may understand numerical literacy as a civil right. Many of the founders of the movement, e.g. Eric Gutstein, were initially mathematics teachers, but the movement has since expanded to include the teaching of mathematics at colleges and universities. Their educational approach is influenced by earlier critical pedagogy advocates such as Paulo Freire and others. Mathematics for social justice has been criticised, however, its proponents argue that it both fits into existing teaching frameworks and promotes students' success in mathematics.

References

External links

• Cambridge University Ethics in Mathematics Society
• American Mathematical Society: Policy Statement on Ethical Guidelines
• Royal Statistical Society: Statistics and the Law.