Category Archives: Values

The diversity statement controversy, III


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

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

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

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

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

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

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

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

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

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

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

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.

The Ted Hill affair and the new Science Wars

the gap is so vast between whatever such studies measure and anything resembling an appreciation of the difficulties of coming to grips with the conceptual content of mathematics… that the label of science simply doesn’t apply.

The full article is at Politics/Letters.  See my article in Science for the People for an idiosyncratic comparison of the New Science Wars with the vintage version.