Category Archives: Values

The inevitable questions about automated theorem proving

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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.

Can mathematics be antiracist? Part II

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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? 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.

 

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 particlesforjustice.org 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 researchseminars.org, for example

Untitled

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

MSRIMIT

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.

Meritocracy

From the Strike4BlackLives page at particlesforjustice.org:

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
institutions.

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.

#SHUTDOWNSTEM

SHUTDOWNSTEM+(1) image

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)

 

WCET

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 )

 

It’s official: the author of MWA is not a philosopher

For anyone who read MWA it’s obvious that its author would never be mistaken for, nor would want to be mistaken for, a philosopher.  Still, three referees for the journal Synthèse were kind enough to put to rest any lingering doubts on that score (there were none) in their reviews of the article I have just posted on arXiv under the title Virtues of Priority.

In the fall of 2018 I received a message inviting me to contribute to “a special issue of the philosophy journal Synthèse on virtues and mathematics.”  The prospective guest editors wrote, “We would be delighted to be able to list you as a prospective contributor. This would, of course, be in no way binding on either party.”  This looked like the perfect excuse to write on a topic that had been much on my mind ever since the controversy broke out among number theorists on the correct attribution of the conjecture on modularity of elliptic curves.  From the very beginning this controversy was marked by the contrast between the acrimony with which certain colleagues addressed one another and the superficiality of the analysis with which they justified their positions.  Even while Wiles labored in secret in his attic, I was already wishing for a philosophical umpire to require the warring parties to base their arguments on general principles rather than on raw chronology and personal affinities.

The story is interesting, well written and the conjecture as well as the main actors play important roles in 20th century mathematics. In that sense the paper was a good read, but a good read is not enough to make a good philosophical paper.… The paper does not connect to the current debates on value ethics in mathematics at all; in fact, none of the papers on the reference list belongs to the philosophy of mathematics, and the most recent reference is from 2001. The paper should be situated more firmly in the recent literature on mathematical values … Along the same line, the paper does not make a clear and substantial contribution to current philosophical debates on virtues in mathematics. The paper does not contain a clear problem statement, and the virtues encountered in the historical case are only commented on en passant, but the paper does not provide a structured discussion or a collected conclusion. … The paper lacks methodological reflections. Why is the case in question a good case to explore the philosophical questions at hand and why are the chosen sources the right sources to explore the case? It should be made crystal clear why a dispute over priority of a conjecture is a good case to explore the nature of mathematical values.

A second referee was more encouraging:

This submission represents an excellent idea for an article and a solid initial effort at fulfilling that idea, not yet suitable for publication in Synthese.

but this indulgence can be dismissed because the referee is someone I know.  And, as this referee accurately perceived,

the virtue ethics aspect currently reads as something tacked on to a stimulating but not philosophy-journal-ready fireside/blackboard-side chat about a curious and gossip-ready extract of the history of the theory of elliptic curves.

The third referee’s objections came under three headings:  “The philosophical upshot of the paper is thin,” “The paper neglects other work on priority disputes,” and most tellingly, “The search for a functional significance of the dispute may be overstated”:

Merton observes that, in some instances, battles over priority have no functional significance (i.e., the authors fight over the priority of a finding even if the discoveries are independent and epistemically equivalent). This is due in part to the reward system of science. Moreover, along the same lines, there is a psychological explanation in terms of ego-protective biases. The paper should examine this possibility more closely.

This last objection is silly.  Referee number 3 may never have met anyone as ego-protective as several of the protagonists of the controversy, but the point of my essay was to ask whether the controversy might not shed some light on the value system driving contemporary mathematics — and “functional significance” is not the point either.

In nearly all other respects all three referees were absolutely right about the article.  It did not connect to current philosophical debates, it did not engage in methodological reflections, it neglects the literature on priority disputes, and it was not written in the style of a philosophical paper.  But this is not what I thought the editors had in mind when they asked a mathematician for a contribution.

I accepted the invitation to contribute to the special issue in good faith, on the assumption that the issue’s editors had good reason to believe that the thoughts of a professional mathematician on the roots of an unusually bitter controversy in the field would have a place in the journal, and could provide useful raw material for analysis by philosophers who are curious about the value systems that actually guide the practice of professional mathematicians, even though the mathematician in question has never claimed to be a philosopher.    Had the editors of this special issue made it clear to me that my submission would be judged on the basis of familiarity with “the current debates on value ethics in mathematics,” as these are pursued by philosophers who “have been taught mathematics at university level,” or by its author’s efforts to situate the submission in relation to “relevant secondary scholarship,” I would have replied that I have neither the time nor the inclination to undertake a project on that basis.  That the editors of Synthèse and the referees find it helpful to erect artificial barriers* to dialogue between professional scientists and those philosophers who claim to be interested in the values of such scientists is not my concern.   But I consider it unprofessional as well as irresponsible on the part of the issue’s editors to have failed at any time to explain to me the unfamiliar standards that would be applied to my article.

This was my response to the rejection letter from Synthèse, which concluded:

I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every success in finding an alternative place of publication.

Finding a place of publication on arXiv was easy and is a perfectly satisfactory alternative, but philosophers may not think to look there for raw material.  I consulted with the philosopher David Corfield — who first convinced me of the relevance of Alasdair MacIntyre’s virtue ethics to mathematical practice in the article he published in Circles Disturbed — and he offered to help draw out the philosophical material through a dialogue on the n-Category Café.  His first comment on the arXiv publication is already online.


*In view of the events of the last few weeks, I am now ready to acknowledge that fears of disciplinary cross-contamination may be justified in some circumstances.

The diversity statement controversy, III

demographics

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

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

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

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

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

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

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

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

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

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

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

The diversity statement controversy, II

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From AMS Notices, January 2020, online only, p. 1

One of the minor virtues of Goodwillie’s piece, quoted in the previous post, is its clarity regarding the meaning of “diversity” in the institutional setting.  The word appears only twice, neither time with an unambiguously positive valence:

Institutional diversity is all very well, but if the “different” people do not feel truly welcome, and if mismatches between the institution and the worlds that the students are coming from are ignored, then the institution has failed them.

I’d like to think that a job applicant who meditated on Goodwillie’s post would be well-prepared to write a genuinely meaningful diversity statement.  But it would be much more than a “cuddly, feel-good” sort of diversity statement;  it might even be seen as dangerously close to the kind of commitment to social justice that the 1978 Supreme Court ruled out as grounds for affirmative action.

In contrast, no one comes off well in this latest controversy.  I had prepared a point-by-point list of some of the problematic arguments made in each of the texts, starting with Thompson’s essay and continuing through the open letters written for and against, as well as Chad Topaz’s blog post at QSIDE.  But a friend made the following comment upon reading an earlier draft:

THINK THIS WHOLE SECTION BELOW IS CONFUSING AND DOESN’T REALLY FOLLOW THROUGH ON YOUR CRITIQUE OF DIVERSITY ABOVE.  THE POINT, IT SEEMS TO ME, IS THAT NO ONE IN THE THOMPSON CONTROVERSY (THOMPSON INCLUDED) TAKES THE COATES POINT.  HER SUPPORTERS OBJECT TO BEING ASKED TO MAKE A DIVERSITY STATEMENT AND HER CRITICS PROTECT DIVERSITY AS IF IT REALLY COULD ADDRESS INSTITUTIONAL RACISM.  ALL YOU DO BELOW IS QUIBBLE WITH EACH SIDE, BUT YOU DON’T NAIL YOUR CRITICISM IN TERMS OF WHAT YOU WROTE ABOVE.

My friend is absolutely right.  I enjoy a good quibble as much as anyone, but it’s best to keep it private.  Besides, the most serious of my points was the suggestion that the AMS Notices open its pages to an extended debate on the important topic of … inclusion and exclusion … including but not limited to the role of diversity statements.   It turns out that this debate already began in the January 2020 issue of the Notices, which arrived in my mailbox yesterday.  The for and against letters are included, and a second for letter again, with all the signatures; the total occupies a 21-page pdf file.  It’s therefore likely that more than 1400 people knew, as I did not, that my suggestion was superfluous.  This is a sign that I should perhaps be expressing myself with more humility.

I note, however, that nowhere in the 21 pages of the Notices file does anyone “take[s] the Coates point,” as my friend put it.  Lewis Powell is not identified as the author of the “diversity” opinion, and the Bakke case is only mentioned once, in passing, and in a way that, perhaps inadvertently, confirms “the Coates point.”  Xander Faber’s letter quotes this comment by Supreme Court Justice Harry Blackmun:

In order to get beyond racism, we must first take account of race. There is no other way. And in order to treat some persons equally, we must treat them differently.

The context of Blackmun’s comment, however, was his Separate Opinion,  written to clarify his agreement with the minority position in the Bakke case.   This is the position that lost out to the “cuddly, feel-good” diversity that, thanks to Powell and four other Justices, has been the limit of what the law of the land protects since 1978.  To me it is counterintuitive to rely on Powell’s vocabulary to “uphold Blackmun’s words,” as Faber writes, when the continuation of the Blackmun comment — “We cannot – we dare not – let the Equal Protection Clause perpetrate racial supremacy.” — was written as an explicit rebuke to Powell’s reasoning.

Faber’s letter has the merit of appealing to evidence, in the form of “an extensive report” produced by UC Berkeley “that documents the effect of hiring with a diversity focus in mind.”  Here is what that report had to say (on p. 49) about the effectiveness of diversity statements:

Beyond the applicant stage … no clear and consistent patterns in the data emerged that would suggest a positive statistical correlation between this practice and diversity.  We suspect there may be considerable variation in how search committees implemented this practice, and we speculate that these differences may have obscured the potential value of some forms of implementation. In addition, different institutions may use information about candidates’ commitment to diversity in different ways, and when these can be studied separately, some may emerge as considerably more promising than others. Anecdotal evidence from other UC campuses suggests that much may depend on the extent to which strong or weak “diversity statements” are used as potential deciding factors during the search deliberations. On the basis of our data and analyses to date, however, we do not think we can conclude that this is a practice showing clear promise.

This is hardly a ringing endorsement of diversity statements as a way to enhance even diversity of the “cuddly, feel-good” variety,  much less as a means of realizing the more ambitious aims of equity and inclusion to which Faber refers in his letter.  I wonder whether Faber disagrees.

Overall I have to assume that when people in this debate use the word “diversity” they have in mind something like “equity” or even “social justice” — the opposite of the meaning  Powell set out in his 1978 opinion.   Institutions like the Regents of the University of California may be confined to the legal straitjacket that Justice Powell designed for them more than 40 years ago, but there is no reason that a colleague who is genuinely committed to the values of equity or social justice should feel obliged to express their values in Powell’s vocabulary.

P.S.  I’m not sure I agree with Thompson’s judgment that “Requiring candidates to believe that people should be treated differently according to their identity is … a political test,” [my emphasis] but it is certainly political. Assuming that the US approach to identity politics has universal political validity is a symptom of the provincialism — not to say cultural imperialism — that comes too naturally to people who live in this country, wherever their opinions fall on the political spectrum.  It is particularly unwelcome as the default position of the inclusion/exclusion blog with regard to decisions that affect the very international population of candidates for jobs in the United States.  Some of these candidates come from countries where treating people “differently according to their identity” is strictly illegal.  Depending on what is meant by “treat,” this is arguably also the case in the United States — the “equal protection clause” of the 14th Amendment to the U.S. Constitution is cited 31 times in the Bakke case that is at the origin of all this talk of diversity.   I sincerely regret that Blackmun’s position did not prevail in 1978, but it doesn’t help anyone to pretend that it did.

 

 

The diversity statement controversy, I

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Supreme Court Justice Lewis F. Powell, author of the legal definition of “diversity”; PD-USGov

Colleagues who are confused by the ongoing controversy surrounding Abigail Thompson’s article in the Notices of the AMS on mandatory diversity statements should reread what Ta-Nehisi Coates had to say about “diversity” in his article “The Case for Reparations“:

Affirmative action’s precise aims… have always proved elusive.  Is it meant to make amends for the crimes heaped upon black people? Not according to the Supreme Court. In its 1978 ruling in Regents of the University of California v. Bakke, the Court rejected “societal discrimination” as “an amorphous concept of injury that may be ageless in its reach into the past.” Is affirmative action meant to increase “diversity”? If so, it only tangentially relates to the specific problems of black people— the problem of what America has taken from them over several centuries. …

America was built on the preferential treatment of white people—395 years of it. Vaguely endorsing a cuddly, feel-good diversity does very little to redress this.

Thompson, a Vice-President of the AMS and Chair of the mathematics department at UC Davis, wrote her essay to object to the UC system’s use of mandatory diversity statements to “screen out [job applicants] early in the search process.”  While she compares these statements to the “loyalty oaths” that the UC Regents required during the McCarthy period, and Melissa Lutz Blouin, speaking for the UC Davis administration, retorted that

Diversity, equity and inclusion statements foster productive discussions on how current and prospective faculty can shape and improve the learning and working environment in higher education…

neither Thompson’s original article nor the subsequent controversy makes it clear whether the UC Regents favor “cuddly, feel-good” diversity statements or are willing to consider statements that relate more than tangentially to the specific problems of the communities whose concerns they are meant to address.

Coates, unlike most of the mathematicians and bloggers who have weighed in on the topic since Thompson’s essay appeared, is deeply familiar with the history of the term “diversity” within the jurisprudence that underlies UC Davis’s approach to affirmative action.   When the Bakke case to which Coates refers was decided, it was considered a defeat by those who hoped to use affirmative action as a means to remedy historical discrimination.  Alan Bakke, the plaintiff, claimed that his constitutional rights had been violated when he was rejected — by UC Davis, of all places! — because the medical school had set aside 16% of its slots for minority students.  The California Supreme Court agreed with him, and the US Supreme Court followed suit — Bakke was admitted later that year.  The Court’s judgment, written by Justice Lewis Powell, did allow affirmative action, but only as a way of “obtaining the educational benefits that flow from an ethnically diverse student body”:

An otherwise qualified medical student with a particular background — whether it be ethnic, geographic, culturally advantaged or disadvantaged — may bring to a professional school of medicine experiences, outlooks, and ideas that enrich the training of its student body and better equip its graduates to render with understanding their vital service to humanity.

(Bakke, pp. 306, 314).  Translating Powell into plain English:  an ethnically diverse student body is desirable as a bonus benefit that can “enrich” the experience of the (presumably white) majority.  Or, to quote Christopher Newfield’s Unmaking the Public University, as I already did three years ago in this post,

…in Powell’s diversity framework, diversity was the expression of an institution’s freedom to choose particularly attractive individuals, and was about ensuring this freedom for powerful institutions like… Harvard College.…Diversity acquired social influence not as a moderate mode in which to pursue racial equality but as an alternative to that pursuit.

I am suspicious of any attempt to ground a progressive approach to any question whatsoever in the ideas of the supremely sinister Powell, author of the notorious Powell Memorandum, which Wikipedia accurately calls “the blueprint for the rise of the American conservative movement.”  While the Regents of the University of California are legally bound by a jurisprudence that serves, as a friend wrote, as a means of “deflecting attention from the structural issues to the individual ones,” why is the AMS inclusion/exclusion blog so attached to the policy?  I suspect it is because its readers and authors, unlike Coates or Newfield, imagine that “diversity” can be translated into the aspirations expressed in Thomas Goodwillie’s post on that same blog.  Goodwillie’s text, which is extraordinary for its thoughtfulness and humility, should be studied before reading the second part of this post.