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What follows are the uncorrected notes for a presentation by videolink at the first workshop on Ethics in Mathematics, held in Cambridge April 20-21, 2018.

It’s a humbling experience for me to be asked to speak at this meeting, alongside some authentically legendary figures. Maurice Chiodo and Piers Bursill-Hall have assembled a stellar lineup in a remarkably short time. This is certainly a tribute to their energy and initiative, but the fact that so many speakers have agreed to participate is also a sign that Maurice and Piers have identified a need whose urgency is increasingly recognized across the profession. I do hope this week’s meeting will be remembered as the start of a genuine international movement to place ethics at the center of our work as mathematicians.

It’s a special honor to be invited to participate in a conference on mathematics and ethics that is taking place in Cambridge, home of G. H. Hardy, a mathematician whose commitment to pacifism and social justice is well-known even beyond the profession. Since mathematicians are constantly being asked why our work is useful, it’s appropriate to recall that Hardy once wrote that

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.

Hardy was thinking particularly of military applications of science, as well as of the mathematical economics of his time. Had he lived a few years longer he would have witnessed the growth of mathematical game theory, whose destructive consequences in both domains have been developed assiduously by the RAND Corporation, which figures prominently in the biography of John Nash, among other mathematical heroes.

I consider Hardy a precursor of current proposals for mathematicians working on various applications to adopt “Hippocratic Oaths,” the ethics of abstaining from doing harm. In an article published last year entitled Do Mathematicians Have Responsibilities?, I mention some of the more recent applications of mathematics that are “useful” in Hardy’s sense, but my focus is different.

While pure mathematicians in particular may have wondered whether much of their work would ever be socially useful, it was generally believed that at least it caused no harm. Events of recent years have called that belief into question. The sophisticated and often opaque derivatives developed by financial mathematics magnified the effects of a downturn in sectors of the US housing market into a global financial crisis whose consequences are still with us. Edward Snowden’s revelations in 2013 served as a reminder that contemporary cryptographic techniques based on number theory can also be used to facilitate general surveillance by governments. The rapid growth of Big Data has made it possible for commercial as well as public actors to track individual behavior with increasing precision, with grave implications for privacy. In each of these applications of mathematics one finds the same three features: an approach to human activity that is purely instrumental; a disdain for democratic decision-making; and the empowerment of experts on the basis of their mathematical training. And in each case, a few mathematical scientists have pointed out that the power of mathematical technology imposes social responsibility on those who develop it, beyond putting trust in experts.

In this brief presentation I want to stress the second and third features, because they make it clear that the call to “do no harm,” important though it is, does not fully discharge our social responsibilities as mathematicians. The fact is that our very expertise, as academics and researchers, contributes to the reproduction of the social order that makes the abuses not only possible but often inevitable. We perceive the universities and research institutes in which we work as protected spaces and spaces to be protected, and this is true as far as it goes. But the primary function of the university is to reproduce existing relations of power and influence. In this sense, Hardy’s refuge in pure mathematics is itself part of the problem. Indeed, A Mathematician’s Apology fairly reeks of the elitism that, even in its current attenuated form, is an essential aspect of the image, or the brand, that distinguishes universities like Cambridge and Oxford and Harvard and Columbia and endows their professors with the expert status that so often serves to undermine the democratic process.

Let me add right away that I am fully aware of the dangers of this kind of talk in the face of climate denial and right-wing populism more generally. Nevertheless, I remain convinced that the primary role of the expert in public policy is to be mobilized in support of dominant interests, in the spirit of Margaret Thatcher’s There is no alternative. The article I just quoted has a good illustration of this in connection with the current massive growth of artificial intelligence, and the feverish promotion of the Internet of Things as a technological inevitability and a promising investment opportunity. The ethical implications of these developments seem to have been entrusted, in particular by the EU, to the AI industry itself:

In connection with [the risks of AI], it was announced that Facebook, IBM, Amazon, Google, and Microsoft had just formed the “Partnership on AI” for the purpose of “conducting research and promoting best practices.”

Since then Apple has joined (the big five + IBM) and there are now representatives of civil society (ACLU, EFF, and Center for Democracy and Technology, among others). Of course the relative weight of the corporate and civil partners in defining “best practices” remains to be seen. My point, however, is that the vision of democratic decision-making still places the expert at the center.

By the way, I have not come to you today with an alternative and more democratic model. The problem is a profound democratic deficit in the society at large. That’s not a problem for this gathering to solve; but in my opinion it is inseparable from any serious reflection on the ethical obligations of mathematicians or any of our fellows in the elite sphere we inhabit.

My aim was rather to make a few remarks about research funding, and I will quote from my article in the Times Higher Education Supplement to indicate how difficult it is to avoid tainted sources.

[Tom Leinster’s] question hasn’t gone away: should we cooperate with GCHQ? The problem is that research funds have to come from somewhere; the survival of number theory depends on it. One veteran colleague likens mathematical research to a kidney; no matter where it gets its funding, the output is always pure and sweet, and any impurities are buried in the paperwork. Our cultural institutions have long since grown accustomed to this excretory function, and that includes our great universities. Henry VIII was a morally ambiguous character, to say the least, and a pioneer in eavesdropping as well as cryptography; but neither Hardy nor his friend Bertrand Russell refused his fellowship at Trinity on that account. It would be nice if the State could provide its own kidneys and impose an impermeable barrier between the budgets for research that is socially progressive, or at least innocuous, and the military and surveillance functions about which the less we know, the better. But States don’t work that way, and for the most part they never have. The only alternative to public funding, from whatever the source, is private philanthropy. America’s great private universities are monuments to the past and present generosity of some of our wealthiest citizens. That is not, however, what is most appealing about them. I find it demeaning to have to express gratitude for my research funding to practices of which I otherwise heartily disapprove — like hedge fund management, for example, or data mining — but that have given a few people the status of Ultra-High Net Worth Individuals … and thus in the position of being able to function publicly as philanthropists. Or to despots like the Emir of Kuwait, whose Foundation used to sponsor a generous lecture series at Cambridge. It seems that anywhere you turn, you’re going to be someone’s kidney. But feeling demeaned is beside the point. As …Cathy O’Neil… put it in January 2014, “We lose something when we consistently take money from rich people, which has nothing to with any specific rich person who might have great ideas and great intentions.…” One of the things we lose: control of how decisions are made: “…the entire system depends on the generosity of someone who could change his mind at any moment.” The more basic problem is that the very existence of UHNWI entails the concentration of power beyond the control of democratic oversight. Among billionaire patrons, Jim Simons stands out for his commitment to the values of working mathematicians — which is natural, given that he was a distinguished geometer before his management of the wildly successful hedge fund Renaissance Technologies made him an UHNWI. But the same high-frequency trading algorithms that fueled Simons’s philanthropy gave us Breitbart, courtesy of Robert Mercer, Simons’s former colleague at Renaissance. Mercer was much in the news earlier this year after it was revealed that, through his connection to Cambridge Analytica, he used psychologically targeted advertising on social media to intervene in the Brexit and Trump elections, possibly tipping the balance in both cases. Mercer has come to personify the sinister side of the UHNWI phenomenon, but even outspoken liberal billionaires like Facebook’s Mark Zuckerberg and Google’s Sergei Brin, who have been subsidizing pure mathematics indirectly through their cosponsorship of the extravagant Breakthrough Prizes, have built their fortunes on mathematical techniques that are no less threatening to privacy than GCHQ surveillance.

I could continue for quite a long time expressing my regret that the need to sustain our research places us in the uncomfortable position of dependence on ethically dubious sources of funding. In the interest of full disclosure, and to highlight the paradoxes of my own position, I ought to mention that this afternoon I will be heading to a conference in the Bavarian Alps, sponsored by the Simons Foundation! The first part of today’s presentation, however, was meant as a reminder that as researchers and academics our very salaries are being paid by institutions whose primary function is the preservation of the status quo. Insofar as the possibility of the most visible aberrations (Cambridge Analytica, NSA undermining of encryption standards, credit default swaps, drone guidance systems and so on) are built into the normal functioning of the status quo, and are justified by an ideology of expertise that is maintained by our universities and research institutes, our very existence as experts guarantees that our profession provides no refuge of ethical purity.

Interjection: How, by the way, did Trinity get to be so rich? I don’t know the answer; instead, I offer this bit of information as an ironic metaphor for our defense of ethics from our perches within the power structure:

At what is today Columbia University, there was a medal issued at graduation every year by the Manumission Society — many of whose members were slaveowners — for the best essay each year that opposed the slave trade (from a report by Eric Foner on Columbia’s website, as quoted in The Trinity Tripod of Trinity College, Connecticut, dated February 11, 2014)

(Of course, Columbia was hardly alone; Harvard, Penn, Dartmouth, William and Mary, and other leading universities of the time had interests in the slave trade.)

As I wrote in the THES piece:

[T]he immense privilege of devoting our lives to the research projects we have chosen freely imposes on us the obligation to speak out when our work is used for destructive ends, or when the sources of our funding do not share our values.

By “speaking out” I don’t mean simply reacting to abuses. I mean actively anticipating possible uses of our work, including our teaching of students, for purposes of which we do not approve. Here I would add that we are no less obligated to acknowledge the role of our institutions, and of our expert status within and through these institutions, in preserving existing power relations that are incompatible with democratic ideals.

The privilege of devoting our lives to our freely chosen profession makes us beneficiaries in the sense described in a recent book by my Columbia colleague Bruce Robbins. A great many people need to perform less rewarding work, or are rewarded less well for what they do, in order to provide us the means to pursue our professional goals.

Nevertheless, I want to conclude by stressing the importance of defending these benefits. I’m sure that each of you has been asked at one time or another some version of “how is what you do useful?” And if you are a pure mathematician you might have resorted not to Hardy’s definition of “useful” but rather to Hardy’s argument that mathematics is an art form, and therefore deserves to be pursued for its own sake. I suspect such an answer provides little defense against accusations of self-indulgence, irresponsibility, and a lack of due regard for the taxpayer’s money. Faced with such accusations — usually by individuals whose own position within the power structure leaves them open to challenge — I like to reverse the terms of the question: if mathematics is not to be pursued for its own sake, then for the sake of what? For profits, or Facebook “likes,” or to give Britain a leg up in the international marketplace? This should immediately pose the question of democracy, which in the present context includes the right to adhere to values that are not determined by the market and its ideologues and functionaries. All work should ideally be for its own sake. But this is an idea I am struggling to articulate, and I hope to have made some progress if and when we meet again.