The diversity statement controversy, II


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:


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


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.




Roundtable video, incorrect proofs, true theorems

The Helix Center has now posted the video of Saturday’s round table on “Mechanization of Mathematics”.  The discussion was lively and everyone agreed that we should meet again, or even that we should organize a conference on the theme.

Since concern about correctness of proofs is one of the primary motivations of mathematicians who are active in automated proof verification, it was interesting to hear several colleagues at the IAS quote the following remark about Solomon Lefschetz:

He had marvelous intuition, and so far as I know, all of the results he claimed in algebraic geometry have now been proved. When I was a graduate student at Princeton, it was frequently said that “Lefschetz never stated a false theorem nor gave a correct proof.”

This is Philip Griffiths reminiscing, in his contribution to the biographical memoirs of Lefschetz (on p. 289).  The Helix Center discussion did raise the question of mechanizing mathematical intuition, but didn’t reach any conclusions.  The mathematicians I know would prefer to have correct proofs of correct theorems, but if our choice were between mechanical generators of false proofs of false theorems and false proofs of true theorems I guess we would pick the latter — especially if they were as consequential as the hard Lefschetz theorem.

And indeed, I was surprised to learn — but perhaps I should not have been — that Griffiths’s description of Lefschetz fits quite of few of the mathematicians I have most admired (I won’t name names).

Several people I admire were in the audience and others were watching the livestream.  Kevin Buzzard congratulated me for finding a way to quote William Burroughs (at 53′).  I repeat the quotation for the reader’s convenience:

[The] junk merchant does not sell his product to the consumer, he sells the consumer to his product. He does not improve and simplify his merchandise. He degrades and simplifies the client.

—William Burroughs, Naked Lunch

UPDATE:  A point I was trying to make at the roundtable, and also in the middle of this article, and in this post, about the inevitability of mechanization of mathematics (and of everything else, and of the monetization of the resulting data by tech companies), is made much more clearly and forcefully by Rose Eveleth in an article published today on Vox.


Roundtable on Mechanization of Mathematics

From the announcement:

Proof, in the form of step by step deduction, following the rules of logical reasoning, is the ultimate test of validity in mathematics. Some proofs, however, are so long or complex, or both, that they cannot be checked for errors by human experts. In response, a small but growing community of mathematicians, collaborating with computer scientists, have designed systems that allow proofs to be verified by machine. The success in certifying proofs of some prestigious theorems has led some mathematicians to propose a complete rethinking of the profession, requiring future proofs to be written in computer readable code. A few mathematicians have gone so far as to predict that artificial intelligence will replace humans in mathematical research, as in so many other activities.

One’s position on the possible future mechanization of proof is a function of one’s view of mathematics itself. Is it a means to an end that can be achieved as well, or better, by a competent machine as by a human being? If so, what is that end, and why are machines seen as more reliable than humans? Or is mathematics rather an end in itself, a human practice that is pursued for its intrinsic value? If so, what could that value be, and can it ever be shared with machines?

With Stephanie Dick, Brendan Fitelson, Thomas Hales, Michael Harris (who will largely follow the script already presented here), and Francesca Rossi.  At the Helix Center, 247 East 82nd St.

Mathematics, music, philosophy, and Alain Badiou


Panel at IRCAM, June 7, 2019.  Left to right:  François Nicolas, Yves André, Fernando Zalamea.  Alain Badiou is seated in the audience on the left.

To celebrate the publication of the third and final volume of Alain Badiou’s Being and Event trilogy, the organizers of the Paris MAMUPHI seminar — MAthématiques, MUsique, PHIlosophie — devoted a two-day conference at IRCAM (Institut de Recherche et Coordination Acoustique/Musique), under the title L’hypothèse du contemporain.

For the 20th anniversary of the Mamuphi seminar (mathematics-music-philosophy), these encounters are dedicated to L’Immanence des vérités, the latest work by the philosopher Alain Badiou, and, more particularly, to his theory of “works-in-truth”. How are works distinguished from “waste” and, incidentally, “archives”? The final part of the work by Badiou formalizes a limitless alternative to the oppression of finality. These days in June gather together mathematicians, musicians, philosophers, and the author to formulate their own hypothesis in the shadow of their reading of the contemporary in the 21st century.

Yves André invited me as one of the mathematicians, and because of my deep respect for André’s writings about mathematics — and of course for his mathematical work — I was pleased to accept the invitation.

Badiou’s three-volume system is heavily based on set theory and much of the third volume is devoted to the theory of large cardinals, with chapters on ultrafilters, theorems of Scott, Jensen, and Kunen, 0#, and much more.  I have no idea what the upcoming Columbia graduate workshop will make of all this.  My own presentation had nothing to do with set theory; my aim was to explain why Badiou was wrong to hint in his book, in passing, that the mathematics of Andrew Wiles belonged with the “waste,” or at best the “archives.”  You can watch my talk or you can read it (preceded by a couple of pages explaining my misgivings about the theme of the conference).

I have to confess a less highbrow motivation, though.  Here is an excerpt from a review by Stanley Chang of Mathematics without Apologies that appeared in Society, dated June 25, 2018.

Other reviewers, both academics and nonacademics, have quite forcefully deprecated his use of ideas without context, the irrelevancy of various sections, an unreadably poor organization, and a purposely opaque stream-of-consciousness that prohibits understand [sic] rather than encourages it. One of my own friends, an anthropologist in academia, laughingly said that his treatment of Badiou is something that you would expect from a bad first-year philosophy essay from a bad student at a bad university.

Although Chang gave excellent reasons for his evident dislike of the book, he went out of his way to give it a fair reading, and I have no problem with his review.  But why did he make up this part about Badiou?  MWA contains no “treatment of Badiou.”  According to the index, Badiou’s name appears three times, and only in endnotes.  Two of the references are direct quotations, without anything that can be construed as a “treatment,” and the third quotes Juliet Flower MacCannell’s comments on a quotation by Badiou regarding Lacan’s theory of love, along with Vladimir Tasić’s gloss on the quotation and the comments.

In the Q&A following my talk in Paris I got a laugh from Badiou by suggesting that the mere mention of his name would provoke the laughter of many American philosophers, not to mention anthropologists.  But I don’t think that explains Chang’s sentence.  Maybe he was confusing Badiou with Bourdieu?  Or maybe the treatment in question was on this blog, for example here?

I would fault the editors of Society for allowing the publication of that last sentence, or any sentence, on any subject whatsoever, that quotes an anonymous anthropologist — laughing no less — for the sole purpose of taking a cheap shot.  But in fact I have no idea what the sentence is about.

Villani is running for Mayor of Paris, but what does he represent?

You can read about it in English in a Reuters article signed by Elisabeth Pineau and Michel Rose, or in French in (among many other places) a Le Monde editorial (not behind a paywall).  But mostly you’ll read about how Macron’s strategy to win a symbolic victory over the established parties of the center-right and center-left has been “plunged into uncertainty.”  That doesn’t make for a very uplifting story.  You can test the argument Villani himself has put forward to motivate his candidacy

“Many complex problems will need to be worked out, which can be done by working together playing to our strengths,” Villani told supporters. “I’ve been tackling complex problems my whole life before entering politics.”

by substituting his fellow Fields medalists, one after another, for the “Lady Gaga of Mathematics”:  are you convinced?

His more relevant “strengths” can be read off the list of supporters who attended the announcement of his candidacy:

…nombre de ses soutiens sont à puiser chez les déçus de la “macronie”.

On y trouve le député Matthieu Orphelin, un proche de Nicolas Hulot qui a quitté le parti présidentiel en février, la députée Anne-Christine Lang, élue du 13e arrondissement, un ancien porte-parole de LaRem, Rayan Nezzar, et Paula Forteza, élue LaRem des Français de l’étranger.

(from the unsigned French Reuters article published on Mediapart but behind a paywall.)

The candidate Macron originally preferred has his own supporters:

Face à [Villani], Benjamin Griveaux peut compter sur l’appui du président de l’Assemblée nationale, Richard Ferrand, de Stanislas Guerini, de son ancien collègue Mounir Mahjoubi – ex-soutien de Cédric Villani – et de ministres comme Marlène Schiappa et Agnès Buzyn.

Meanwhile, the incumbent Socialist mayor Anne Hidalgo has yet to start her campaign for reelection, but her chances are looking considerably better since Macron’s movement split.  Here’s Hidalgo, looking very mayoral at a ceremony last year honoring the exiles of the Spanish Republic who played a crucial role in liberating Paris in 1944.


The Reuters article will tell you that this split

… could help Hidalgo win re-election, despite her own unpopularity due to the congested streets and polluted air of Paris.

This claim, which is typical of the English-language media, should not be taken at face value.  The bitterest attacks on Hidalgo have come from drivers, often from the wealthy western suburbs of Paris, who complain about her administration’s closure of parts of the city center to automobile traffic.  This policy has been promoted by her Green party allies (EELV — Europe Écologie les Verts) in the Paris city council.  Yannick Jadot, EELV’s candidate in the 2017 presidential election, has no problem with Hidalgo on that score:

“Le bilan d’Anne Hidalgo en matière d’écologie est celui des écologistes. Donc cette partie là, j’en suis très fier”, déclare Yannick Jadot.

Villani, meanwhile, announced that

he would be Paris’ first “truly environmentalist mayor”

But what does that mean?