Ethics in Mathematics–why is it so hard?

By Dr. Maurice Chiodo, Fellow and Teaching Officer at King’s College, Cambridge. Lead investigator of the Cambridge University Ethics in Mathematics Project. @mauricechiodo

Mathematics is never done in complete isolation, and mathematicians need to consider the way in which their work impacts the lives of others, including those outside of their professional community. Anyone doing mathematical work, be they in academia, industry, government, or elsewhere, has an obligation to consider the impact of such work on the world around them. With frequent use in big data, finance, cryptography, and AI, mathematical tools and techniques are now being used to have a substantially large-scale influence on people's lives.

I am deeply concerned about the potential harm that might come from the use of mathematics in society by the mathematically-trained, and that some important ethical issues which arise are not being adequately addressed. In the past few years, I've written numerous articles on Ethics in Mathematics (EiM), including two in the London Mathematical Society Newsletter on The Importance of Ethics in Mathematics, and Teaching Ethics in Mathematics. And I am not alone in doing so. The chief executive of the MAA, Michael Pearson, has written a three-part series of MAA blog posts on The Critical Study of Ethics in Mathematics, and Carrie Eaton has written one on Ethics, Big Data, and the Mathematics Community. Catherine Buell and Victor Piercey co-authored an article in MAA's FOCUS Magazine on Ethics in Mathematics, discussing material from the Ethics in Mathematics Conference I organised and at which they were both speakers.

So obvious and important are the potential ethical issues that arise in mathematical work that, since 2016, I've taken it upon myself to volunteer a lecture series in the mathematics faculty at Cambridge, titled Ethics for the Working Mathematician. This has since led to the formation of the Cambridge University Ethics in Mathematics Project, which has developed teaching resources and published papers on EiM. However, even with all the articles listed above, and all the content now in existence, I am still concerned that there are some fundamental challenges to raising the issue of ethics with mathematicians.

Firstly, those undertaking mathematical work might brush aside social and ethical concerns by saying “It's not my problem”, or “That's not mathematics”. In my lectures, I've given Bonnie Shulman's oil pipe problem from her paper Is There Enough Poison Gas to Kill the City?: The Teaching of Ethics in Mathematics Classes, where I've asked students to come to the front and compute the “optimal” path for an oil pipe in the ocean. Setting aside instances where the students have turned it into a race (they claimed “Mathematics is always a competition”), I've brought up issues in discussion about other factors to consider and ask about; perhaps a coral reef in the ocean, or a protected habitat or school on the shoreline. Their response: “Then this is not a mathematics question; we just do mathematics”.

In addition, the mathematically-trained may mistakenly expect other people to take responsibility for considering all ethical implications, thus avoiding their own personal ethical responsibilities. The number of times I have heard students say “It's up to management to think about any ethical concerns” is staggering. In a discussion about GDPR, and its relative strengths/weaknesses, some students said “Surely there were some mathematicians involved in the drafting process of this law”; the students were genuinely surprised to hear that there were none.

And finally, the abstract nature of mathematical work may mask or obscure how it is being used and the impact it may have. Given that mathematical training often removes context from problems, it is almost to be expected that mathematicians see their work as “detached” from reality. We train mathematicians to be passive, with questions like “Let G be an abelian group ....” or “Consider the following function h ...”; it would be rare for a student to respond with “Why are we considering this group?” or “Where does this function come from?” That unquestioning detachment persists outside the classroom, lecture theatre, and exam hall, and into industry. So when mathematicians are asked to create techniques to harvest, decrypt and analyse trillions of emails, or to work on large data sets to create tools that send targeted political adverts, no-one asks why.

Discussions about the impact of mathematical work and what to do in various scenarios, such as who should a self-driving car hit when faced with an unavoidable collision scenario, are important, and complicated. But they overlook one simple observation: that so many mathematicians simply see ethical considerations as “Not my problem”; a student of mine, Phoebe Young, so aptly conveyed this in a comic series on EiM. At best they aren't attuned to identifying them; at worst they are outright dismissive. Don't believe me? Then bring this up the next time you sit down for coffee with mathematics friends and colleagues, next time you participate in a mathematics conference, or next time you discuss careers in mathematics. It may be obvious to you, but I doubt it is obvious to those around you.