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While the ethical implications of technological advancements - especially with a view to Artificial Intelligence - has been the subject of much debate among computer scientists, lawyers and policy makers over the past few years, other academic disciplines intimately concerned in the development of digital technologies have yet to participate fully in these dicussions. The Faculty of Mathematics at Cambridge has since 2018 held a number of events to explore how ethics can be embedded in the mathematics curriculum to address this shortfall.


The case for embedding the study of ethics in mathematics

Dr Maurice Chiodo and Dr Piers Bursill-Hall

That the practice of mathematics can invoke ethical issues is probably obvious to everyone – but not to most mathematicians. It is also obvious that high-powered and sophisticated mathematics is ubiquitous in modern technology, finance, the nation’s infrastructure and defence, and social media. And pretty much anywhere else in the 21st century. Much of mathematics can be used for good – but simply put: it can also be a tool for harm. We think it is clear that mathematical research and practice may take its practitioners to deep and professionally specific ethical issues.

So far as we know, there is no university in the world that currently offers a wide-ranging specifically mathematical ethical training for mathematicians. For lawyers, medics, biologists, computer scientists, physicist, and others, the question of subject specific ethics is not news – it is part of their training, part of their professional practice and regulation, and part of their understanding of their work as professionals. It is striking that this is not the case for mathematicians.

There have been a number of studies and smaller or larger projects that have looked at specific ethical questions in mathematics; it is well known that statistical practice and the public dissemination of statistics is dense with ethical questions, and the use of algorithms in all sorts of decision making systems has, in the last few years, elicited some public and professional investigation. The role of mathematicians developing financial instruments that were little understood by the rest of the financial industry has come to light because of the financial crisis of the 2000s. Moreover, the use of extremely sophisticated mathematical tools by the state security institutions around the world has raised deep questions about cyber- security and privacy – and it is mathematicians who are developing the tools that enable these bodies to place the entire population under extraordinary and detailed surveillance.

But such studies have been limited, and focussed on the very particular technical details in each of these domains. Many of these studies have been both fascinating and deeply worrying. However, all of this has focussed on narrow issues – and they have succeeded exactly because of this focus. It is now time for a broader discussion to start, a discussion about all mathematicians in society, about the professional social responsibility and the ethics of which mathematicians are often quite extraordinarily ignorant.

Whereas such training is normal in other disciplines, for mathematicians it simply doesn't exist, anywhere. Until now. In Cambridge we have recently set up and run an annual seminar series titled Ethics for the working mathematician, where we developed entirely new content including case studies, and analysis of ways that ethics enters into mathematics. A reasonably large minority of undergraduates have attended these seminars, and they are – to some extent – working: there are now some undergraduate mathematicians who have taken on board the idea that regardless of what mathematical work mathematicians end up doing as a professional, they will most likely come up against ethical issues.

The 2018 workshop is – we think – the first such meeting aimed at bringing together some of the people (that we in Cambridge happen to know of) who have worked on issues of ethics in mathematics, who have tried to start a teaching course on ethics for mathematicians in their universities, or who have published something about ethics in mathematics. The recurring problem we have observed is that almost all such people are "singletons" working alone, sometimes with mere disinterest from their institutions, sometimes meeting active hostility from colleagues. We want to bring these people together to make a community - and the tiny kernel of a new discipline: the study of Ethics in Mathematics. Not just the ethics of algorithms, or mathematicians working for the intelligence services, but all mathematics and all mathematicians. We want to broaden the discussion to grasp the role of mathematics that has grown in the last 20-30 years, where almost everything we have or we do has a vast amount of highly technical, highly specialised mathematics behind it, and which is utterly incomprehensible to almost everyone who is not a trained mathematical professional. Mathematicians have become one of the most powerful communities in the world, yet they do not know it, and do not know how to take responsibility for their actions; nobody ever tells them.

Nobody can do this from outside the profession. Only mathematicians can talk to mathematicians about ethics: the discourse of philosophers (which is infinitely more sophisticated than anything we can hope to achieve) will go over the heads of most mathematicians, and simply will not address the specifically mathematical, technical ethics we face. The ethical questions of computer scientists or economists, physicists or geneticists, are pressing and important – but they are not those of the professional mathematician and they are not going to teach her how to deal with the issues that she may face in the working environment of mathematicians. So only mathematicians can do this, and we need to begin the process of forming a community: supporting each other, sharing knowledge, experiences, best practice, and a vision of what we can teach our students.

The workshop we are organising is a small first step in doing something really innovative and creating a new (and deeply multidisciplinary) project. It will be the first such meeting, and it will necessarily be a small pilot project, bringing together a small group of mathematicians we know to be interested in ethics in mathematics and who have tried, one way or another, to research or teach this. We will bring together some experts in fields outside mathematics to talk to the mathematicians about the particular properties of the nature of the mathematical community and mathematicians, and the reasons for the failure of mathematicians to contribute to policy and ethical considerations outside their own very narrow domains. This group of mathematicians already knows about the issues of ethics in mathematics, but they have no working community and little experience with those outside mathematics who may be able to inform or deepen their own thinking about the ethics of mathematical research and practice.

Ethics for the working mathematician, lecture 4: Fairness and impartiality in algorithms and AI
by Dr Maurice Chiodo (2018)
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.

Workshop Programmes and Speaker Lists, EiM Project: Workshop 1, Workshop 2

Workshop 1 Recordings, EiM Project

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