Michaelmas 2025
This course on Ethics in Mathematics aims to give an overview of the sorts of effects mathematicians and mathematical work can have on society, detail the instances where this work can cause harm, and discuss what leads to this work being harmful and what might be done to possibly avert such harm.
This is not a course on ethical frameworks, nor is it a philosophy course. We will not be discussing what is right and wrong, but instead explore the fact that there is right and wrong when doing mathematical work. This is a course to raise fundamental ethical awareness among mathematicians, not to give axioms of ethics or an algorithm for ethical decision-making.
This year, we are again working with the Ethics in Mathematics Project (EiMP) to deliver this course. CUEiMS will be hosting and chairing weekly seminars, given by Dr. Maurice Chiodo; these will consist of an interactive lecture followed by a discussion session.
Next seminar
Ethics in modelling.
16:00, Monday 20th October
MR13, Centre for Mathematical Sciences
These lectures will be held at 16:00–18:00 every Monday from 13th October to 1st December in MR13 in the CMS. The first hour will be a delivered lecture, and the second hour will be a discussion and Q&A session, with a 5 min break between the two.
The eight sessions will be as follows. (Click on titles for further details.)
Mathematicians sit at the heart of technological advancement and industrial progress. Mathematics is a universal tool. It can be used for good, and it can be used for harm. To begin, we look at where harmful situations may arise, and what exactly we as mathematicians are doing to contribute to that harm. Though this harm may not (necessarily) come from intentional malice, there are many situations, and people, who can influence and manipulate us into carrying out harmful acts as mathematicians. It is important to be able to recognise and react to these scenarios, as we cannot always rely on external forces such as management to guide what we do.
We all know about examples of mathematicians misbehaving in finance, and even being jailed as a result: Tom Hayes and Ke Xu are two examples. But more subtle are the modelling tools mathematicians produce. Mathematical modelling is ubiquitous in understanding the way the world works, from finance to physics to climate patterns. Understanding how to develop and use a model, as well as its limitations, and the way it interacts with the world, is indispensable in preventing it from causing harm. Unfortunately, as we saw in the financial crash of 2007, such models are sometimes poorly understood, with devastating consequences.
Mathematicians have always played a central role in the making, and breaking, of cryptography. We also play a key role in developing surveillance tools, both for state actors and private organisations. Thus, we have several ways of enabling the infringement of the privacy of others. We can do so deliberately, by designing tools to break strong encryption, or indirectly, by creating systems and platforms which collect massive amounts of personal data of individuals. And we can do it accidentally, by being careless or sloppy in the way we store the data of others. In all of these cases, our work determines how much privacy people can have.
Algorithms run the world, and mathematicians are designing them. Algorithms decide what people read, what they buy, and when then can get a loan. We often design these systems to remove human subjectivity from decision making processes and to make them impartial, as is being done with predictive policing algorithms and prison sentencing algorithms. But how impartial, or fair, can a system designed by humans ever be? Moreover, the internet and big data have given rise to massive new potential, from targeted political advertising as done by Cambridge Analytica, to AI technology such as deepfake videos and self-driving cars. Our ‘solutions’ in these instances can bring about a whole new set of problems.
The work of mathematicians in industry is now very close to its tangible applications; we produce output that is extremely quick and easy to use. Just look at machine-learned algorithms that compute credit scores. Now that we sit so close to the applications, we need to consider what sort of responsibility we have. There are things we are, and aren’t, legally allowed to do. And there are consequences we might face if we fall foul of the law. Moreover, given that our work is often cutting-edge, we must self-regulate to prevent the types of harm that legislators and others have yet to realise is even possible.
Just like every other academic field, mathematicians form their own community, with their own conventions, common beliefs, and schools of thought. We hand our teachings down through the generations, and this process goes all the way back to Euclid. But the ways of thinking we employ when doing mathematics in an abstract research setting may not serve us well in an industrial setting. It is important to be aware that not all the actions that make us good at mathematics will necessarily lead to us producing good solutions to industrial or social problems. In fact, some of our ways of viewing and approaching problems will hold us back when working outside academia.
All mathematicians will, eventually, form some part of the workforce. The abstract nature of mathematics may lead us to believe that our role is ‘special’, and that we won’t need to worry about the usual workplace interactions, issues, conflicts and dangers that may arise in other professions. This is simply not true. We face the same issues, and need to know how to deal with them. Our focused and dedicated nature means that we may easily overlook instances of others trying to exploit or manipulate us at work, resulting in harm to ourselves, and our work becoming harmful to wider society. We need to know how to identify such people and situations, and to protect ourselves against them.
Being aware of the ethical issues that you as a mathematician may face is an extremely important step. But this is only the first in a sequence of potential steps. You can take this further, by starting to tell other mathematicians you work with or interact with. You can try and get involved with decision-making processes, by taking a seat at tables of power and authority. And you could even work towards identifying the unethical behaviour of other mathematicians completely unrelated to you, and call out their harmful actions to the community and to the public. This is fairly new and uncharted territory for mathematicians, and they’re exactly the sorts of activities we shy away from. But now is the time to step up and take responsibility, because if we don’t do it, then no-one else will.
There are very few written resources relating to ethics in mathematics; as an area of study and understanding it is remarkably new. In terms of textbooks, there is nothing. The closest one can conceivably come is the following book, which is a popular science book (thus not written for a mathematical audience):
However, there is now a decent collection of articles and other publications on Ethics in Mathematics one can read. For convenience these are below divided into four sections. It would be wise, and easy, to read through the short articles in sections 1 and 2 above. These cover what Ethics in Mathematics is, and how one can go about learning it. The book by O’Neill is a fine, if somewhat superficial and mathematically-lacking, broad introduction to where some ethical issues in mathematics lie. Section 3 is much more involved, and would bring you up to speed on the ‘state of the art’ of Ethics in Mathematics. Section 4 then covers the complexities present in this rather nascent field of research and study.
None of these are required reading for the course, though may be of interest and some use in helping you to put Ethics in Mathematics into some more context.
SECTION 1: What is Ethics in Mathematics?
M. Chiodo, T. Clifton,
The Importance of Ethics in Mathematics, EMS Newsletter
114, 34–37, December 2019.
https://doi.org/10.4171/news/114/9
M. Chiodo, D. Müller,
Why mathematics is not neutral, and other myths,
LSE Higher Education Blog, October 2024. 2 pages.
https://blogs.lse.ac.uk/highereducation/2024/10/10/maths-is-not-neutral-and-other-myths/
M. Chiodo, D. Müller,
Questions of Responsibility: Modelling in the Age of COVID-19, SIAM news 53, No. 7, 6-7, September 2020. 3 pages.
https://sinews.siam.org/Details-Page/questions-of-responsibility-modelling-in-the-age-of-covid-19
M. Chiodo, D. Müller,
Mathematicians and Ethical Engagement, SIAM News
51 No. 9, p.6, November 2018. 3 pages.
https://sinews.siam.org/Details-Page/mathematicians-and-ethical-engagement
M. Chiodo, D. Müller,
A Field Guide to Ethics in Mathematics, Notices of the American Mathematical Society, August 2024. 9 pages.
https://sinews.siam.org/Details-Page/questions-of-responsibility-modelling-in-the-age-of-covid-19
C. Praeger, Math Matters: The Profession of Mathematics,
AustMS Gazette 31 No. 4, 217–221 (2004).
https://austms.org.au/wp-content/uploads/Gazette/2004/Sep04
P. Ernest,
A Dialogue on the Ethics of Mathematics. The Mathematical Intelligencer 38, 69–77 (2016).
https://www.researchgate.net/publication/305919923_A_Dialogue_on_the_Ethics_of_Mathematics
P. Ernest,
A Dialogue on the Deep Ethics of Mathematics. For the Learning of Mathematics 41 No. 3, 47-52 (2021).
https://flm-journal.org/index.php?do=details&lang=en&vol=41&num=3&pages=47-52&ArtID=1356
R. Hersch, Mathematics and ethics, The Mathematical
Intelligencer 12 No. 3, 12–15, June 1990.
https://link.springer.com/article/10.1007%2FBF03024013
https://core.ac.uk/download/pdf/70985053.pdf
M. Chiodo, P. Bursill-Hall,
Teaching Ethics in Mathematics, EMS Newsletter
114, 38–41, December 2019.
https://doi.org/10.4171/news/114/10
M. Chiodo, R. Vyas,
The role of ethics in a mathematical education, Ethics in
Mathematics Discussion Papers, 2018/1 (2018). 5 pages.
https://ethics-in-mathematics.com/pub
J. Franklin,
A “Professional Issues and Ethics in Mathematics” course,
AustMS Gazette 32 No. 2, 98–100 (2005).
https://austms.org.au/wp-content/uploads/Gazette/2005/May05
B. Schulman,
Is There Enough Poison Gas to Kill the City?: The Teaching of
Ethics in Mathematics Classes, College Math. J. 33, 118–125 (2002).
https://www.researchgate.net/publication/270390701_Is_There_Enough_Poison_Gas_to_Kill_the_City
M. Chiodo, D. Müller,
Manifesto for the Responsible Development of Mathematical Works - A Tool for Practitioners and for Management, Journal for Theoretical and Marginal Mathematics Education 33, No. 1, Article 0404 (2025). 53 pages.
https://zenodo.org/records/16729482
A more nicely formatted, and identical, version of the 10 pillars in the manifesto can be found on the arxiv preprint:
https://arxiv.org/abs/2306.09131
M. Chiodo, D. Müller, R. Shah,
Teaching Resources for Embedding Ethics in Mathematics: Exercises, Projects, and Handouts. Preprint at arXiv:2310.08467. 106 pages.
https://arxiv.org/abs/2310.08467
D. Müller, M. Chiodo,
Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics. Preprint at arXiv:2308.04871. 23 pages.
https://arxiv.org/abs/2308.04871
D. Müller, M. Chiodo, J. Franklin,
A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematics, Science and Engineering Ethics 28, 41: Article 41, 1-30, (2022).
https://doi.org/10.1007/s11948-022-00389-y
M. Chiodo, P. Bursill-Hall,
Four Levels of Ethical Engagement, Ethics in Mathematics
Discussion Papers, 2018/1 (2018). 25 pages.
https://ethics-in-mathematics.com/pub
P. Rogoway,
The Moral Character of Cryptographic Work (2015). 48
pages.
https://web.cs.ucdavis.edu/~rogaway/papers/moral-fn.pdf
D. Müller, M. Chiodo, Michael Meyer,
The Ethical and Sustainable Concerns Triangle: A Framework for Navigating Discourses in Mathematics and Its Education. Preprint at arXiv:2510.11327. 86 pages.
https://arxiv.org/abs/2510.11327
D. Müller, M. Chiodo,
Ethical and sustainable mathematics is localised: why global paradigms fail and culturally-situated practices are essential. Preprint at arXiv:2510.05892. 35 pages.
https://arxiv.org/abs/2510.05892
D. Müller,
Situating "Ethics in Mathematics" as a Philosophy of Mathematics Ethics Education. Ethics and Mathematics Education. Advances in Mathematics Education. Springer, Cham. (2024). 15 pages. Preprint at arXiv:2202.00705.
https://arxiv.org/abs/2202.00705
D. Müller,
The Ethical Turn in Mathematics Education. Preprint at arXiv:2503.23454. 80 pages.
https://arxiv.org/abs/2503.23454
P. Ernest,
The Ethics of Mathematical Practice. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice, p. 1-38. Springer, Cham (2021).
https://www.researchgate.net/publication/367017275_The_Ethics_of_Mathematical_Practice