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.

Can mathematics be antiracist? Part I


If a disease like Covid-19 could push higher education to the brink of collapse, perhaps something is rotten in the system. This is what we should be addressing.        (Cinzia Arruzza, Chronicle of Higher Education)

Mathematics is deeply democratic.  You can be Black or White or any other color; male, female, or gender non-conforming; European or African or an extraterrestrial giant; ten years old or dead more than 40000 years.  As long as you know the rules, you are welcome to play; and history has shown that the rules are always flexible.

Mathematics is deeply antidemocratic.  Mathematics is not a “marketplace of ideas”; arguments are settled with QED and then they will never again be unsettled.  The rules have been established once and for all, and there is no room for dissenting opinions.

This post will not attempt to reconcile these two apparently incompatible visions of mathematics, both of which are at least implicitly invoked whenever the reasons for the field’s visible demographic imbalance are discussed.  Instead, I will take up the challenge proposed on the AMS inclusion/exclusion blog under the title #ShutDownMath:

Our goal needs to be to create an environment in which any person who WANTS to be a mathematician, can.



On second thought, I’m going to pass on this particular challenge, which, if taken literally, would necessitate a “full-blown social revolution,” to quote just different‘s comment on this blog — and the comment seems to suggest, reasonably enough, that “social revolution” talk can serve as an excuse for postponing action indefinitely.  But I do hope that whoever wrote that sentence will agree that an environment in which any person who WANTS to be gainfully employed as a mathematician — or gainfully employed at all, for that matter — has never existed; that according to Friedrich von Hayek such an environment would be impossible; and that therefore creating such an environment would require not only a thorough rejection of neoliberal thinking but more importantly a thorough reorganization of work and of the social distribution of wealth  — a social revolution, in other words.

So I will interpret the word “goal” in that sentence as “aspiration” and stick to challenges that can be accomplished, to continue quoting just different, provided “higher ed institutions radically change their curricula and admissions practices.”  This “change” may or may not be radical enough to qualify as the “change” in the sentence in #ShutDownMath that immediately follows the last one:

To change mathematics itself so that it actually serves Black and Indigenous communities.

Let me suggest as a friendly amendment, “to change North American mathematics itself…”  Leaving aside whether the rest of the world is really responsible for the aftermath of what have rightly been described as our Republic’s twin original sins, it’s wise to avoid hinting that even the wokest mathematicians in this highly militarized country are plotting to change the practice elsewhere.  Halfway through the second week of the protests following George Floyd’s murder, my French colleagues were grumbling yet again about the AMS’s soft imperialism through what they perceived as extortionate prices for MathSciNet subscriptions.   And I’m sure that they and most of my colleagues around the world would find grating the insistence of #ShutDownMath on individual rather than collective action.  (But because I don’t want to let my French colleagues totally off the hook, I advise everyone who reads French to check out this extremely timely article about French racism by filmmaker Raoul Peck (I Am Not Your NegroYoung Marx).)

But to return to the point, I don’t see any necessary connection between the last two sentences quoted.    If by “be a mathematician” #ShutDownMath means “obtain academic positions” (and not to work as quants or defense analysts or spooks or data miners), then the problem is well posed:  find the “any person[s] who WANT” to obtain such positions, and then match them through an expansion of the normal training process — unaltered — with the positions.  I’m going to pretend to share the inclusion/exclusion authors’ unfounded optimism that higher education as we know it will not collapse in the near future and there still will be stable academic positions in the numbers to which we have been accustomed.  And, just to make the speculation more lively, I will admit the next sentence from #ShutDownMath —

White and non-Black POC don’t need to recruit people as props to make us feel better, we need to get out of the way.

— and assume that the requisite number of positions for Black and Indigenous people who WANT to become mathematicians are not already occupied by White and non-Black POC.

Granting all these assumptions, I have no doubt that the people in question can actually be found by a concerted effort — something like a vastly expanded version of the Math Alliance program, together with the (possibly massive, but possibly not) funding needed to coordinate the process and to provide support as needed for Ph.D. students who presumably (because just different has taken social revolution off the table) have not enjoyed the unearned privileges of the typical Ph.D. students of the current generation.  This is probably the right place to insert an otherwise completely incongruous

White Privilege Anecdote

In January I rented a car in Manhattan for a day trip with my family to Long Island, which is home to many people (2.8 million, more or less, past Brooklyn and Queens) but for us counts as uncharted territory.  None of us had ever been to a Hampton before, and we frankly didn’t know what to make of it when we finally saw one, even after we had explored it past sundown.  On our way back, and close to the City, I stopped to refill the gas tank, then turned left down a side street, at the end of which the internet had chosen a place for our dinner.  I had hardly driven three blocks when I saw the lights of a police car flashing in my rear view mirror.  Although I had no idea what was going on, I duly pulled to the side and waited for the officer to shine a flashlight into the front seat and ask for my license (which I provided) and registration (which the rental agency had not provided).  He then explained that I had driven through a red light (which I had not seen, but which I believed was perfectly possible).  After a few minutes of cordial conversation, he told me he would not write a ticket but admonished me to stop at red lights in the future.  I thanked him (naturally) and as he left he also advised me to turn on my headlights, which I had forgotten to switch back on when I left the gas station, as I often do in a rental car.

“To change mathematics itself”

So with a good deal of attention, a commitment to funding that is (possibly, but possibly not) massive (but still negligible compared to budgets for police, not to mention the military), and considerable good will, I claim that the demographics of mathematics departments can be transformed in the space of a generation (the time to dispatch current professors to a comfortable retirement) to match those of the wider North American population, where the “environment” will be no more uncomfortable than that of society at large.  The authors of #ShutDownMath will now be justified in complaining that I either unwittingly or maliciously missed the point of the post, namely the sentences that preceded the one about “creat[ing] an environment”:

We also want to make a distinction here — the problem is systemic racism, not just underrepresentation (even “underrepresented minority” is a terrible term to use). If we continue business as usual, it is disingenuous to focus only on recruiting more Black, Indigenous, Latinx students into our programs.

My problem is interpreting the juxtaposition of “business as usual,” which presumably refers to the practices that, as we read in the next paragraph, “have marginalized many groups” and may even “cause irreparable harm,” with the image of the person who “WANTS to be a mathematician.”  No person WANTS to suffer irreparable harm, so either (a) the person doesn’t see “business as usual” as irredeemable, or (b) what the person WANTS involves “chang[ing] mathematics itself” into something about which we know primarily what it is not — not “entrenched in systems of white supremacy,” not a source of “structural and systemic oppression,” not marginalizing, not the status quo… not business as usual.

Now I have a hunch that it will be difficult to change business as usual in mathematics into something else without confronting the business as usual of higher education itself, with its hierarchies within hierarchies and a financial model whose sustainability has been visibly in question since the student debt crisis exploded in the wake of the 2008 financial crash.  But that once again leads us, if not into the treacherous landscape of social revolution which just different has taken off the table, at least into its foothills.  So let’s leave that aside for the moment and just acknowledge that there is an endless gradation between tinkering as in (a) above with hiring practices and bad attitudes and a thoroughgoing metaphysical transformation as in (b).  For example, I found this minimal list of the changes needed to “business as usual” in John Rice’s article in The Atlantic, where he calls it “third-degree racism”:

(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.

Rice’s list is addressed to “major employers” but I suspect a majority of colleagues would agree that the changes would be welcome in mathematics departments, where the obstacles to bringing them about would nevertheless be formidable.  At least one prominent university department is already making what seems to me to be a good faith effort into working to overcome these obstacles.  And they seem perfectly compatible with Federico Ardila-Mantilla’s Four Axioms, which have been widely quoted and have been adopted by another (probably more than one) prominent university department.

However, these changes can be implemented while leaving the content and the professional practice of mathematics intact (not to mention its presumed metaphysical underpinnings).  And I worry that Rice’s talk of “delivering outcomes,” like the good faith effort mentioned above, looks dangerously like what Ibram X. Kendi calls assimilationism in his #1 New York Times bestseller How to Be an AntiracistFor Kendi assimilationism is one of the principal forms of racism.   The changes we were ready to celebrate in the last paragraph fall far short of (b), and if the “business as usual” of mathematics is already racist, none of the concrete measures I’ve seen suggested goes nearly far enough.

Is the metaphysical basis of mathematics intrinsically oppressive?  Is the mathematical hierarchy racist?  Can the metaphysics and the hierarchy even be separated?  Is the inclusion/exclusion blog’s perspective on inclusion and exclusion reformist or revolutionary — Antiracist or merely assimilationist?

It’s also worth examining whether or not this initiative to boycott police work is business as usual or a reaction against business as usual…

This was originally going to be a post about the unbelievably dreary details of the hiring process under “business as usual” in a typical pure mathematics department.  My aim was to identify stages in the process where a well-timed intervention could effectively outflank “third-degree racism,” change the delivered outcomes, and maybe even spark the beginning of a metaphysical as well as sociological transformation in the field as a whole.  But this post has gone on long enough, so those questions will have to be reserved for Part II, or for the social revolution — whichever comes first.


Ivar Ekeland’s letter on anti-Black racism

I copy this post from (mathematician and economist) Ivar Ekeland‘s letter to the presidents of the Société Mathématique de France and the Société de Mathématiques Appliquées et Industrielles, published on the Médiapart website .  For those who don’t read French online translations capture the meaning surprisingly well.

Ce 10 juin est une journée internationale de grève pour marquer la volonté des universitaires et des chercheurs de lutter contre le racisme antinoir dans leurs rangs. Le mouvement est parti des Etats-Unis sous les hashtags #ShutDownAcademia, #ShutDownSTEM,  et  partout dans le monde les institutions les plus prestigieuses se sont interrompues pour marquer leur solidarité.  Partout, sauf en France. Pourquoi ? Croit-on vraiment que cela ne nous concerne pas ? J’ai adressé aux présidents des deux sociétés savantes auxquelles j’appartiens, la SMAI (Société de Mathématiques Appliquées et Industrielles) et la SMF (Société Mathématique de France) la lettre suivante. L’AMS (American Mathematical Society) et SIAM (Society for Industrial and Applied Mathematics) sont les sociétés correspondantes aux USA.


Le 2 Juin, la présidente de l’AMS écrivait à tous les membres de la Société pour marquer le soutien de celle-ci au mouvement populaire qui se développe aux Etats-Unis contre le racisme antinoir et les violences policières. A cette occasion, elle écrit « We must accept the shared responsibility of changing our world for the better, and examining our own biases as part of that ». Le 3 Juin, la présidente de la SIAM faisait de même et écrivait : « We recognize that we are all accountable for making change happen, and we offer our solidarity to those who are deeply impacted, especially our Black colleagues, students, and staff in the SIAM community ». Le 4, le directeur de l’IAS de Princeton parlait au nom de l’institution : «  At IAS, we all must stand together against racism—in the U.S. and in all parts of the world—and, in our work, strive to be leaders in understanding and dismantling the ways that discrimination and injustice are perpetuated. «


Je regrette que ni la SMAI, ni la SMF, ni aucune de nos prestigieuses institutions n’aient jugé bon de prendre une initiative de ce genre. Il y a pourtant bien des raisons de le faire. Le racisme antinoir et les violences policières ne sont pas l’apanage des Etats-Unis, la France en a largement sa part. Je rappelle que la répression violente contre les gilets jaunes a été condamnée par une résolution du Parlement Européen, et que dans son dernier rapport le défenseur des droits, Jacques Toubon, dénonce l’emploi d’armes « non léthales » (ce qui veut dire qu’elles ne tuent pas nécessairement, mais qu’elles peuvent laisser de très graves séquelles) contre des manifestants pacifiques et l’impunité des forces de l’ordre.


Quant au racisme antinoir, nous le constatons tous les jours dans nos universités. En cinquante ans de carrière, j’ai rencontré en tout et pour tout trois professeurs d’université noirs – un en France, un aux Etats-Unis, un au Canada. Par contre, chez les appariteurs, les vigiles, et ceux qui nettoient nos bureaux la nuit, ils sont là, et l’habitude fait qu’on ne les remarque même plus.


Je vous rassure : il n’y a pas que chez les matheux ! Je me souviens d’avoir discuté avec un collègue économiste. Je lui disais : « Est-ce que tu connais un professeur d’université noir? ». La réponse a été: « Mais qui tu verrais? ». Si nous en sommes au point qu’un professeur ne se rende pas compte que c’est justement là le problème, qu’il n’y a personne parce qu’il n’y a pas de candidat, et qu’il n’y a pas de candidat justement parce qu’il n’y a personne, c’est vraiment que nous sommes malades, et beaucoup plus malades que les Etats-Unis. Eux, au moins, savent qu’il y a un problème et s’en préoccupent.


Je pense que la SMAI, et la SMF, et les autres sociétés savantes françaises, devraient prendre exemple sur l’AMS, et proclamer comme elle que « Nous devons accepter notre responsabilité collective de changer le monde en mieux, et pour cela de remettre en question nos propres préjugés ». En particulier, je demande qu’elles se saisissent de la question de la sous-représentation des noirs parmi les enseignants du supérieur. Peut-on la mesurer? [This is an allusion to the illegality of collecting ethnic statistics in France, MH.] Après tout, je ne peut faire état que d’une expérience personnelle, et il faudrait l’étayer par des données statistiques. Comment lutter contre elle ? Les racines du problème plongent certainement très loin, et y remédier demanderait sans doute que l’on intervienne dès le lycée et les classes préparatoires. Il est urgent de lancer une enquête.


Je regrette que la communauté mathématique française n’ait pas suivi l’exemple de nos collègues américains, et ne se soit pas mobilisée comme eux le 10 juin, suivant l’appel #ShutDownAcademia. Ecoutons au moins leur appel : il faut lutter contre les violences policières et le racisme antinoir. Et si on ne l’a pas fait avec eux, faisons le après eux. C’est urgent ! Le déni n’est plus possible.

Thoughts on #ShutDownSTEM day

Colleagues who thought that #ShutDownSTEM had nothing to do with mathematics will have been surprised to read this on Wednesday morning in place of their usual list of prepublications:

arXiv will not mail a daily announcement on the evening of Tuesday, June 9, 2020. Submissions received at or after 14:00 ET Monday, June 8 and before 14:00 ET Wednesday, June, 10 will be announced at 20:00 ET Wednesday, June 10.
 We also encourage authors to pause their submissions on Wednesday, June 10 to participate in the #strike4blacklives.

We encourage arXiv readers to use the time they would normally spend reading the daily announcement or submitting an article to instead read about and discuss racism and how they will work in their own local and professional communities to address it. If you choose to participate, please consider tagging @arXiv on Twitter to let us know what you are doing.

When I first posted a link to the #ShutDownSTEM website I never expected the call would be adopted by the staff at arXiv, much less by the AAAS, Nature, the American Physical Society, the MIT School of Science, and laboratories and universities around the world.  That a political program that is potentially so destabilizing to the status quo could attain mainstream status in the space of a few days is practically unprecedented in my experience.  At the same time, it strongly suggests that people in positions of authority believe its destabilizing potential can be kept under control.

The concise explanation of the purpose of the day-long hiatus at hints at its inherent radicality:

as physicists, we believe an academic strike is urgently needed: to hit pause, to give Black academics a break and to give others an opportunity to reflect on their own complicity in anti-Black racism in academia and their local and global communities. This #strike4blacklives is in dialogue with a call from colleagues in astronomy to #shutdownSTEM and #shutdownacademia for at least the day of June 10.

Complicity in anti-Black racism?  That’s strong language!  To help understand what is meant here by that challenging word, here is Charles Blow of the New York Times, a more effective writer than most activist scientists.

We must make ourselves comfortable with the notion that for the privileged, equality will feel like oppression, and that things — legacy power, wealth accumulation, cultural influence — will not be advantaged by whiteness.…

How will our white allies respond when this summer has passed? How will they respond when civil rights gets personal and it’s about them and not just punishing the white man who pressed his knee into George Floyd’s neck? How will they respond when true equality threatens their privilege, when it actually starts to cost them something?

He is talking about true equality in our departments, dear colleagues.  Mathematics has seen a few public initiatives in support of the #ShutDown — check out the top line at, for example


or this announcement of the postponement of a trinational seminar, these announcements from MSRI and the MIT and Duke mathematics departments,


Dukemore extended and apparently permanent announcements at Stanford and Barnard, and finally this image that greets today’s visitors to the AMS:

AMS screen capture

So I am spending Wednesday writing down my thoughts about structural obstacles to change in the profession.


From the Strike4BlackLives page at

We must confront the institutional barriers to justice for Black people in academia and beyond, challenge the notion of the meritocracy whereby “objective and neutral” criteria infused with systemic racism are used to exclude Black people from physics and other academic disciplines, and rebuild our institutions and collaborations in a way that is just and equitable.

Chapter 2 of MWA is devoted to the way something I call charisma structures not only the profession’s functioning in practice but its very self-image as a coherent activity, and suggests that the profession’s value system is inseparable from the existence of a hierarchy that to all intents and purposes is consensual among practicing mathematicians.  This does not — necessarily — mean that mathematics would collapse if the hierarchy were disturbed, but it does mean that eliminating systemic racism from mathematics, insofar as it exists as a recognizable phenomenon, will require a painstaking (and frankly tedious) examination of how meritocracy works in mathematics.

I guess I know something about that.  I have taken part in departmental hiring decisions on two continents and was involved in several national committees for promotions and honors in France, and on the committee choosing candidates for grants at the European level.  I was once the editor-in-chief of a journal and continue to be on the editorial boards of several journals.   My files for the last year alone include 26 reference letters for positions or promotions or honors, about half at the request of the candidates and half at the request of their institutions.  And so on and so forth.  The only reference I have ever seen to race in connection with any of these activities has come in my membership in my department’s Diversity Hiring Committee (more on “diversity” below) and in sentences like

We especially encourage participation from junior
mathematicians, women, under-represented minorities,
and mathematicians from primarily undergraduate

that are among the few “systemic” features of the process of including or excluding colleagues from professional activities in the United States and a few other English-speaking countries.

So, although I have no doubt that some senior colleagues harbor characteristically racist ideas, there is no blatant conspiracy to keep Black mathematicians out of the profession.  Nevertheless, the number of African-American colleagues in visible positions in mathematics has hardly changed over the course of my career — the New York Times estimated in 2019 that there are “only perhaps a dozen black mathematicians among nearly 2,000 tenured faculty members in the nation’s top 50 math departments” — not even 1%.   Fixing that gross imbalance is the modest challenge the #ShutDownSTEM action addresses to “non-Black” mathematicians.  The much more modest challenge I set myself for today is to analyze some of the stages of the creation of that imbalance in which mathematical gatekeepers like myself can intervene directly.

After thinking it over, however, and reading Louis Menand’s subtle New Yorker article on meritocracy, I decided to postpone this analysis to a future post.  Changing the structure of the decision process would require nothing less than a social revolution, albeit one on a much smaller scale than the one required to transform the so-called pipeline that leads through life in a profoundly racist society to the stage at which mathematical gatekeepers can become cognizant of the problem.  Fortunately for this discussion, people like Bernie Sanders have done much to take the sting out of the notion of “revolution,” so most readers will not immediately have images of guillotines and the Battleship Potemkin when they read that word.  Nevertheless, reviewing these decision processes has lost some of its urgency in view of the hiring freeze decided by at least 396 colleges and universities, in the wake of the COVID-19 pandemic.  And the larger question of the dependence of mathematics on the existence of a consensual hierarchy; the reasons for placing “objective and neutral” in scare quotes in the above quotation; and the extent to which the decision process leads to an unquestionably racist outcome because it is based on criteria that are “infused with racism”:  these are questions that call for a book-length analysis.  For now I just want to urge my fellow gatekeepers to acknowledge the seriousness of the questions, and to resist the temptation to dismiss them with superficial answers.

But I do want to include Corey Robin’s concise metaphor for what passes for meritocracy in higher education in the US (but not only in the US):

This is the song of culture in our society. The bass line is wealth and profit; the melody is diversity and opportunity.


Taking action

In view of the problematic history of “diversity” as a juridical category in the United States, I’m pleased to see that the initiators of #Strike4BlackLives do not share the illusions of some of our colleagues with regard to diversity statements and diversity training.

Importantly, we are not calling for more diversity and inclusion talks and seminars. We are not asking people to sit through another training about implicit bias. We are calling for every member of the community to commit to taking actions that will change the material circumstances of how Black lives are lived — to work toward ending the white supremacy that not only snuffs out Black physicist dreams but destroys whole Black lives. In calling for a strike, we call on people who are not Black to spend a day undertaking discussion and action that furthers this work, while providing Black scientists with a day of rest.

Even with the best of intentions, commitment to diversity as codified in the jurisprudence initiated by Supreme Court Justice Lewis Powell will not go far to remedy the pathological scarcity of Black mathematicians, much less to overcome the systemic and frankly criminal racism at the origin of the uprisings of the past few weeks.  Commitment to “taking actions” is clearly necessary.

But where to start?  Fortunately, a group of geoscientists has proposed a very helpful list of 15 classes of actions on a petition that at the time of writing has already been signed by more than 14000 people.  I am surprised to learn that the American Geophysical Union claims 62000 members, so maybe everyone who signed is actually a geoscientist; and a number of the actions suggested (like the ones about fieldwork, or the reference to mining and fossil fuels) don’t transpose naturally to mathematics.  But some of them do, and the others can serve as a stimulus to our imagination.  For example, Points 1 and 3:

  1.  Post anti-racism statements publicly and accessibly, and incorporate anti-racism into codes of ethics.

   3. Identify ways each society and organization has previously failed Black,         Indigenous, and Latinx People and other minoritized groups both structurally and individually.

would be too obvious to mention if more institutions had taken the initiatives listed at the beginning of this post.   The AMS has been acting on Point 14:

14. Publish annual, data-rich reports of the self-reported, intersectional demographics of members, including demographic data about who is getting awards and who is engaged in leadership in the organization.

for well over a decade — and I would be able to provide a link to the data if the AMS website were not shut down today! — but it’s less clear that departments (like mine) have been studying the data systematically and drawing conclusions.   On the other hand, I can well imagine that implementing Point 9:

9.  Address issues of workplace culture that are active threats to safety, wellbeing, and careers, and acknowledge, address, and promote the safety and success of Black, Indigenous, Latinx, and other minoritized geoscientists and students who have been historically marginalized in education and the workplace.

would make colleagues extremely uncomfortable, especially in departments (like mine) where North American colleagues of any race are in the minority (and I say this on the basis of my experience in France, where it took me years to understand “workplace culture”).

(Cautious) optimism

Now that (some) colleagues are paying attention, I actually think that the proportion of Black colleagues will increase significantly, and it won’t take as long as the 27 years that elapsed between the Best Adapted Screenplay nomination for Do the Right Thing and the Best Picture award for Moonlight.  For reasons already discussed here, young mathematicians are much more sensitive to questions of political injustice than (most of) their senior colleagues, and I anticipate that the situation described in a private message from a scientist at one of the major research institutions involved in #ShutDownSTEM

The strike was endorsed by the Graduate Student Council, and is close to being endorsed by the [NAME REDACTED] Postdoctoral Association; this has given trainees a sense of safety in numbers.  Trainees have organized their labs and communicated with PIs together, which has helped get whole labs on board.  Grad students and postdocs have also organized together to send joint statements of support to their Departments as a whole.  A few [NAME REDACTED] faculty pledged to participate early on.

will be reproduced by the future decision makers in mathematics departments (assuming there will be mathematics departments in the future).   Attitudes and practices will improve, structural obstacles will be removed, and initiatives like the Math Alliance will help to solve the pipeline problem.

I’m less convinced that getting racism in mathematics under control will have much of an effect on the problems that led to the current uprising.  Research mathematics, like Hollywood, is a compact and prosperous institution and can expand its demographic base — it has done so repeatedly over the course of the past century — without calling into question its dependence on existing power relations in the larger society.

At this point I was planning to insert some text from Adriana Salerno’s post on the AMS inclusion/exclusion blog, and to add some of my own thoughts on how training in financial mathematics has contributed to the problems highlighted in this book by Keanga Yamahtta-Taylor.  But the blog is shut down for the day, like the rest of the AMS website, so this will have to wait.

UPDATE:  Some more statements from Columbia:  The Department of Astronomy  has a statement that ends with these thoughts:

Society is facing an inflection point, fueling new awareness. We recognize the need for sustained actions that lead to real change. These may build on on-going efforts or may involve new initiatives and resources. They must also be derived from the exchange of ideas within our academic community of faculty, students and staff.

We commit to not only taking this moment to reflect and learn but also to using the momentum of the present to make concrete plans for the future.

The Department of Ecology, Evolution, and Environmental Biology has uploaded a diversity statement to its home page that does not explicitly refer to ShutDownSTEM.  The Dean of the School of Engineering and Applied Sciences, which includes the Department of Applied Physics and Applied Mathematics, sent a long statement to faculty and students at the school, including this commitment to practical action:

At the school level, we will begin by coordinating our current programs and actions into a more cohesive and visible effort, from K-12 outreach on through student and faculty recruitment and mentoring. This will enable further expansion of these initiatives and greater participation of our community in these impactful endeavors. This will also provide a clearer framework and foundation for us to build out these programs, identify gaps, and outline needed actions. I will be inviting your active participation in these efforts.
Other departments and schools may have sent similar messages to their members.

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.



This is one of the many projects that grew out of the uprising against racism and police violence that began barely a week ago, in response to the murder of George Floyd by four Minneapolis police officers.  What I find especially striking in this case is that most of the initiators are physicists and astronomers, with a particular concentration at Caltech and some of the other campuses in the Los Angeles area.

Here is some of the relevant text:

In the wake of the most recent murders of Black people in the US, it is clear that white and other non-Black people have to step up and do the work to eradicate anti-Black racism. As members of the global academic and STEM communities, we have an enormous ethical obligation to stop doing “business as usual.” No matter where we physically live, we impact and are impacted by this moment in history.…

Here I would like to interject, for the sake of my French colleagues, that there is no need to focus on developments in the United States.   French practices provide ample scope for action and reflection.

To continue:

…For Black academics and STEM professionals, #ShutDownAcademia and #ShutDownSTEM is a time to prioritize their needs— whether that is to rest, reflect, or to act— without incurring additional cumulative disadvantage.

Those of us who are not Black, particularly those of us who are white, play a key role in perpetuating systemic racism. Direct actions are needed to stop this injustice. Unless you engage directly with eliminating racism, you are perpetuating it. This moment calls for profound and meaningful change. #ShutDownAcademia and #ShutDownSTEM is the time for white and non-Black People of Color (NBPOC) to not only educate themselves, but to define a detailed plan of action to carry forward. Wednesday June 10, 2020 will mark the day that we transition into a lifelong commitment of actions to eradicate anti-Black racism in academia and STEM.

Up to now I have seen no similar initiatives on the part of mathematicians, but I found it encouraging that John Bergdall used the expressions state-sponsored killing of African-Americans and American police terrorism in his opening remarks during the “local” panel at last week’s online CARTOON conference.  Finding the right names for the many visible and persistent consequences of racism within our own profession as well is a good place to start.  And studying the history of the mathematical institutions’ attempts to find ways to react to even the most blatant manifestations of racism places current practices in valuable perspective — Michael Barany’s sobering account of the creation of the AMS Notices should be read by everyone who still believes mathematics is intrinsically apolitical.





Challenges the math community faces in the future

These are the notes I prepared for the “Global panel” at the CARTOON conference on May 30, 2020.  There is only time to discuss a small fraction of this material, which itself is a minuscule selection of the massive literature inspired by thoughts about what our life, academic or otherwise, will be like if and when the pandemic is brought under control.

I expect to add resources and references as the summer progresses.


We have all been reading about the difference between “getting back to normal” and “adjusting to the new normal.”  There turns out to be fairly broad agreement that not only were some features of the “old normal” highly undesirable — like inequality, pollution, xenophobia, dependence on fossil fuels, austerity in public services, or the gig economy, or the for-profit health care system in the United States — but that the current crisis provides a once-in-a-lifetime opportunity to eliminate or at least to attenuate some of these undesirable features.

In the face of the coronavirus, a small window has opened in our societies to gain scope for action. It is important to keep this window open a bit.

(Bernd Scherer, Director, Haus der Kulturen der Welt)

Or, to quote Juliette Binoche, Iggy Pop, Vaughan Jones, Béla Tarr, Madonna, and Tim Gowers, among many other celebrities, it is time

to leave behind the unsustainable logic that still prevails and to undertake a profound overhaul of our goals, values, and economies.

In that spirit, I’m going to focus on the challenge to the mathematics community of using the current opportunity to address some aspects that need to be reconsidered of the system that makes our profession possible.  I will divide these artificially into four groups:  relations with the broader society, relations with universities and higher education, relations within the profession, and relations with ourselves.


Relations with broader society

The crisis has revealed something we already suspected:  that we are not essential workers.  This has two sides:  on the one hand, our mathematical activities are not necessary for the basic functions of civilized society; on the other hand, our material circumstances are safer and much more comfortable than those of nurses, sanitation workers, transport workers, food handlers, and so on.  What we owe in exchange for our comfort is a serious reflection on what is the “essence” of our work, with regard to the broader society.

Serious reflection on our essence requires in the first place speaking out about the ethical challenges posed by the many spectacularly problematic applications of mathematics — financial engineering, Cambridge Analytica, algorithmic weapons of math destruction, surveillance, as well as strictly military applications.  That doesn’t mean we necessarily have to refuse funding from the Heilbronn Institute, as Tom Leinster argued a few years ago; but it does mean owning up to what accepting such funding entails.

One direction I strongly advise avoiding is to reduce our essence to the market value of applications of mathematics, in scientific modeling or commercial innovations.  The argument can and should be made that these applications depend in multiple ways on a robust community of pure mathematicians, but promising spinoffs and startups in exchange for support of our profession is a toxic habit of concession to neoliberal thinking, and that habit clouds our thinking at every level.  For many reasons we should take advantage of the crisis to seal the collected thoughts of Margaret Thatcher and Ronald Reagan in a time capsule and bury them permanently in a toxic waste dump.

I will return to the essence of our work at the end.  In the meantime, avoiding the neoliberal reading of our essence as far as the broader society is concerned means taking on the neoliberal model of the university.  To quote the petition Refonder l’Université et la Recherche pour retrouver prise sur le monde et nos vies (more than 7000 signatures since March 20, including mine):

Le corollaire de l’autonomie du monde savant est son engagement sur un principe : sa responsabilité vis-à-vis de la société.  L’usage politique, technique et industriel des travaux scientifiques doit se décider dans un cadre pluraliste et démocratique, en accord avec l’intérêt commun.


Relations with universities  

In the neoliberal model the university provides the service of enhancing the student’s market value, and we, as teachers, are service workers.  This vision has the merit of relieving our fear of being seen as social parasites.  But the relief is short-lived, because the model of university education built on massive student debt is not sustainable, and other models are actively being discussed.  In March Stefan Collini wrote this in the Guardian:

The “marketisation” of universities in the past decade has changed their ethos as well as their funding. Older notions of an academic community, or a scholarly career, have been replaced by economic analyses that look to reduce unit costs per output. Replacing permanent staff with cheaper, disposable temporary ones reduces the power of academics and increases that of managers.

The rich Ivy league and similar universities have already announced hiring freezes; Johns Hopkins has gone even further, sending signals that even tenure may not guarantee the expected level of material comfort for much longer.

Suddenly anticipating losses of over $350 million in the next 15 months, the university imposed a hiring freeze, canceled all raises, and warned about impending furloughs and layoffs. Most extraordinarily of all, it suspended contributions to its employees’ retirement accounts.

(François Furstenburg, Chronicle of Higher Education)

The Times Higher Education Supplement has this headline story:

            Mergers and ‘FE future’ predicted for some English universities 

While many universities would need “pretty big cuts in teaching and research staff” as a result of the coronavirus crisis, such action would not be enough to save some institutions, which would be forced to merge as a condition of receiving extra funding…

Sir Steve Smith, vice-chancellor of the University of Exeter, adds

The future prosperity of the UK depends on having a strong university research base, which is subsidised by international student income.

Lurking in the background in this and similar articles is the prospect that the existing system of higher education will be replaced by one where universities become content providers to fit the respective business models of leading national industries — Silicon Valley in the US, for example.

The promise of freedom of subjective development and the democratization of knowledge was, however, increasingly functionalized through business models that use the orientation of citizens on the internet to collect data and sell them as goods for digital capitalism.

(Bernd Scherer, loc. cit)



A few of the sponsors of the 2020 WICHE Conference on Educational Technology

Some of the initiatives to preserve what we see as the values embodied by universities focus on protecting the most precarious university workers.  Among them are colleagues who have undergone the full academic apprenticeship process but who have not acquired the professional stability that is one of the chief attractions of the academic life.   I am one of 2800 signatories, including only 25 mathematicians, of the Covid-19 Academic Solidarity Statement, which

calls on universities to protect the lives and livelihoods of its contingent academic workers, including non-tenure track (NTT) teachers and graduate students. … Signatories to the statement further pledge not to accept speaking invitations during the 2020-21 academic year at institutions that have extended tenure clocks for their tenure-track faculty, but have not similarly extended contracts for all currently employed NTT teachers and graduate students.

(All eight Ivy League universities, including my own, are on the list of institutions whose invitations are to be refused, along with many others, public as well as private.  See also the long list of Related Campaigns, mainly by graduate workers and non-tenure-track faculty.)

It usually comes as a surprise to our colleagues in the humanities that mathematicians can be uniquely effective in campaigns in defense of progressive values.  A good example is Tim Gowers’s pledge in 2012 to boycott Elsevier, which inspired the Cost of Knowledge statement that quickly collected over 10000 signatures (17000 by 2018).


Relations with the profession

And with inevitable pressure on the job market as a result of the collapse of public budgets as well as the economy more generally, the priorities of the profession will come into question in a way that has not been seen since the 1950s — except in Russia, where mathematics has not recovered and may never recover from the collapse of the USSR.  Even before the financial crisis of 2008 the internal contradictions of the model of the reproduction of the humanities through graduate programs were widely recognized (as early as 1970, according to Christopher Newfield).  In mathematics, the imbalance between entering graduate classes and the job market (but why do we accept the “job market” as a fact of nature?) has been mitigated by the possibility of employment in the toxic “old normal” industries I already mentioned.

A recent Intercept article by Naomi Klein spells out how the tech industry, in partnership with local governments, plans to cash in on installing “smart” technology in the wake of the crisis.  She quotes Eric Schmidt:

Congress should meet the president’s request for the highest level of defense R & D funding in over 70 years, and the Defense Department should capitalize on that resource surge to build breakthrough capabilities in A.I., quantum, hypersonics and other priority technology areas.

Jobs in these sectors may well help PhDs in mathematics and the sciences survive the loss of stable university positions.  And this need not be a social and political disaster — if these developments are placed under democratic control, so that the benefits do not all accrue to Silicon Valley billionaires and the power is not designed to favor autocracy.  To quote Klein again:

Will that technology be subject to the disciplines of democracy and public oversight, or will it be rolled out in state-of-exception frenzy, without asking critical questions that will shape our lives for decades to come? Questions like, for instance: If we are indeed seeing how critical digital connectivity is in times of crisis, should these networks, and our data, really be in the hands of private players like Google, Amazon, and Apple? If public funds are paying for so much of it, should the public also own and control it? If the internet is essential for so much in our lives, as it clearly is, should it be treated as a nonprofit public utility?

However, even if one’s conscience is willing to forget that the expansion of employment opportunities for mathematicians to develop the tools of speculative finance and monetization of personal data that are at least partially responsible for the conditions that made the present crisis much worse than it had to be, there’s no guarantee that these industries will be able to absorb the surplus of mathematics PhDs when the crisis is over.


Relations with self

If you want to continue in this profession, your main task is to ask yourselves what you find important and valuable about the mathematical vocation, and then to acknowledge that much of this is likely to come under attack, precisely for the reasons that you find it appealing, and that preserving what is important and valuable is really up to you.  Ultimately this means placing the economic model and political justifications that sustain higher education, including those discussed above, under scrutiny; drawing the appropriate conclusions; and then doing whatever is necessary, as indicated by these conclusions, in order to preserve whatever drew you to the mathematical life in the first place.

In other words, if the values of mathematics are important to you, you will have to become activists.  If you have been reading or rereading Camus’ The Plague, you will have seen that there was “no great merit” in doing what Tarrou chose to do, “because they knew it was the only thing to do and not to have decided to do it would have been incredible.”

Humanistic scholars are much more skillful than we are in finding the language to justify their activism.

In a time in which public education must struggle to establish itself as a public good, it is incumbent upon faculty to clarify in what senses higher education is a value in our public worlds and why it should be supported. The answer provided by the recent AAUP statement …  relies on a notion of progress that is hardly explained, and given that experts have surely led us astray (experts in neoliberalism, technologies of indefinite detention, nuclear war), we would have to know which version of expert knowledge is advanced and judge whether its advancement is really a public good. Since we need to know and evaluate the direction and aim of such an “advancement,” we would have to rely on those humanistic disciplines explicitly devoted to critically interrogating the problem of value, justification, and the various senses of the public good.

(Judith Butler, Academe)


This text predates the COVID-19 crisis but the conclusions remain valid, and they challenge us to explain how the values that motivate us as mathematicians — the values that arise authentically from our practice, not those that are assigned to our work by the market — contribute meaningfully to “various senses of the public good.”  I think we can meet the challenge, but more of us will have to put more effort into our explanations than most of us have done so far.

Mathematicians have made considerable progress in recognizing ethical challenges within the profession.   The AMS has gone so far as to institutionalize the language of inclusion and exclusion in its publications.  But the scope for inclusion will be severely diminished if we don’t  find the language to address the challenges to the profession within the broader society.


1-minute summary

Forget everything you think you know, look for allies outside of mathematics, figure out what is most precious and hold on to it, and be prepared to fight to preserve it, because I guarantee there are political and economic forces that will take it away from you if left unopposed.



SOME CHOICE QUOTATIONS (some behind paywalls)

Once hard decisions have been made about academic offerings, high-level estimates of required faculty can be calculated with existing load levels, class sizes, and student-to- faculty ratios. Each of these items should next be analyzed as part of the second key question: How productive can our faculty be?

…Many argue that the traditional professorial model of tenure, lighter teaching loads, long vacations, and sabbaticals was formed when salaries were lower in higher ed but has been maintained even though salaries have risen.

(Chronicle of Higher Education, How to Address the Elephant in the Room: Academic Costs)


Faced with an education minister, Jean-Michel Blanquer, who has been bypassed by events, teachers have themselves invented new practices, working school by school and class by class. Away from the education authorities and the school inspectorates, the great majority of teachers have taken it upon themselves to choose and organise the details of the return to school.

…what this flurry of initiatives and mobilisation, and this capacity for self-organisation and innovation, have also shown is the extent to which a health crisis has ended up revealing the dangerously archaic nature of our political system.

(MediapartHow virus crisis is changing the face – and politics – of French society)


This crisis affords a rare chance to make personnel changes that have historically been resisted by strong campus cultures of inertia or by union agreements.

…Be prepared for big-change efforts and major cost-cutting (both administrative and academic), and invest in strategic differentiation to advance your college’s long-term health as well as survive this short-term crisis. In general, you will want to strive to cut more rather than less, and if things turn positive, you will be in a position to re-invest according to your strategy.

(Chronicle, Under Covid-19, University Budgets Like We’ve Never Seen Before )


The real Fields Medal curse?


The 2014 Fields Medalists in Seoul with former President Park Geun-Hye (now serving a 25-year prison term) and IMU President Ingrid Daubechies

(This is a revised version of a post published on March 12, under a much longer title.  The revision takes into account the later dramatic developments in the case of retired King Juan Carlos I of Spain.  If  you missed János Kollár’s article about the curse that, according to two economists, afflicts Fields Medalists with an alarming loss of productivity, you probably have the time to do so now.  It’s very entertaining and I guarantee it will take your mind off the pandemic and your lockdown for a few minutes at least.)

I had been preparing a blog post on the history of holding the International Congress under the patronage of figures of political authority.  This patronage has been symbolized in recent times by inviting important politicians — often heads of state — to place the Fields Medals in the hands of the year’s Laureates.  This has been the consistent practice since at least 2002, when I was in the Great Hall of the People to witness Chinese President and CCP General Secretary Jiang Zemin handing the Fields Medals to Laurent Lafforgue and Vladimir Voevodsky.  Like most of my colleagues I assumed this was a sign of the importance the host country attached to the ceremony, and to mathematics as a whole.  By extension I concluded that an ICM at which the head of state was absent from the opening ceremony was on some level a symbolic failure for the host country’s organizers as well as for the international mathematical community.

On the other hand, as readers of this blog have probably guessed, I was motivated to write about the topic because I wonder whether this kind of high patronage is still a good idea in an age when practically no important political leader in the world enjoys the kind of respect that would do honor to the ideals that motivate the International Mathematical Union, and when so many leaders of major countries (and smaller countries as well) are authoritarians or crooks or both at once.  It turns out that the practice of placing ICM under the sponsorship of the highest political spheres has not been consistent.  The IMU has helpfully made the proceedings of all past congresses available, and the reading of the early pages of the earliest congresses is pleasurable as well as enlightening.  How would I have learned otherwise that the 1920 Congress in Strasbourg cost 83,525 F, and that the most generous sponsor was the Ministry of Foreign Affairs (10,000 F), followed closely by the 7,000 F provided by the Commissariat générale d’Alsace-Lorraine (restored to France only two years earlier) and the 5,000 F donation of Solvay, headquartered (still) in Brussels?  I focused, however, on the congresses at which Fields Medals were awarded, starting with the Oslo congress in 1936, and specifically on whether the honor of presenting the Medals to the winners was entrusted to heads of state, to lesser politicians, to mathematicians, or to other representatives of civil society.

Reports on the opening ceremonies contain gaps, and I am not certain that I am reading them correctly, but I believe that the 1936 proceedings affirms that King Haakon VII of Norway was indeed in attendance, but that it was Elie Cartan who presented the first Fields Medals to Lars Ahlfors and to Norbert Wiener, representing Jesse Douglas who was too “fatigué” to attend.  In Cambridge (Massachusetts) in 1950, it was the turn of Harald Bohr to hand the Medals to Laurent Schwartz and Atle Selberg, and in 1954 in Amsterdam Hermann Weyl transmitted the prize to Kunihiko Kodairo and Jean-Pierre Serre.  Mathematicians — respectively Academician Mstislav Keldysh, Rolf Nevanlinna, Wladislaw Orlicz, Lars Ahlfors, and Beno Eckmann — again did the honors in Moscow in 1966, in Helsinki in 1978, in Warsaw in 1983, in Berkeley in 1986, and in Zürich in 1994.   And it appears that Yuri I. Manin presented the Fields Medals in Berlin in 1998 — but I can’t figure it out from the report on the opening ceremonies, which include lengthy speeches by a series of high officials from various levels of the German government, and this is particularly embarrassing because I was actually in the audience (or maybe I wasn’t) and I don’t remember what happened.

On all the other occasions the prizes were presented by politicians.  Here is a rundown:

1958, Edinburgh:  The prizes were presented by the Right Honorable Ian Johnson-Gilbert, Lord Provost of Edinburgh (not to be confused with Prince Philip, Duke of Edinburgh).

1962, Stockholm:  “The International Mathematical Union considers it a great honour that His Majesty the King has agreed to be present here and to give the Fields Medals to the winners of the Prizes” (ICM Proceedings, p. xl)

1966, Moscow:  Georges de Rham introduced the laureates. “Unfortunately, A. Grothendieck, was unable to come. May I call Messrs. Atiyah, Cohen and Smale to come forward and receive these medals from the hands of Academician Keldysh.”  I have already  mentioned this but I repeat the information because (as I just learned) Академик Мстислав Келдыш is the name of a 6,240 ton Russian scientific research vessel which played a role in the filming of James Cameron’s Titanic.  Not a bad fate for the name of a mathematician!

1970, Nice:  The congress was placed under the highest possible patronage:  “Monsieur Georges POMPIDOU, Président de la République Française, a accordé son haut patronage au Congrès. Monsieur Jacques CHABAN-DELMAS, Premier Ministre, a accordé son patronage au Congrès.”

However, neither the President nor the Prime Minister made the trip to Nice. Instead,

Monsieur Olivier GUICHARD, Ministre de l’Éducation nationale, remet les médailles Fields aux quatre lauréats, qu’il félicite.

The financial sponsorship for the congress was prominently displayed in the Nice proceedings, as it had been in the 1920 Strasbourg proceedings — in other words, I had to skip over the account of financial sponsorship before finding the report on the opening ceremony — and I thought readers might like to see that as well:

Le Congrès a bénéficié de l’aide d’un Comité de soutien pour la diffusion des travaux du Congrès, composé comme suit : Président : M. Georges DESBRIèRE, Vice-Président de Péchiney, Président de l’Association pour le Développement de l’Enseignement et des Recherches auprès des Facultés des Sciences de l’Université de Paris (A.D.E.R.P.). Membres : MM. BAUMGARTNER, Président de Rhône-Poulenc, CHASSAGNY, Prési-dent de l’Union syndicale des industries aéronautiques et spatiales, DELOUVRIER, Président de l’Électricité de France, DONTOT, Président de la Fédération nationale des industries électroniques, FERRY, Président de la Chambre syndicale de la sidérurgie, GALICHON, Président d’Air France, GLASSER, Président du Syndicat général de la Construction électrique, GRANDPIERRE, Président de l’Institut des hautes études scientifiques, HAAS-PICARD, Président de l’Union des Chambres syndicales de l’industrie du pétrole, HOTTINGUER, Président de l’Association professionnelle des Banques, HUVELIN, Président du Conseil National du Patronat Français, LESOURNE, Président de la S. E. M. A. (METRA International), d’ORNHJELM, Président de la Chambre syndicale des Constructeurs d’Automobiles, Ambroise Roux, Président de la Compagnie générale d’Électricité

1974, Vancouver:  H.M.S. Coxeter, President of the Congress,

announced that a telegram would be sent to His Excellency, the Right Honourable Jules Leger, C. C, C.M.M., Governor General of Canada, Patron of the Congress. The text of the telegram is as follows: We much appreciate your agreeing to serve as Patron of the first meeting in Vancouver of the International Congress of Mathematicians. We regret your inability to be present and we convey our warmest wishes for a complete recovery.

At the end of the opening ceremony, Professor Chandrasekharan, chairman of the Fields Medals Committee, made a speech that concluded:

May I offer them our warmest congratulations, and invite them to come forward to receive the medals from the hands of His Honour, the Lieutenant Governor of British Columbia.

1990, Kyoto:  “The winners came forward and received their medals and prize checks from Mr. Kosuke Hori, Minister of Education, Science and Culture.”

The Medals were presented by mathematicians in 1994, and 1998, as I already explained. As you can see, the practice of receiving Fields Medals from high-ranking politicians is not so well established as some of us believed.   And recent history has shown a curious correlation between getting close to the Fields Medal ceremony and being investigated for corruption.  The prime example is that of former President Park Geun-Hye, shown above in Seoul in 2014, charged less than 3 years later with “abuse of power, bribery, coercion and leaking government secrets.”  She will be in jail for a long long time, and although it was no fault of the four Fields Medalists, can they honestly say that it was an honor to accept the medals from an individual who enjoys such a dubious distinction?

The 2018 Fields Medal ceremony narrowly escaped being tainted by the participation of a no less corrupt politician:


Former Brazilian president Michel Temer [here shown in his official portrait] was arrested on Thursday as part of the sprawling five-year Car Wash investigation into political corruption.
Mr Temer was picked up by federal police officers at his home in São Paulo less than three months after he handed over the presidential sash to his successor, far-right former army officer Jair Bolsonaro.  (Irish Times, March 21, 2019)

From France24, May 15, 2019:

Former Brazil president Michel Temer left prison on Wednesday less than a week after returning to a Sao Paulo penitentiary in relation to a wide-ranging corruption scandal that has engulfed several high profile South American politicians.

The 78-year-old left the Military Police Battalion in Sao Paulo at 1.30 pm (1630 GMT) in a heavily guarded convoy as he headed to his home in an upmarket neighborhood in the sprawling city’s west.

His release was ordered by all four judges on the Superior Court of Justice under the writ of habeas corpus, which demands that a prisoner who claims unlawful detention be brought before a court.

However, several conditions were attached, including a freezing of his assets and the seizure of his passport.…

He is suspected of having been at the head of a criminal organization that diverted up to 1.8 billion reais ($460 million) and has been operating for 40 years.

Temer participated enthusiastically in the impeachment of Dilma Rousseff in 2016 and was still President during the ICM in Rio de Janeiro.  In that capacity it was expected that he would hand out the Fields Medals at the opening ceremony.  However (according to a colleague in Brazil with whom I spoke at the time) Temer found a diplomatic excuse to justify his absence at the ceremony, where his presence would certainly have been met with a loud and embarrassing protest — his approval rating had dropped to about 3%, a record low for any sitting President, anywhere in the world, even before his indictment.

It was India’s President, and not the better-known (and more powerful) Prime Minister, who brought the dignity of state to the opening ceremony of the ICM in Hyderabad in August 2010.

The officers of the IMU could have anticipated that the ordinary corruption of state, the ubiquitous kind to which most of us rarely pay attention, would accompany her presence, especially since she had already been under investigation:

From Wikipedia:  Patil was a chairperson of the [Pratibha Mahila Sahakari] bank and also one of its directors, along with many of her relatives. She is one of 34 respondents in an ongoing case [as of 2007, according to Wikipedia] before the Aurangabad bench of the Bombay High Court regarding alleged mismanagement of the bank and misappropriation of funds.… The Reserve Bank of India … revoked the licence of the bank in 2003 after it was found out that the bank had engaged in various irregularities, including illegally waiving interest on loans given to many of Patil’s family members.

At this point in my chronology I was hoping to be able to point to an exception in the person of former King Juan Carlos I of Spain.  While few (probably none) of my Spanish friends are monarchists, they all recognize the role he played at a crucial moment in the consolidation of the still-fragile democracy that was installed after Franco’s death, and for the most part he was comfortable in his role of titular head of state in the system that reserves the actual power of government for the elected parliament.   Moreover, unlike his successor and son, King Felipe VI, he has not intervened pointlessly in the Catalan independence crisis.

Madrid 2006

Overall, then, King Juan Carlos enjoyed broad respect in Spain and did bring a certain dignity to the 2006 ICM in Madrid, as did King Haakon VII in Oslo in 1936 (and even more in retrospect, for his refusal to recognize the Nazi occupation of Norway during the Second World War).  But a week before I revised this post the following story broke in El País:

This followed the revelation that “A public prosecutor in Switzerland has been investigating a multi-million-euro donation received by Corinna Larsen, a friend of former Spanish King Juan Carlos I, from a Swiss bank account linked to a Panamanian foundation.”  The donation of $100 million to Corinna Larsen — also known as Corinna zu Sayn-Wittgenstein — was apparently a kickback in connection with the construction of the Haramain high speed rail connection between Medina and Mecca, which was completed in 2018 by a consortium of 12 Spanish companies.

When I originally wrote this post I had not found allusions to this story in the English-language press.   The Spanish Socialist Party (PSOE), the leading force in the current coalition government along with the parties pressing the case (Unidas Podemos etc.).  was reluctant to investigate the economic activities of Juan Carlos is based on their reading of the Spanish constitution, which — as was demonstrated in a similar case two years ago — literally places the King above the law:

“las prerrogativas de inviolabilidad y no sujeción a responsabilidad del Rey, consagradas en el artículo 56.3 de la Constitución, son absolutas, abarcan a la totalidad del periodo en que se ejerce la Jefatura del Estado y tienen efectos jurídicos permanentes”

Ultimately King Felipe VI, son of Juan Carlos, renounced his inheritance and cut off his father’s stipend in a belated recognition that the individual standing in the middle of the above photo, and many other photos during his long reign, did not in retrospect lend dignity to the ceremony (and many other ceremonies) to the extent that the (figurative) crown on his head must have led the organizers to expect.

I am tempted to extend the disgraceful list back to the 2002 ICM in Beijing when I read questions like this:

Why is Xi Jinping afraid to jail Jiang Zemin even though there’s a lot of evidence of corruption against him and his alleged involvement in Beijing blasts to shake Xi’s authority? (Question answered on Quora.)

But I am aware that rivalries among factions of China’s ruling stratum take many unexpected forms and I know too well not to take this kind of comment at face value.

Mathematical platonists like to argue that our work is devoted to the discovery of truths that transcend any merely human laws.  This sheds a novel light on the decision to invite  heads of state who are above the law — whether they enjoy this status by virtue of a political system disposed in their favor, as was at least temporarily the case in 2018, 2014, 2010, and arguably in 2002, or by an exception carved into the law itself, as in the case of Spain’s former King — to lend their aura of inviolabilidad for a moment in order to enhance the solemnity of transfer of the Fields Medal.   Advancing the 2022 Fields Medal ceremony to the week following Donald Trump’s successful evasion of his Constitutional responsibilities, with the help of the (very favorably disposed) US Senate, would have been a perfect illustration of this principle.

But we missed the opportunity and will therefore have to wait another two years for a more exemplary native of the imponderable innermost sanctum of politics, where words like “corruption,”  “grace,” and “raw power” become practically synonymous, to dignify the St. Petersburg ICM with a moment of transcendence.

Colleagues who attended the São Paulo IMU General Assembly meeting, at which St. Petersburg was chosen over Paris as the venue for the 2022 ICM, informed me that the promise that President (for life?) Vladimir Putin himself would be on hand, to present the Fields Medals, was one of the arguments that clinched the decision.  I have just provided a quasi-theological rationale for this thesis but I still find it hard to grasp, and I prefer the materialist explanation:  namely, that  Russia’s team had promised a much more generous budget than the French; the Chambre syndicale des Constructeurs d’Automobile, the Association professionnelle des Banques, and the rest of the list, not to mention Solvay and their 5000 F, carry much less weight in today’s globalized economy than they did 50 or 100 years ago.

It’s all about the Benjamins, in other words; or more precisely, about the николай николаевичи —  the External Goods to which MWA devotes such obsessive attention.  The money for the ICM has to come from somewhere.  Who would seriously argue that private sources like the Union des Chambres syndicales de l’industrie du pétrole are really less tainted than the funds provided by the Russian government  or the St. Petersburg administration?   Besides, the many countries represented at the São Paulo meeting were perfectly aware that xenophobia had been a dominant theme in French elections for over 30 years — remember that at the same meeting they had voted to remove the name of Rolf Nevanlinna, who had presented the Fields Medals just 40 years earlier, from the computer science prize, because of his Nazi sympathies.  And they knew all too well that France’s next presidential elections would be taking place before the 2022 ICM, with unpredictable results.


The candidate elected in 2022 will still be French President in 2026.  But this may be irrelevant.  The rumor is that New York will be bidding for the honors, with External Goods to be provided by the city’s robust financial services industry.  I estimate that something like $30 million would be needed to cover the difference between 10 nights of hotel accommodations for 10000 participants in New York as compared to Paris, under normal circumstances; but maybe New York’s team knows how to transcend normal circumstances.  Most intriguing, of course, is the prospect that the United States will have a very different kind of head of state by then.


Photo September 20, 2018, Union Square, New York




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?