Category Archives: Ethics

Can mathematics be antiracist? Part II


Brooklyn Bridge, July 4, 2020


All we can do here is think critically about our personal lives, our culture, and the places where we live and work and consider how we might make them more equitable⁠—from making meaningful efforts to hire, admit, or represent the historically underrepresented to establishing norms that ensure they can be heard and respected. (Osita Nwanevu, The New Republic, July 6, 2020)

A few weeks ago I promised to continue the previous post, which described two alternative visions of anti-racist mathematics, which can be described briefly, but in reverse order, as:

(b) “To change mathematics itself” — presumably including the content of mathematics, and not just racist practices and bad attitudes — “so that it actually serves Black and Indigenous communities” and at any rate does not “cause irreparable harm.”

(a) “Business as usual” as far as content is concerned, but with more Black people, along the lines suggested by John Rice in The Atlantic, which I quote again:

(1) acknowledging what constitutes third-degree racism so there is no hiding behind a lack of understanding or fuzzy math, (2) committing to developing and executing diversity plans that meet a carefully considered and externally defined standard of rigor, and (3) delivering outcomes in which the people of color have the same opportunities to advance.

I’ve spent much of the last two weeks puzzling over what option (b) entails.   Here I should acknowledge belatedly that the title of this three-part post was already used, before COVID, before George Floyd was murdered, by Tian An on the AMS inclusion/exclusion blog.  The question in the middle of An’s essay

what kind of “pure” mathematics might be useful for antiracist mathematics?

bears on option (b) but only as interpreted by the word “useful”; it does not address the contents or the forms of reasoning or the underlying conceptual structures that compose what is currently understood as pure mathematics.

This is not the first time I’ve come up short when trying to imagine a thorough metaphysical transformation of algebra, or even the simpler task of replacing the standard introductory sequence in the training of a pure mathematician — abstract algebra, various kinds of analysis, differential geometry, topology — with something different.  James Baldwin warns that the challenge is not to be taken lightly:

Any real change implies the breakup of the world as one has always known it, the loss of all that gave one an identity, the end of safety. And at such a moment, unable to see and not daring to imagine what the future will now bring forth, one clings to what one knew, or dreamed that one possessed.  (James Baldwin, “Faulkner and Desegregation“)

At the height of the Science Wars authors called the very notion of scientific objectivity into question and treated it as a form of domination, a convenient alibi for racist, sexist, and neo-colonialist power relations, or at the very least an unwarranted claim on university resources.    Very few of these authors wrote about mathematics — this is probably why mathematicians’ memories of the Science Wars usually involve French philosophers.  The main text of the time that dealt with mathematics is contained on pp. 48-52 of Sandra Harding’s The Science Question in Feminism.  The arguments are worth reading for their helpful reminder that the meanings of mathematics are not immutable. But they are of little help in imagining how one might “change mathematics itself,” and that’s because Harding was trained as an analytic philosopher, and as such is subject to the professional confusion between the mathematics practiced by mathematicians and the Mathematics that exists only as a topic for speculation by philosophers.  So when she writes “no conceptual system can provide the justificatory grounds for itself,” she is denying the possibility of precisely one of the main kinds of Apologies that MWA dismisses as irrelevant to the concerns of practicing mathematicians (except, of course, during the brief period of the Foundations Crisis which is when analytic philosophy and mathematics last engaged in fruitful exchange).

The logic of that last sentence is rather convoluted, so if you read it quickly you probably missed the point.  In fact, if you believe that mathematics has a special duty to justify itself then you disagree with the main thrust of MWA.  This first epigraph to an influential text by Rochelle Gutiérrez, entitled Living Mathematx, is closer to the mark than the philosopher’s concern with “justificatory grounds”:

We need to be constantly considering the forms of mathematics and what they seek to deal with. As society presents new demands, new technologies, new possibilities, we must ask ourselves whether our current version of mathematics is adequate for dealing with the ignorance that we have.

The allusion to the “current version of mathematics” is a gesture (nearly 10 years old) in the direction of option (b).  But the author of MWA is uncomfortable with the vision of mathematics as a short-order cook to which “society presents… demands,” not least because “society” doesn’t speak with a single voice — chapter 10 of MWA invites readers to draw their own conclusions about the “demands” of funding agencies, for example Anyway, once we have agreed that “society” is (among many other things) racist, or at least is not spontaneously and effectively anti-racist, then we are entitled to treat its spontaneous “demands” with a good deal of caution.

I can tell I’m going to have to return to option (b) and its “demand” for a transformed mathematics, but if I continue to follow this particular stream of consciousness I’ll never get back to the dreary and dispiriting mechanics of the hiring process, which is what we’ll need to understand if we’re going to disregard Hazel B. Carby’s warning, in her chapter in the book Identity Politics in the Women’s Movement, about the “contradictory nature of the Black presence in the academy”:

Do existing power relations remain intact?  Are the politics of difference effective in making visible women of color while rendering invisible the politics of exploitation?

and fall back on option (a).   Anyway, maybe the creation of this Task Force by the AMS, whose stated goals are to

  1. help the mathematical community understand the historical role of the AMS in racial discrimination; and

  2. consider and recommend actions addressing the impact of discrimination and inequities to the AMS Council and Board of Trustees.

already counts as a step toward transforming mathematics as required by option (b).

The AMS will inevitably have its role to play in either option, because the composition of mathematics departments in North America will be mediated for the foreseeable future by MathJobs, the AMS website that provides a unifying structure for the job market.  (In the absence of a social revolution, jobs will continue to be allocated by a market.)  And I was planning to devote most of this post to an analysis of how using MathJobs may or (more likely) may not help mathematics become antiracist.  But once again this post has gone on too long.  So I will have to sign off before getting to the point; and I promise that I will not allow myself to be distracted in Part III from the discussion of option (a) and the hiring process.




Can mathematics be antiracist? (while awaiting Part II)


June 17, 2020, activists rename the Paris metro station “Gallieni” in honor of the combattant-e-s de l’indépendance algérienne Josette and Maurice Audin

Before I attempted to describe the “business as usual” of the hiring process, I wanted to remind readers of the contrast between conflicting visions of the university, as articulated by Stefan Collini:

a partly-protected space in which the search for deeper and wider understanding takes precedence over all more immediate goals; the belief that, in addition to preparing the young for future employment, the aim of developing analytic and creative capacities is a worthwhile social purpose; the conviction that the existence of centres of disinterested enquiry and the transmission of a cultural and intellectual inheritance are self-evident public goods

or the notion, more easily understood by decision-makers, of

market-driven corporations that are governed by the financial imperatives of global capitalism

This reminded me of the equally striking contrast between the essential conservatism of the comment by just different — asking why a social revolution would be necessary to change the curricula and admissions (and presumably hiring) practices while leaving the underlying “market-driven” structure of higher education and “global capitalism” intact — and the frequently encountered suggestion that racism is inherent in the content and practice of contemporary mathematics, not least because it is embedded in the racist as well as “market-driven” structures of the modern university.

I’m not yet ready to address the latter, more radical, elements of a critique of mathematics, because I haven’t yet seen a comprehensible synthesis (there is, on the other hand, quite a lot of radical material about mathematics education, but that’s not really the question at hand).  I was planning instead to get started on the dreary and tiresome aspects of hiring reform (number of available positions, how MathJobs serves as an initial hurdle, that sort of thing) but I was sidetracked by two articles, published in the space of three days in the Chronicle of Higher Education and the Times Higher Education Supplement, and making exactly the same claim:  that the “academic solidarity statement” signed by all the familiar academic left celebrities as well as a host of lesser lights (yes, you’ll find my signature too), in reality expresses nothing more than “the feudalistic mentality of even the most radical leftist scholars.”  The THE article goes on to argue that the suggestions in the solidarity statement

perpetuate the myth of academic meritocracy and the atavistic desire that tenure, the job market and universities as we know them will survive in a post-Covid world.

and reminds the reader that

some commentators have already proposed the re-evaluation of tenure criteria. Others have even challenged tenured professors who are sympathetic to the plight of their contingent colleagues but are reluctant to take action to “renounce their own tenure” and step into the fray as at-will employees themselves.

while the Chronicle article insists that

The overemphasis on research is a direct obstacle to the change universities need. To reshape a university to meet basic standards of equity and justice, we must put teaching ahead of research.

But neither article breaks with the vision of universities as “market-driven corporations.”  What I find inexcusable is that neither author seems even remotely aware that the French trade union movement has for years been resisting successive revisions of labor law that have eliminated protection for workers in France, where until very recently a version of tenure — the contrat de duration indéterminée (CDI) — was considered the norm in all sectors, and not just in academia.  Before the pandemic there was a series of protests and strike actions, met in some cases with very real police violence, in opposition to the loi de programmation pluriannuelle de la recherche (LPPR), Opposition was particularly acute to the proposal to introduce tenure-track positions, with a higher salary scale but with no guarantee of tenure, as an alternative to the current system in which all hiring is in principle permanent — except, of course, for the increasing recourse to ad hoc arrangements with more than a passing resemblance to the system of adjuncts and contingent faculty with which we are all too familiar.

After the comprehensive rejection of Macron’s party in this spring’s municipal elections, I expect resistance to the LPPR to intensify.   There is no guarantee that the resistance will succeed, of course.  In the meantime, it’s comforting to see the name of a mathematician taken as a symbolic alternative to the celebration of French colonialism, as in the image at the beginning of this post; or to see a Columbia colleague trained as a philosopher of mathematics invited to compare racism in its French and American variants.

What would we build instead?

This post was intended to follow up on the panel discussions at last week’s CARTOON conference, and on last week’s post of the materials I prepared for my participation.   Events have taken a surprising turn in the meantime, and for now I prefer to focus on the issues raised by this important initiative.

Here, meanwhile, is what I had written as of a few days ago.

Simon Torracinta has just published one more gloomy forecast on the n+1 website:

Once the taboo of firing tenured faculty is broken, the floodgates will open. Under the cover of the crisis, university administrators will finally undertake the massive restructuring they have dreamed of for years.

The effect on existing staff and faculty will be painful enough, and worse still for those who lose their jobs.   For the cohort of PhDs in or graduating into the current academic job market, this amounts to a generational extinction event. There will not be a ‘poor’ market in 2020–21 and perhaps beyond, even by the anemic standards of the present: there will simply be no market.

and concludes

…the first step forward always requires an act of imagination. What would we build instead?

Torracinta is a Ph.D. candidate at Yale in History of Science and Medicine.  Naturally he is primarily thinking about the humanities.  But last week’s panels at the CARTOON conference made it clear that acts of imagination are required in our field as well.  Here is an example.   Editorial boards of French journals have taken a stand against neoliberal reforms continued by the current French government, in continuation of a policy pursued for more than 10 years:

The unemployment benefits reform is also expected to exacerbate the already great vulnerability of the very large numbers of precarious workers who contribute extensively to the day-to-day operations of universities and laboratories: they account for over 25% of teaching staff and far greater proportions of support staff.… In academia and research, the so-called Pécresse law on the liberties and responsibilities of universities of 2007 (commonly referred to as LRU) was the cornerstone of a twofold, seemingly contradictory shift: the state’s budgetary disengagement, reflecting a neoliberal approach, and the authoritarian strategic management of research by the very same state. The rationale behind the law consists in having the ostentatious (budgetary) autonomy of universities serve as a smokescreen for the deregulation of job statuses, the generalization of competition at all levels and the increased dependence of research on economic and industrial interests, ultimately threatening the actual autonomy of research.

Mathematical journals, and journals in the sciences more generally, are conspicuously absent from the list of participating publications.  And my sources tell me that at least one publisher of French scientific journals has explicitly refused to participate on the grounds that there is no place for opinion in their publications.

A mathematical home for the socioeconomically inappropriate

SWP copy

The author’s childhood home in Philadelphia, recent photo by Google Street View

A month or so before the conference that closed the special semester I had helped to organize at MSRI in 2014, two of my colleagues at a dessert reception challenged me to deny that, overall, life was pretty good — maybe the claim was that it was better than it had ever been.  The question left me flabbergasted.   My colleagues came armed with statistics alleging a dramatic rise in the average family’s standard of living.  I was unprepared:  I didn’t know about the Berkeley study that would be published a few months later, under the title The High Public Cost of Low Wages, reporting that 7% of families of part-time faculty at US colleges were in receipt of food stamps; I didn’t know the statistic, reported by the Federal Reserve Board two years ago and now familiar thanks to Bernie Sanders, that 40% of Americans could not meet a $400 emergency expense without resorting to borrowing or selling something.  All I knew is that I had read about homeowners trapped in underwater mortgages, college graduates with unsustainable student debt who had moved back with their parents, growing pressure on employees at France Télécom that had led to a rash of suicides, long time residents forced out of their neighborhoods by gentrification, and many more manifestations of a general malaise that was not merely widespread but that was represented in multiple instances among my own extended family and friends.

(Gentrification is in a sense the opposite of blockbusting, which is the technical name for what happened to the working class neighborhood pictured in the photo above.)

It dawned on me a few days after our confrontation that my extended family and network of close friends included an excessive proportion of the wrong kind of people, from the standpoint of my professional milieu.  This led me to entertain the counterfactual suspicion that I had not done enough to break off lingering ties to the particular wrong category of people from which I myself had undoubtedly issued.  And since the guiding principle of MWA, which I had recently finished proofreading, was that information from my own biography is only of interest insofar as it sheds light on significant social trends, I decided to devote my remarks at the conference dinner to the question of whether there was still a home for people from “inappropriate socioeconomic backgrounds” in the big tent of the mathematical community.  Here are the remarks, slightly edited.


I will try to be brief, because many of you have already heard me several times this year and you may feel you’ve had your dose. It was not always this way.  The first time I was an invited speaker at a genuinely international conference was in 1988, at the Ann Arbor conference organized by Laurent Clozel and Jim Milne. I took advantage of the opportunity to announce a special evening session to talk about the Science for the People program in Nicaragua with which I was deeply involved at the time.  In the end exactly three people came — so my ratings have definitely improved since then — but it was a select group: Don Blasius, Marie-France Vignéras, and Richard Taylor, whom I met for the first time at the conference. I’m still talking to all three, and in a sense I think it’s accurate to trace the beginning of my collaboration with Richard to that presentation. So that alone made the conference productive; but Steve Zucker and I also started working together in Ann Arbor, and Steve Kudla and I worked out the idea for our Annals paper there, and a lot of the other things I’ve done since then also started there.

So my belated thanks to the organizers of that conference, and to all my collaborators before and since, the ones who are here and the ones who couldn’t make it.  I hope those of you who have spent time at this program have also found your time productive.  If you have — I certainly have — thanks on your behalf and on my behalf are due in the first place to Richard Taylor, who came up with the idea and convinced me to sketch the first proposal and to come here in January 2011 to sell it to the SAC.  As you all know, I have many reasons to thank Richard, probably more than he himself knows,* but this is the most pertinent today.  I also thank my fellow organizers, who not only did all the work, as per agreement, but also decided to forego NSA funding for any part of the semester, after I explained to them who the NSA was — this was before the Snowden revelations — and thus spared all of us a lot of awkward explanations. I thank my students for coming and for persisting in the illusion that they have to be patient when I ask them even the most pointless questions. For making the semester run smoothly I want to thank the MSRI staff, and for this dinner a special thanks to Chris Marshall, who managed to communicate with several layers of administration in France as well as with my old friend Jon Koritz, who selected and supplied the wine. And I also have to thank Christine le Sueur, Kahina Bencheikh, Etienne Gouin-Lamourette, and Célia Chauveau for taking care the bills, as well as the European Research Council and the del Duca Foundation for actually providing the funds. For the stunning poster I have to thank the photographer Bruno Fert, who took the picture; the person I know only as Christophe Cornut’s little brother, who designed the poster; and Ariane Mézard who put it all together.

In all honesty I also need to thank U.S. Senator Ernest McFarland, D-Arizona, and
Warren Atherton, California Republican, for the Serviceman’s Readjustment Act of 1944, better known as the G.I. Bill of Rights, which sent my father to college and thus started the process of upward mobility that has propelled me to this podium. When I was a student it was possible for someone of my rather modest origins to indulge the fantasy of doing something as fanciful as devoting one’s life to mathematical research.  Even then, as I’ve since learned, it was not so common, and my impression is that it has become much more difficult since then, certainly in the US and Britain, and increasingly in continental Europe as well.  So if there is one message to take away from this banquet, it’s that it’s important to do everything possible to guarantee that people from inappropriate socioeconomic backgrounds are always welcome in mathematics.

But enough about me. There are many things more serious than mathematics in this world, and it’s unfortunately the case that we are increasingly finding ourselves forced, just by virtue of being mathematicians, either to face or to pretend to ignore a new type of ethical challenge. I’m thinking in the first place of the use of mathematical techniques for surveillance by organizations like the NSA, because this was explicitly discussed recently on the n-category café website, but there are many other issues: finance mathematics, big data, artificial intelligence, drones, or the increasing dependence on the generosity of UHNWI’s or Ultra High Net-Worth Individuals. It seems there is room for a place, in the virtual sense, where mathematicians can reflect on these ethical challenges, and perhaps come up with ways to respond to them — an association, or committee, or website, or discussion circle. After reading the n-category café discussion I wrote to Tom Leinster, the Edinburgh topologist who has taken the lead in raising the question of the responsibilities of mathematicians in the development of new techniques of surveillance, and to Tom Hales, who has been increasingly outspoken about the activities of the NSA in undermining security of communications, and I asked whether they would be interested in thinking about how to promote the form such an association might take. Both of them immediately wrote back to express their interest. So this discussion will be taking place, and I invite you to send me a message if you would like to be part of it. I’m eager to get started as soon as this conference is over.

Much to my disappointment, only one or two people wrote to express interest in creating the kind of association I described in the last paragraph.  Several mathematicians did commit to writing chapters for a hypothetical book on ethics in mathematics, and I even drafted an introduction, but after several years the chapters hadn’t appeared and when Trump was elected I decided to extract the useful part of the introduction for a contribution to a volume in celebration of Reuben Hersh.  Quite independently, however, initiatives to explore the ethical issues in mathematics have been developing over the past few years.  The most visible manifestations of this new trend may be the Cambridge University Ethics in Mathematics Project, already mentioned on this blog, founded in 2016;  the Ethics in Mathematics Wikipedia page, created in 2017; and the AMS Bertrand Russell Prize, established by Tom Hales and first awarded in 2018.  But I discovered many other activities on a smaller scale this past January when I attended the annual Joint Mathematics Meeting in Denver.  I was there, among other reasons, to participate in the very first Mathematics and Ethics panel hosted by the AMS Committee on the Profession (and I will be posting my notes for the panel at some point); but I had the impression that ethical concerns in the broadest sense — including, crucially, the question of opening up mathematics to people of a wider variety of socioeconomic backgrounds — were expressed in many other JMM sessions, and that mathematicians are giving them much more attention than they were willing to do just five years ago.

Of course, perhaps I just saw what I was hoping to see.  This stand and others like it at the JMM also received quite a lot of attention:


Taken at the Joint Mathematics Meeting, Denver, January 18, 2020


*There was no need for me to be so mysterious.  What I had in mind was a message Richard sent in 1996, after my father died.  The message was simple and straightforward but it came at the right time and it made a real difference.

UPDATE:  When I was a Princeton undergraduate I determined, on the basis of socioeconomic data that was somehow made available, that I was in the 11th percentile of the class of 1973, which means that 89% of my classmates came from more affluent families than mine.  (I hasten to add that, as far as I could tell, I enjoyed all the benefits of a middle-class lifestyle during the period of postwar prosperity, especially after Philadelphia schoolteachers obtained their first union contract a few years before I arrived at Princeton.)  The Board of Trustees decided in the wake of the demonstrations against the Vietnam War — notably the occupation of Nassau Hall, led by mathematics graduate students — that there were too many troublemakers in the lower income brackets, and if I had been admitted a few years later I would have fallen somewhere between the 5th and 8th percentile.  To judge by Louis Menand’s article in New Yorker last year, the socioeconomically inappropriate are now even more unwelcome at Princeton than they were during the boom years:

According to the Harvard economist Raj Chetty, children whose parents are in the top one per cent of the income distribution—roughly 1.6 million households—are seventy-seven times more likely to attend an Ivy League college than children whose parents are in the bottom income quintile (about twenty-five million households). … The most extreme case, according to [journalist Paul] Tough, is Princeton, where seventy-two per cent are from the top quintile and 2.2 per cent are from the bottom.

This is only apparently a sex scandal


From the cover page of the report

The news that several departments at Harvard, including the mathematics department, maintained connections with Jeffrey Epstein for many years after his conviction in 2008 “on charges related to soliciting minors for prostitution” has provided an opportunity for expressions of Schadenfreude on the part of several of my French colleagues.  Last September, after Harvard President Lawrence S. Bacow described Epstein’s actions as “utterly abhorrent . . . repulsive and reprehensible,” Harvard undertook a systematic review of Epstein’s donations to Harvard.  The report on that review can now be consulted online.

Attentive readers will have understood that the true scandal is not that one particular philanthropist turned out to be repulsive and reprehensible.  Dig into the backgrounds of the founders and funders of our most cherished institutions of higher learning and you will see that reprehensible actions are a frequent feature of their biographies.  Nor is it that the sexual exploitation of minors is one of the reddest of red lines, and that few of even our most intrepid colleagues would want to be caught red-handed on its wrong side.  What is really scandalous about the new story is that it is just the latest version of the old story, that the pursuit of the values of our profession, the internal goods in the language MWA borrowed from Alasdair MacIntyre, remains dependent on the continuous supply of external goods from benefactors who, practically without exception, have all crossed red or reddish lines in order to attain the status of Ultra-High Net Worth Individuals that allows them to play the role of benefactors in the first place.

Reddish lines have been shading redder in recent years.  Institutions have been cutting their ties with the intermediaries who brought them the embarrassing associations with Epstein; they have de-Sacklerized at an accelerating rate from one month to the next.  The to which I alluded in an earlier post

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.

— is growing increasingly unacceptable to mathematicians, as it is in the wider culture.  Can our profession every hope to be free of association with scandal?

Update:  you really should read the Vox article about the MIT Media Lab, specifically these two segments:

The argument that anonymous donations from bad people are good, explained

Who would you rather have $5 million: Jeffrey Epstein, or a scientist who wants to use it for research? Presumably the scientist, right?


“Everyone seems to treat it as if the anonymity and secrecy around Epstein’s gift are a measure of some kind of moral failing,” Lessig writes. “I see it as exactly the opposite. … Secrecy is the only saving virtue of accepting money like this.”

This from the former director of the Edmond J. Safra Center for Ethics at Harvard University.  After 5000 years of ethical reflection, is this the best we can do?

The diversity statement controversy, III


Chad Topaz was scheduled to speak at 9:30 this morning at the Joint Mathematics Meeting in Denver, at the AMS Special Session on the Mathematics of Social Justice.    His title was Diversity through a Data Science Lens, and you can read his abstract here.  His talk was cancelled, however, so I won’t be able to tell you whether or not he touched on the topic of the article excerpted above.   Since his name is out of alphabetical order I assume he was the lead author.  The article sheds a not entirely unexpected light on the controversy over diversity hiring statements to which I have already devoted three blog posts.  Here is the summary:

We report on a study of the signatories’ demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them “a mistake,” and claiming that their usage during early stages of faculty hiring “diminishes mathematical achievement.” Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities.

There is a very interesting rhetorical move here.  It can be presumed that many of those who signed Letters B and C take their “professionally secure positions at highly research intensive universities” as license to speak out with authority on matters affecting the discipline.  Although the report by Topaz et al. does not say so explicitly, it seems to imply that it is precisely the “professionally secure position” that disqualifies its holder as an objective observer.   In other words, the article questions the legitimacy of the charismatic hierarchy that is the subject of chapter 2 of MWA:  to the hierarchy’s claim to be based on professional merit, the article replies with a reading that sees it as a self-sustaining system designed to maintain undeserved (disproportionately white male) privilege.

This is not a new perspective; it was commonplace during the period of the science wars, from the late 1980s to the early 1990s, when it became less noticeable in the aftermath of the Sokal affair.  Thirty years ago, however, this point of view was not widely shared among mathematicians.  Please correct me if I’m wrong, but I don’t think there were regular sessions on Mathematics of Social Justice at Joint Mathematical Meetings in the 1980s and 1990s.

The starting point of the diversity statement controversy, I believe, is the undeniable fact that the community of professional mathematicians in the US is demographically extremely skewed relative to the country’s population.  “Underrepresented minorities,” in particular, are really underrepresented.  All the mathematicians I know see this as a real problem.   Some of the positions mentioned at the Mathematics of Social Justice session suggest that mathematics as currently constituted — in its pedagogy, its recruitment, and its charismatic hierarchy— is designed in such a way as (not necessarily intentionally) to exclude the underrepresented populations.  The solution would then be to replace the existing structures of mathematics by something new.

How might we imagine that something new?  Over the past few days in Denver I learned a great deal about a variety of inspiring initiatives at universities and schools around the country.  Some of them can be found at this list on the AMS inclusion/exclusion blog (which certainly did not exist thirty years ago).   I will be studying them over the coming weeks — I encourage readers to do the same — and it’s likely I’ll be writing about some of them.

I am pretty sure, though, that none of the new initiatives has anything to do with diversity statements.  I strongly believe that in the controversy that (as Topaz et al indicates) has not yet died down, the diversity statement itself is serving as a proxy for some more substantial objective.  This is confirmed by a message I received from one of the signatories of Letter A:

At this point the fight seems to be about whether understanding and working with students’ different backgrounds should be treated as part of the professorial job description, with Thompson representing what is probably the majority default of something like “colorblind racism”. So I think there’s value in saying loudly that the colorblind position is no longer an acceptable starting point for a worthwhile contribution to diversity/equity/justice, with the emphasis being on using diversity frameworks as a stepping stone to what we really want, which is a justice-based framework.

Where I come from, “colorblind racism” counts as fighting words.  The most obvious defect of Letter A is its inclusion of the expression “reverse racism” in quotes, when it appeared nowhere in Abigail Thompson’s letter.  For all I know, many people who signed Letter A sincerely believed that Thompson had accused the supporters of diversity statements of “reverse racism.”  But leaving misrepresentation aside, I have tried to argue that diversity frameworks are a particularly slippery stepping stone, since they were explicitly designed as an alternative to a “justice-based framework.”  The author of this comment believed as well that “[i]f you belong to the ‘fundamentally not fair’ camp, then you’re stuck with the unfortunate ‘diversity’ formulation, but at least from there the door can be wedged open.”  As far as I’m concerned this is magical thinking, as is the claim in the same comment that support for diversity statements is “an affirmative sign of where the institutional leadership stands” — as if the very institution targeted by the Bakke decision would make any effort to use the decision’s framework to undermine the decision.

Here, on the other hand, is a comment from a colleague who signed Letter B:

I thought the letters in support of Abigail were not about the diversity per se, but rather about the bullying that she became the subject of. Typical exclusion in the name of inclusion …
I objected to the use of the word “bullying.”
Has she been attacked by powerful people, or only by noisy but mainly powerless people?  I would reserve the term “bullying” for the former.
And my colleague replied:
Not sure who is powerful anymore, your allegedly powerless people can easily destroy people’s lives and, certainly, careers.
It seems to me that the threat to Abigail Thompson’s career — presumably from Chad Topaz’s initial reaction to her article — was no less exaggerated than her comparison of diversity statements to loyalty oaths, but it also seems to me likely that most of the people who signed Letters B and C were responding to this imagined threat — I didn’t sign any of the letters but I am no more inclined than they to trust “institutional leadership”  — and not to defend their privileged status of overrepresentation.  This is one reason the Topaz et al. article is so interesting; because it aims to undermine the presumption that privileged positions are awarded solely (better to say almost solely) on the basis of merit.
I would like to hear from the authors of that article how they imagine mathematics would look if the charismatic hierarchy were undermined.  But that’s a complicated issue, and I would like to end on an observation that Topaz et al. may have missed.  The article calculates that women made up 27.8% of the signatories of Letter C — making them underrepresented by some measure and within the representative range by others.  I went through the list and discovered that, of the 45 women who signed, exactly 4 were from the US (though a few may have acquired US citizenship).  I can attest that students in France are not taught to look to the US for good ideas about managing race relations, and I suspect something similar is true in the countries where most of these women grew up.

Reuben Hersh, 1927-2020 (with text)

Here is the introduction to my article Do Mathematicians Have Responsibilities, published in Humanizing mathematics and its philosophy.Essays celebrating the 90th birthday of Reuben Hersh.Edited by Bharath Sriraman. Birkhäuser/Springer, Cham (2017) 115-123.

I have been an admirer of Reuben Hersh ever since I received a copy of The Mathematical Experience, then brand new, as a birthday present.  At that stage, of course, I was admiring the tandem Reuben formed then, and on other occasions, with his co-author Philip J. Davis.  It was only almost 20 years later, after I started reading What is Mathematics, Really? that I could focus my admiration on Reuben — and not only on the mathematician, the author, the thinker about mathematics, but on the person Reuben Hersh — the unmistakable and unforgettable voice that accompanies the reader from the beginning to the end of the book.  So unforgettable was the voice, in fact, that when Reuben, wrote to me out of the blue three years ago to ask me what I thought about a certain French philosopher, I so clearly heard the voice of the narrator of What is Mathematics, Really? (and no doubt of many of the passages of his books with Davis) that I could honestly write back that I felt like I had known him for decades, though we have never met and until that time we had never exchanged a single word.

The voice in question is the voice of an author who is struggling to put words on an intense and intensely felt experience, who has intimate knowledge of how it feels to be a mathematician and also a knowledge no less intimate of the inadequacy of the language of our philosophical tradition to do justice to that experience, so that all attempts to do so inevitably end in failure; but this knowledge is compensated by the conviction that the stakes are so important that we can’t choose not to try.   What makes Reuben’s authorial voice compelling is that it sounds just as we expect the voice of a person in the middle of that struggle must sound.[1]   It’s the strength of this conviction that comes across in Reuben’s writing, so that reading his books and essays is remembered (by me, at least) as a conversation, a very lively conversation, filled with the passionate sense that we are talking about something that matters.  Also filled with disagreements — because I don’t always agree with everything I read in Reuben’s books and essays; beyond questions of detail the difference might come down to my sense that Reuben is trying to get to the bottom of the mathematical experience, whereas I apprehend the experience as bottomless; or I might say that it’s the effort to get to its bottom that is at the bottom of the experience.  But the differences are of little moment; what stays with me after reading a few pages of Reuben’s writing is the wholeness of the human being reflected in his words, a human being who cares so deeply about his mathematical calling that he is ready to add his own heroic failure to the long list of admirable failures by the most eminent philosophers of the western tradition to account for mathematics; and without these inevitable failures we would not begin to understand why it does matter to us.

[1] As I wrote that sentence I remembered that I have still not met Reuben, nor have I ever spoken to him; but I checked one of the videos online in which he appears and, sure enough, his literal voice is very much as I expected.

Will Cédric Villani’s reputation survive his association with Macron?

Cédric Villani’s political orientation has come under increasing scrutiny since his election as deputy on the “République En Marche” (LREM) list created by French President Emmanuel Macron, whose own popularity has fallen precipitously over the first two years of his mandate.  Villani’s announcement that he would run, and occasionally dance, for the LREM slot in next year’s race to replace Paris Mayor Anne Hidalgo — Villani was president of her campaign committee in 2014 — roughly coincided with the development of the Yellow Vest movement in protest against Macron’s policies, which are perceived (quite rightly) as undemocratic and upwardly redistributive.  Macron’s approval rating has dropped to 27%, while the Yellow Vests were enjoying up to  60-75% approval, in spite of repeated attempts by the press to depict them as a Trojan Horse for the far right. Such attempts have been considerably more successful abroad than in France. No doubt this is because, for at least 25 years, every time a popular movement arose in France in opposition to the neoliberal trickle-down consensus that united the two main governing parties — the socialists (apparently fatally damaged by former President Hollande’s undistinguished record) and the right, currently called “Les républicains” — the mainstream press warned that such protests could only benefit the far right; the warning lost its force as living standards declined for much of the population, whichever party was in power, and the decline continues under Macron’s post-partisan leadership.

Each of the two major governing parties has been hit repeatedly by scandal. Macron was supposed to put an end to that, but the “Jupiterian President” quickly got caught up in a particularly sordid and growing scandal involving the unconventional and largely illegal employment of a security staffer named Alexandre Benalla (this is too complicated to explain here, but you can find an account here, not including the most recent developments).

Inevitably, Macron’s unpopularity has rubbed off on Villani.  His Tweets now routinely provoke mocking suggestions that he should stick to mathematics:  he is taken to task for failing to address the shocking consequences of police repression of Yellow Vest demonstrations — 18 eyes lost to flashballs as of this writing, 4 hands lost to dispersal grenades, and hundreds of other injuries, many of them disfiguring; for his silence on the Benalla affair; and for many of his votes in the National Assembly (his vote on the Loi Asile-immigration is the focus of an open letter by the mathematician Charles Boubel  published in the CNRS magazine Image des Mathématiques).

It didn’t have to be this way. Maurice Chiodo and Piers Bursill-Hall, in the first of an ongoing series of Ethics in Mathematics Discussion Papers, identify “four levels of ethical engagement,” in increasing order. Villani examplifies the third level, “Taking a seat at the table of power.” “[B]eing at that table,” they write, “gives a participating mathematician the potential to influence the ethical consequences of what is done with the maths.” In his insightful report on Villani in The New Yorker, Thomas Lin quotes Villani’s collaborator and former student Clément Mouhot:

Many mathematicians are glad that Villani is willing to participate in public life, Mouhot said, so that they don’t have to.

Chiodo and Bursill-Hall note with approval that a committee under Villani’s direction recently prepared a thorough and remarkably persuasive report for the French government on how to prepare France for the arrival of AI in mainstream society.  The particular strength of this report is that its authors have a deep grasp of the technology and the mathematics behind AI, and that gives them a particular political authority.
Chiodo and Lara Gordon elaborate on this in a later Discussion Paper, arguing that Villani’s report compares favorably, in both its ambition and its attention to ethical issues, with a British report on the topic.

In view of Villani’s remarkable success in persuading Macron’s administration to admit France’s responsibility in the torture and murder of the mathematician Maurice Audin — perhaps his most notable achievement to date — one would also have thought that Villani would be sensitive to the question of police repression.Villani Audin - 1

Villani at the Père Lachaise cemetery June 11, 2019, at the ceremony
in honor of Maurice and Josette Audin

As of this writing it’s not clear how far Macron’s administration will follow the suggestions of Villani’s report. One recommendation —

Doubling salaries in the early stages of their careers at the very least is a vital starting point, otherwise the pool of young graduates interested in higher education and academic research will definitively dry up. [Villani et al, p. 11]

was mentioned prominently in Le Monde‘s coverage. Not surprisingly, it was welcomed by French researchers, most of whom have seen the graph circulated in 2008 that predicts a straight-line evolution of starting research salaries to the French minimum wage, with convergence scheduled for 2025; as far as I know the evolution continues on track.  The salary recommendation was intended “to make public research careers more attractive” in the face of competition from the GAFAM tech giants. This particular suggestion disappeared without a trace, and one naturally suspects that Villani, in taking on the mission assigned to him, missed the point of neoliberalism, which is precisely its ideological commitment to market solutions to practically all problems.  Encouraging public academic research, on this reading, is perfectly inconsistent with Macron’s signature policies — lowering taxes on the rich and on corporations while raising them on the less fortunate; deep cuts in public services in health and education; elimination of favorable conditions for workers in the national railroad and plans for its future privatization; a “reform” of university admissions that has left hundreds of thousands of high school graduates with no options whatsoever; and a plan to multiply fees by 10 for students from outside the EU, including doctoral students. Attacks on the national pension system and privatization of the Paris airports are on this year’s agenda.   (See Didier Fassin’s report in the London Review of Books for a thorough analysis of Macron’s “authoritarian neoliberalism.”)
But perhaps it did have to be this way, after all.  Villani and Macron are both alumni of the French-American Foundation France, where they overlapped as “Young Leaders” in 2012. The existence of the think tank seems not to be well-known, but former “Young Leaders” include some of the French welfare state’s most prominent gravediggers, and an astonishing proportion of presidential contenders as well as leading cabinet members and political figures in both countries (included are Alain Juppé, François Hollande, both Bill and Hilary Clinton, General Wesley Clark, LA mayor Eric Garcetti, current French Prime Minister Edouard Philippe, and two directors of Le Monde, among many, many others).   Not all alumni are neoliberals — Didier Fassin’s brother Eric, a prominent leftist intellectual, is on the list, as is filmmaker Charles Ferguson — but you could do worse than to use the list to map the boundaries of mainstream political opinion.

Macron’s party is scheduled to choose their candidate this coming week for next year’s Paris mayoral election.   The French president reportedly prefers Benjamin Griveaux, but Libération reported on July 5 that it’s increasingly likely Villani will be chosen to face incumbent mayor Anne Hidalgo.  Villani was president of Hidalgo’s support committee in 2014, but he now claims to be dissatisfied with her record.  There are sensible reasons to be dissatisfied with Hidalgo, but most of the complaints I read seem to have to do with cars and bicycles.  Villani himself explained that

Quand on entre aujourd’hui dans Paris, on arrive à des portes qui sont souvent taguées, sales, dans une ambiance d’embouteillage phénoménale et ce n’est pas possible.

All true, but not more so than 20 years ago.  Many of my mathematical colleagues are convinced that Villani’s true goal is the French presidency.  How many more compromises will this “Young Leader” have to accept before he gets there?

UPDATE:  Macron’s party’s chose Benjamin Griveaux, not Villani, to run for mayor of Paris next year.  Villani is considering his next steps.  Meanwhile, yet another member of Macron’s government, François de Rugy (Minister of Ecological Transition), is caught up in a huge scandal, involving (among other things) lobsters.