Announcing a new newsletter on mechanizing mathematics

I have finally got around to creating a newsletter, tentatively entitled Silicon Reckoner, to be published on Substack. This will be a continuation of the recurring discussion on this blog of the implications of projects to mechanize mathematics, for example in this post or this post.

You can read more about the goals of the newsletter below, in excerpts from the first entry. There will be no additions to the MWA blog (the blog you are now reading) for the foreseeable future. However, at least at the outset I plan not to allow comments on Substack; instead, the comments section of this post will be reserved for discussion of the newsletter. As always, I will decide whether or not to approve comments. This is a form of censorship but the purpose is not to exclude (legitimate) points of view but to keep control of the amount of time I spend on this part of my agenda.

I don’t expect to set up paid subscriptions on Substack, but that may change at some point.

And the disclaimer, to appear in the first newsletter entry:

I will not claim familiarity with any of the formal systems used in the design of automated proof checkers, nor to understand any of the software that implements the actual automatic verification, much less to understand the details of current or future work on AI, whether or not it is applied to mathematics.  Even when I have a pretty good idea of what is going on with some of these systems, I will fiercely deny any technical understanding whatsoever, because my understanding of the technicalities should never be an issue. 

Here, then, is what Silicon Reckoner will be about:




Is artificial intelligence on track to meet the expectations of its investors, who just in 2020 poured $50 billion into the industry?  AI’s record of missed deadlines for predicted milestones is as old as its name.  But literary production on the subject could hardly be more extensive.  Reading all the non-technical books on my local bookstore’s AI shelf would be more than a full-time job, leaving less than no time for my real job, which AI has not yet eliminated.  Even the sub- or parallel discipline of AI ethics now occupies 10 pages of footnotes on the English-language Wikipedia page and 1400 pages published in the last two years by Oxford University Press, on my own bookshelf; practically every day I discover another 100 pages or so.   I have nevertheless forced myself to dip into a representative sample as preparation for an experiment that is beginning to take shape with this text. 

Most of what I’ve read tries to address the question of just how “intelligent” the products of this industry have been up to now, or will be in the near future, or what it would take for actually existing AI to deserve to be called “intelligent,” or whether it would be a good thing, or whether it’s even possible.  None of these is my problem.  Or rather, they are my problem, but only as a citizen of my country, or of borderless civilization, concerned, like everyone else, by what the massive implementation of ostensibly intelligent artificial systems would entail for what matters to me — not least, whether it would make sense for these things to continue to matter to me, or perhaps more accurately whether what matters to me would still matter to anyone or anything else, if the ambitions of AI’s promoters even minimally come to fruition.…

My motivation in undertaking this experiment is to understand the consequences of this way of thinking for my own vocation of pure mathematics, which is marginal to the concerns of most of those at risk of the AI project’s collateral damage but which has been central to the project’s imagination and its aspirations from the very outset. 

It is possible to view the growing interest in automated proof verification and artificial theorem proving, two aspects of a still largely hypothetical AI future of mathematics, as stemming from purely internal factors that govern the profession’s development as it evolves to meet its autonomously defined goals.  The ideal of incontrovertible proof has been bound up with mechanization since it was first articulated, and the logic that ultimately made digital computers possible is a direct outgrowth of the attempt to perfect this ideal in the development of symbolic and philosophical logic in the late 19th and early 20th century, and can even be seen as a byproduct of the proof of the absolute impossibility of realizing this ideal.  I don’t think this view is plausible, given the saturation of our culture with AI themes and memes, that goes well beyond bookstores’ overloaded AI shelves.… 

This post is meant to be the first of a series of texts exploring the reasons for the absence of any sustained discussion of these issues on the part of mathematicians, in contrast to the very visible public debate about the perils and promises of AI.  Much of my book Mathematics without Apologies was devoted to a critique of claims regarding the “usefulness” of mathematics when, as is nearly always the case, they are not accompanied by close examination of the perspectives in which an application of mathematics may or may not be seen as “useful.”  Similarity with the intended critique of the uncritical use of words (like “progress”) that accompany the ideology surrounding mechanization — mechanical proof verification and automated theorem proving, in particular — will be apparent.  The reason should be obvious:  unless we can conceive an alternative to conventional measures of utility for which human mathematics is a positive good, the forces that make decisions about this sort of thing will declare my vocation obsolete.  Most of my colleagues who are involved in advancing the mechanization program have conceded the rhetorical battle and some are already forecasting the demise of human mathematics.  So the plan is to continue the discussion in this new format, and gradually to phase out the blog that I launched when Mathematics without Apologies was published, as I have already tried and failed to do once before. 

Because I will be forced to draw on so many different disciplinary perspectives in the course of exploring the topic of mechanization, there is a real danger that these texts will lose any chance of forming a coherent whole.  For my own sake, then, as much as for the sake of potential readers, I propose a slogan that is meant to hold everything together until I come up with a better slogan.  Here it is: 

Current trends in mechanization belong to the history of mathematics, both as events in a historical process and in the creation of common narratives about the meaning of the process. …

A Portrait of Jacques Rancière in Fruit Stickers

Several footnotes in MWA quote the philosopher Jacques Rancière’s Aisthesis:

Jacques Rancière writes that “Art exists as an autonomous sphere of production and experience since History exists as a concept of collective life” and dates this existence back to the mid-18th century…. Replacing Art by (small-m) mathematics in the above sentence, it says that the existence of mathematics as a self-conscious tradition-based practice is tied up with its projection in history, which is consistent with the themes of Chapter 2. The timing for mathematics may be different.

(note 70 to Chapter 3)

The questions of where (or whether) to draw the line between art and technique, or between the artist and the artisan, dominate many of the aesthetic debates of the 19th and 20th centuries, as reconstructed in (Rancière 2011).

(note 40 to Chapter 8)

For the educational benefits of the arts in France, see (Rancière 2011), Chapter 8, especially pp. 173-175. The aesthetic theorists Rancière treats in this chapter, which covers a period stretching from Ruskin through the Paris Exposition Universelle of 1900 to the Bauhaus, have in common a vision of art as “the power to order the forms of individual life and those in which the community expresses itself as community in a single spiritual unity” (p. 178). This ethic of art is much more familiar than the model on which Hardy draws and it is hard to imagine its application to mathematics in any way.

(note 18 to Chapter 10)

But Rancière’s influence on MWA is pervasive in the chapters that attempt to characterize what mathematics has in common with the arts, and goes well beyond what is contained in these few quotations. So I am pleased to share this portrait, created by the French artist who goes by the name Chaix et les étiquettes, at the request of a group of the philosopher’s admirers.

Chaix’s portraits are composed entirely of stickers that he collects surreptitiously, by the hundreds, during visits to the fruit departments of local supermarkets. The detail below reveals that the red background was liberated from a batch of pears, whereas the philosopher’s wavy white hair originally enlivened a stack of Royal Gala apples. The blue eyes are too blurry for me to read.

Does mathematics “progress”?

American Progress, 1872 painting by John Gast; this image is available from the United States Library of Congress‘s Prints and Photographs division under the digital ID ppmsca.09855.

Mechanization of mathematics, at least in certain aspects, has been welcomed as “progress,” notably in a comment on this blog. Most readers of this blog, I suspect, will embrace the “progressive” label, if the alternative is what is being promoted on the Killing Obama’s Radical Progressive Agenda Facebook page. Nevertheless, as the above image reminds us, the notion of “progress” in its current usage is so thoroughly entwined with technological determinism, European colonialism, genocide, and environmental devastation, that it is a struggle to find an interpretation of the word, applicable to mathematics, whose connotations are unequivocally positive.

The OED traces the first use of the word, in the (originally metaphorical) sense of

Advancement to a further or higher stage, or to further or higher stages successively; growth; development, usually to a better state or condition; improvement…

to 1457 in the Acts of Parliament of Scotland, in the sentence

Sen Gode..hes send oure souerane lorde sik progres and prosperite, that [etc.].

The word’s current use evolved from the mid-18th through 19th centuries, from the Enlightenment through the Industrial Revolution. The OED quotes Benjamin Franklin using the word in 1780. In 1794 the Marquis de Condorcet wrote his Sketch for a Historical Picture of the Progress of the Human Mind, “perhaps the most influential formulation of the idea of progress ever written” according to Wikipedia, while hiding on the “rue des Fossoyeurs” (the present-day rue Servandoni) in Paris from the warrant for his arrest issued by the Convention. (By dying in prison, Condorcet escaped the guillotine, “a symbol of the penal, technological and humanitarian progress inspired by the Enlightenment” according to the Open University website.) In the 19th century “progress” was a watchword for thinkers as diverse as Hegel, Comte, Marx and Engels (“entire sections of the ruling class are, by the advance of industry, precipitated into the proletariat [… and] also supply the proletariat with fresh elements of enlightenment and progress”), Darwin, and Herbert Spencer (“the civilized man departs more widely from the general type of the placental mammalia than do the lower human races“).

Gast’s painting is one illustration of the principle, that was generally accepted by European colonizers, including the American settlers, and given clear expression by the German Rudolf Cronau in 1896:

The current inequality of the races is an indubitable fact. Under equally favorable climatic and land conditions the higher race always displaces the lower, i.e., contact with the culture of the higher race is a fatal poison for the lower race and kills them…. [American Indians] naturally succumb in the struggle, its race vanishes and civilization strides across their corpses…. Therein lies once again the great doctrine, that the evolution of humanity and of the individual nations progresses, not through moral principles, but rather by dint of the right of the stronger.

Rudolf Cronau, in Friedrich Hellwald, Kulturgeschichte in ihrer natürlichen Entwickelung, 4th ed., 4 vols. (Leipzig: Friesenhahn, 1896 ), IV: 615-16

Other colonial powers used the notion of progress in similar ways. Gast’s painting is well-known but I only became aware of it last month, when I watched Raoul Peck’s indispensable four-part documentary Exterminate all the Brutes, whose title is a quotation from the character Kurtz in Conrad’s Heart of Darkness, characterized as “an emissary of pity and science and progress, and devil knows what else.” “By the simple exercise of our will we can exert a power for good practically unbounded,” Kurtz said, a few lines before arriving at the words that served as Peck’s title. This was the intellectual matrix in which Hitler formed his world view. The word “progress,” in expressions like “human progress” or “progress of mankind,” appears dozens of times in Mein Kampf. A typical example:

“Not through [the Jew] does any progress of mankind occur.”

Mein Kampf, Chapter XI.

Now that Godwin’s law has been reconfirmed, possibly for the first but certainly not for the last time, in connection with mechanization of mathematics, I can quickly come to the point of this post, which is to draw attention to the questions that are not being asked when the desirability or feasibility of mechanization of mathematics is under debate. Arundhati Roy asked one such question in her first non-fiction book, about the Narmada Dam project:

How can you measure progress if you don’t know what it costs and who has paid for it?

Arundhati Roy, The Cost of Living, Random House of Canada, 1999

Twenty years after the book’s publication, when the dam has submerged at least 178 villages in Madhya Pradesh, Tina Stevens and Stuart Newman defended the precautionary principle as protection from the “hidden agendas of BioTechnical science”:

Precaution does not derail progress; rather, it affords us the time we need to ensure we progress in socially, economically, and environmentally just ways.

Tina Stevens and Stuart Newman, Biotech Juggernaut, Routledge, 2019

Most of the mathematicians and philosophers who promote mechanization are perfectly candid about their agendas, and cannot be suspected of genocidal tendencies. But the potential implications of the widespread adoption of technological solutions to perceived mathematical problems — “what it [will] cost… and who [will pay] for it,” not to mention the question of who stands to benefit — are simply not being acknowledged.

This post is meant to be the first of a series of texts exploring these questions and the reasons for the absence of any sustained discussion of these issues on the part of mathematicians, in contrast to the very visible public debate about the promises and dangers of AI. Much of MWA was devoted to a critique of the notion of “usefulness” in mathematics when, as is nearly always the case, it is not accompanied by a close examination of the perspectives in which an application of mathematics may or may not be seen as “useful.” The similarities with the intended critique of the uncritical use of the word “progress” are evident, but now I want to keep focused on the ideology surrounding mechanization — mechanical proof verification and automated theorem proving, in particular. So the plan is to continue this discussion in a different venue, and gradually to phase out this blog, as I have already tried and failed to do once before.

Freedom for Azat Miftakhov!

miftahov_0

To quote the petition that you are all invited to sign:

In February of 2019, the Moscow State University mathematics PhD student Azat Miftakhov was arrested and detained for manufacturing explosives. Later these charges were dropped. As soon as he was released, he was arrested and detained for another unrelated crime: breaking a window in the office of United Russia, the ruling political party in the Russian Federation. We, along with the international civil rights society Memorial, consider Azat to be a political prisoner, unfairly framed due to his anarchist views. The court extended his pre-trial period multiple times — a year and a half in total — without reason. Law enforcement officials have tortured him, restricted his access to scientific literature, and threatened his relatives’ personal safety.

The Société Mathématique de France published an update on December 21, and called for its membership to sign the petition:

Le procès d’Azat Miftakhov approche de sa conclusion. Les débats sont prévus le 23 décembre. Le verdict devrait tomber peu de temps après.

Le 14 novembre 2020, la SMF a exprimé sa profonde préoccupation face à la détention prolongée  du jeune probabiliste et activiste politique russe qui fut  incarcéré début février 2019. Il est resté emprisonné depuis et a été torturé. Azat Miftakhov est accusé d’avoir cassé une vitre dans un bureau de la “Russie unie”, le parti politique  au pouvoir. Il plaide non coupable.

UPDATE: Azat faces sentencing tomorrow (January 11). This article published in Novaya Gazeta refers to this letter to the organizers of the ICM, and to this letter by the President of the AMS. The petition has meanwhile been signed by more than 2700 mathematicians, and Azat has received support from the Unione Matematica Italiana and the Sociedade Brasileira de Matemática.

The inevitable questions about automated theorem proving

PastedGraphic-1

The author and René Guitart at the conference Alain Badiou:  l’hypothèse du contemporain, IRCAM, June 7, 2019, still from https://medias.ircam.fr/x0f989d

I’ve been saying for some time that most articles about controversies regarding the AI future of mathematics focus primarily on two questions — “Is it good or bad?”  and “Will it work or not?” — while neglecting to reflect on the presuppositions that underlie these questions — what is the good of mathematics, and work to what end? — not to mention what should always be the first question to be addressed to any significant social development — cui bono, in whose interest?  Within the limitations imposed by this conventional frame of reference, last week’s article in Quanta by Stephen Ornes was a good one.  It provided a clear introduction to the subject matter for the well-informed amateurs as well as professionals who read Quanta, recalled the history of attempts to automate proofs — with a helpful reminder that these attempts were originally motivated by the need for computer scientists to verify the reliability of their programs, a theme treated in depth by Donald MacKenzie in his classic Mechanizing Proof — and surveyed some of the most ambitious contemporary projects and their applications within mathematics.

When I agreed to be interviewed for the article it was in the hope of nudging the discussion in the direction of the questions that are typically neglected.  In responding to Ornes’s first message I made only one request:

If you decide you do want to use one or more quotations from me, I would want at least one of them to address this point:  that what pure mathematicians find valuable about what we do is precisely that it provides a kind of understanding whose value is not determined by the logic of the market.
Note my abusive and rather underhanded implicit definition of the pure mathematician as one whose values conform to an impossibly unrealistic ideal.  The impulse to cash in must surely be alive in my professional community as it is in every other corner of neoliberal civilization.  And yet, if the products of our imagination cannot provide an escape from the market, what can?
The sentence quoted above was in the last draft of the article that Quanta showed me, but it did not make the final cut.  (And the editors also disregarded my invitation to use the photo reproduced above, which better conveys my mixed feelings about the whole business than the photo they did use.)  The article’s only hint of the cui bono question was a brief allusion to Christian Szegedy’s group at Google Research.  I don’t know what was in the back of Google’s mind when they decided to sponsor research into automating mathematical proof.  Their business is computing:  maybe they are simply looking to improve software verification, like the original proof automaters.  Or maybe they really are interested in mathematics as such; but I would not count on them to care about “a kind of understanding whose value is not determined by the logic of the market.”  To a very great extent, Google and its Silicon Valley companions are the market.  If Google’s aim is to reproduce what drives us to invent things like homotopy theory and pseudodifferential operators, it can only be because they think they can bottle it and sell it back to us, just as they have done with our search histories and the keywords they extracted from our gmail.
Whether or not you find that “evil” depends on your frame of reference.  Just yesterday I received a notification of an NSF Program Solicitation entitled “National Artificial Intelligence (AI) Research Institutes”:
Artificial Intelligence (AI) has advanced tremendously and today promises personalized healthcare; enhanced national security; improved transportation; and more effective education, to name just a few benefits. Increased computing power, the availability of large datasets and streaming data, and algorithmic advances in machine learning (ML) have made it possible for AI research and development to create new sectors of the economy and revitalize industries. Continued advancement, enabled by sustained federal investment and channeled toward issues of national importance, holds the potential for further economic impact and quality-of-life improvements.

The 2019 update to the National Artificial Intelligence Research and Development Strategic Plan [1], informed by visioning activities in the scientific community as well as interaction with the public, identifies as its first strategic objective the need to make long-term investments in AI research in areas with the potential for long-term payoffs in AI. The President’s Council of Advisors for Science and Technology has published Recommendations for Strengthening American Leadership in Industries of the Future [2], including AI, and calls for new and sustained research in AI to drive science and technology progress. The National AI Research Institutes program enables longer-term research and U.S. leadership in AI through the creation of AI Research Institutes.

This program is a joint government effort between the National Science Foundation (NSF), U.S. Department of Agriculture (USDA) National Institute of Food and Agriculture (NIFA), U.S. Department of Homeland Security (DHS) Science & Technology Directorate (S&T), and the U.S. Department of Transportation (DOT) Federal Highway Administration (FHWA). New to the program this year are contributions from partners in U.S. industry who share in the government’s goal to advance national competitiveness through National AI Research Institutes. This year’s industry partners are Accenture, Amazon, Google, and Intel Corporation.

This program solicitation invites proposals for full institutes that have a principal focus in one or more of the following themes, detailed in the Program Description:

• Theme 1: Human-AI Interaction and Collaboration
• Theme 2: AI Institute for Advances in Optimization
• Theme 3: AI and Advanced Cyberinfrastructure
• Theme 4: Advances in AI and Computer and Network Systems
• Theme 5: AI Institute in Dynamic Systems
• Theme 6: AI-Augmented Learning
• Theme 7: AI to Advance Biology
• Theme 8: AI-Driven Innovation in Agriculture and the Food System

(Emphasis added.)  I’d guess Automated Theorem Proving fits best with Theme 1.  So the researchers quoted are unwittingly (or maybe wittingly) contributing to a logic of national competition.  This sort of language always strikes me as ironic, given the international nature of projects like proof automation, and given my own failure to muster much enthusiasm for French national competitiveness during my years teaching in Paris, in spite of frequent exhortations from the authorities using identical language (but in French, of course).

I shouldn’t complain that Quanta did me the honor of giving me the last word but when I read it in the draft —
Even if computers understand, they don’t understand in a human way.
— I couldn’t believe that I had actually written anything so imprecise.  And I’m still pretty sure I never did; but unfortunately I did speak those words at this roundtable.  The thought is hardly original to me; mathematicians have been saying this in various ways for years, at least since the Appel-Haken solution of the Four-Color Problem.  I tried to add some content by revising the sentence to restore the context in which it was spoken:
Even if we do want to attribute understanding to computers, it won’t be the kind of understanding we attribute to human beings.
This amendment, too, was included in the last draft I saw, but the sentence reverted to the shorter version.  I should not have been surprised:  the published sentence is meaningless but is admittedly more journalistically effective.  On this blog I’m not constrained by a word limit, so let me revise the sentence one more time:
Even if we do want to attribute understanding to computers, it won’t be the kind of understanding we currently attribute to human beings.
The word “currently” reflects my expectation that the industrial version of proof automation, which is where I suppose this is all heading, will lead not only to a reconsideration of the purpose and nature of mathematical proof — hardly for the first time — but also to a new adaptation of human understanding to the needs of machines.  This is in line with the industrial imperative Shoshanna Zuboff sees in what she calls surveillance capitalism:

With this reorientation from knowledge to power, it is no longer enough to automate information flows about us; the goal now is to automate us.

(S. Zuboff, The Age of Surveillance Capitalism, p. 15.)  On Zuboff’s telling, Google, naturally, was the pioneer in this process.

Whom shall we cancel?

MbembeSo much virtual ink has been virtually spilled over a letter in Harper’s, signed by intellectuals and authors and public figures with an unlikely range of political orientations, but united by opposition to “a new set of moral attitudes and political commitments that tend to weaken our norms of open debate and toleration of differences in favor of ideological conformity” — what the media call “cancel culture” — that it’s time to ask whether the history of mathematics also contains episodes or individuals we might want to consider cancelling.  A ripe candidate for cancellation is Oswald Teichmüller, who explained in the fall of 1933 why he organized a boycott of Edmund Landau’s lectures, after the Nazis came to power earlier that year:

Through yesterday’s action a completely new situation has now been created. In order to restore peace in our institute it is necessary, above all, to clear up the fundamentals behind it. You spoke of your belief that what happened yesterday was an anti-Semitic demonstration. My standpoint was, and continues to be, that an anti-Jewish individual action might rather be directed against everyone else than against you. I am not concerned with making difficulties for you as a Jew, but only with protecting – above all – German students of the second semester from being taught differential and integral calculus by a teacher of a race quite foreign to them. I, like everyone else, do not doubt your ability to instruct suitable students of whatever origin in the purely abstract aspects of mathematics. But I know that many academic courses, especially the differential and integral calculus, have at the same time educative value, inducting the pupil not only to a conceptual world but also to a different frame of mind. But since the latter depends very substantially on the racial composition of the individual, it follows that an Aryan student should not be allowed to be trained by a Jewish teacher.

What I find troubling is not so much that courses on “Teichmüller theory” are being taught in Bonn — practically every year, apparently — but that this year, in the very same state of Nordrhein-Westfalen (NRW), an otherwise little-known member of the Landtag for the Free Democratic Party named Lorenz Deutsch called for cancellation of  the invitation of the philosopher and political theorist Achille Mbembe (pictured above) to give the opening speech at the Ruhr Trienniale arts festival.  Deutsch accused Mbembe of antisemitism for having signed a South African BDS petition, and of “relativizing” the Holocaust, rather than recognizing its Einzigartigkeit.    What began as a provinzielles politisches Hickhack, in the words of Deutsche Welle, turned into “Causa Mbembe,” the dominant theme in the spring’s German social debate (“beyond” Coronavirus, again according to Deutsche Welle) in which the full resources and richly polysyllabic vocabulary of German speculative philosophy were brought to bear on a handful of marginal passages in Mbembe’s collected works, both in support of and in opposition to their author.  The multiple ironies of the debate were not lost on the 700 African intellectuals whose open letter to German Chancellor Angela Merkel and President Frank Walter Steinmeier recalled Germany’s own bloody history as a colonial power (Mbembe’s native Cameroon was for a time a German colony).

Soon after “Causa Mbembe” began, the Ruhr Triennale was cancelled, ostensibly because of Coronavirus, although the festival’s director had offered to maintain the event in another form; Mbembe’s speech was cancelled along with it.  That this decision was part of a pattern of cancellations of intellectuals and artists, whose positions on the Boycott, Divestment, and Sanctions movement were considered out of bounds for German public discourse, was noted in a letter signed by 426 artists and intellectuals, but the Harper’s letter ignored this state-sponsored version of “cancel culture.”

But to return to mathematics, how would we go about cancelling Teichmüller (and Ernst Witt, and Ludwig Bieberbach, just for starters)?  We could rename Teichmüller spaces after a prominent victim of the Nazis — Anne Frank, for example — or after Landau himself.   Colleagues who object that neither Frank nor Landau had anything to do with Teichmüller spaces (or Witt vectors, or the Bieberbach Conjecture) can be referred to Stigler’s law of eponymy — which is applicable well beyond mathematics:  Medici didn’t design the Medici Chapels, Rockefeller didn’t build Rockefeller Center, Saint John the Divine didn’t build his Cathedral…

The whole tradition of assigning names to things in mathematics is totally out of control and always has been; mathematics has no central naming authority comparable to the Internet Corporation for Assigned Names and Numbers, although names of theorems and mathematical structures undoubtedly have a longer half-life than domain names on the internet.  Whether or not we eventually choose to embark on a full-scale iconoclastic renaming campaign — and to run the risk that we will soon find reason to regret our choices once again — it would be wise to remember that our profession’s patron saints were not only flawed human beings but that, in many cases, benefiting from racism was among their flaws.  Thus Science magazine pointed out just over a year ago that Isaac Newton’s theory of gravitation was developed with the help of figures “from French slave ports in Martinique,”  and reminds us that the Royal Society “invested in slaving companies,” as did many of my own university’s early benefactors.   (Leibniz, on the other hand, did once develop the argument that chattel slavery is morally impermissible.)

Gaspard Monge, who participated in Napoleon’s expedition to Egypt — the first modern European attempt to dominate the Middle East — had been the Minister of the Colonies under the Girondin government; at no point in his career did he allude to the Sainte-Domingue slave revolt of 1792, the main event that took place while he was Minister, and there is no indication that he protested when Napoleon reestablished slavery in 1802.  A bit later we have the case of Charles Dupin, remembered as a politician rather than a mathematician, but still a member of the Académie des Sciences and sufficiently concerned with mathematics to have managed to get Legendre’s pension restored. If he is indeed remembered as a “liberal” politician it was for his defense of slavery, “with the help of statistics”:

Il est l’auteur, en 1838, d’une brochure intitulée Défense des intérêts coloniaux confiés au Conseil des délégués pendant la législature de 1833 à 1838 dans laquelle il vante la situation des esclaves dans les colonies françaises en l’opposant au sort des Noirs libres des colonies anglaises, en présentant, à grand renfort de statistiques, une moindre mortalité infantile chez ceux qu’il appelle les « non-libres » pour ne pas avoir à utiliser le terme « esclave », ce qui est, selon lui, une « nouvelle preuve de la douceur et des bons soins que les maîtres prodiguent aux mères ainsi qu’à leurs enfants esclaves.

It makes no sense to say that Dupin’s ideas were in the spirit of the times; Condorcet had already refuted them 50 years earlier, in his Réflexions sur l’esclavage des nègres.  Even if Condorcet’s proposal, that would have fully eliminated slavery only after 70 years, is hardly compatible with current values, I would think twice before voting to cancel this particular mathematician, whose statue in Paris was already cancelled to provide metal for the Nazi war effort.

There is a substantial literature on the behavior of mathematicians and their institutions in Nazi Germany (see Michèle Audin’s review  of the book by Reinhard Siegmund-Schulze, and the references at the end).  When a comparable study of the role of mathematics and mathematicians with regard to slavery and colonialism is available, we can ask the question raised in the Science article mentioned above:

Now that the link between early science and slavery has come to light, an important question remains: What should scientists do about it?

The article continues:

Historians say acknowledgment is a start…

Can mathematics be antiracist? Part II

BrooklynBridge

Brooklyn Bridge, July 4, 2020

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

 

 

Can mathematics be antiracist? (while awaiting Part II)

Metro_audin

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.