Author Archives: mathematicswithoutapologies

Mathematicians on strike in Paris

maths-en-lutte

As a public service, I am copying the message that just arrived on my Jussieu account:

Pour les collègues présents à Jussieu qui souhaitent aller manifester (mes excuses pour les autres), il y a un rendez-vous :
Vendredi 24 janvier, 10h devant la tour 26.
And here are the minutes of a meeting between students and faculty on the ongoing strike, held on January 20:
CR_REUNION_UFRMATH_20_01_2020

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.

Reuben Hersh, 1927-2020 (with text)

Here is the introduction to my article Do Mathematicians Have Responsibilities, published in Humanizing mathematics and its philosophy.Essays celebrating the 90th birthday of Reuben Hersh.Edited by Bharath Sriraman. Birkhäuser/Springer, Cham (2017) 115-123.

I have been an admirer of Reuben Hersh ever since I received a copy of The Mathematical Experience, then brand new, as a birthday present.  At that stage, of course, I was admiring the tandem Reuben formed then, and on other occasions, with his co-author Philip J. Davis.  It was only almost 20 years later, after I started reading What is Mathematics, Really? that I could focus my admiration on Reuben — and not only on the mathematician, the author, the thinker about mathematics, but on the person Reuben Hersh — the unmistakable and unforgettable voice that accompanies the reader from the beginning to the end of the book.  So unforgettable was the voice, in fact, that when Reuben, wrote to me out of the blue three years ago to ask me what I thought about a certain French philosopher, I so clearly heard the voice of the narrator of What is Mathematics, Really? (and no doubt of many of the passages of his books with Davis) that I could honestly write back that I felt like I had known him for decades, though we have never met and until that time we had never exchanged a single word.

The voice in question is the voice of an author who is struggling to put words on an intense and intensely felt experience, who has intimate knowledge of how it feels to be a mathematician and also a knowledge no less intimate of the inadequacy of the language of our philosophical tradition to do justice to that experience, so that all attempts to do so inevitably end in failure; but this knowledge is compensated by the conviction that the stakes are so important that we can’t choose not to try.   What makes Reuben’s authorial voice compelling is that it sounds just as we expect the voice of a person in the middle of that struggle must sound.[1]   It’s the strength of this conviction that comes across in Reuben’s writing, so that reading his books and essays is remembered (by me, at least) as a conversation, a very lively conversation, filled with the passionate sense that we are talking about something that matters.  Also filled with disagreements — because I don’t always agree with everything I read in Reuben’s books and essays; beyond questions of detail the difference might come down to my sense that Reuben is trying to get to the bottom of the mathematical experience, whereas I apprehend the experience as bottomless; or I might say that it’s the effort to get to its bottom that is at the bottom of the experience.  But the differences are of little moment; what stays with me after reading a few pages of Reuben’s writing is the wholeness of the human being reflected in his words, a human being who cares so deeply about his mathematical calling that he is ready to add his own heroic failure to the long list of admirable failures by the most eminent philosophers of the western tradition to account for mathematics; and without these inevitable failures we would not begin to understand why it does matter to us.

[1] As I wrote that sentence I remembered that I have still not met Reuben, nor have I ever spoken to him; but I checked one of the videos online in which he appears and, sure enough, his literal voice is very much as I expected.

Stéréotypes genrés problématiques

patiente

Long-time readers of this blog will remember how I solved a sticky gender stereotype problem, with the help of my friends, by replacing the “Actress” character in the dialogues in the chapters entitled “How to Explain Number Theory at a Dinner Party” with a “Performing Artist.”  The problem has now resurfaced during the preparation of the French version of the book, to be published by Éditions Cassini, whose director is a retired former colleague of mine at Paris 7.

The French translator has done an outstanding job.  I started writing in English upon moving to France in 1994, and I saw this as an emergency measure to protect my ability to express thoughts that I believed could not be captured in French.  I was still convinced that my English prose was untranslatable when I wrote MWA, and it is partly to guarantee that this would be the case that the syntax is often so convoluted.  But the translator — you’ll discover her name when the book is in print – managed to convey my intentions brilliantly.

Gender neutrality, however, is a challenge in French.  The translator initially used the word Actrice for “Performing Artist,” but I explained the issue and the dialogue is now between an Artiste and a Théoricien des Nombres.  This doesn’t completely solve the problem, however, and I’m not sure the problem, evident in the above excerpt, can be solved.

Non-binary gender grammar does exist in French, though you will not be surprised to learn that “L’utilisation de ces néologismes et de toute autre forme de langage inclusif est rejetée par l’Académie française32.”  Most of the stereotypes you have heard about the fustiness of the Académie française are true, but I don’t know how a thorough reform of the French dictionary would solve the problems indicated above.  A French number theorist is either a (male) théoricien or a (female) théoricienne.  Reactionaries (including some of my colleagues, I suspect) are still arguing that théoricien is adequate for all genders.  Progressives have for some years been addressing their exhortations to a gender-diverse community of théoricien(ne)s, or sometimes théoricien.ne.s.  But an individual is one or the other — or a self-identified non-binary individual might be a théoricæn (top choice, followed by théoriciem and theorician), if I am extrapolating correctly from the results of a survey published on the blog lavieenqueer.  But French doesn’t offer a genuinely gender-neutral translation of Number Theorist; non-binary is another box, alongside male and female.   The same goes for the adjective that specifies the Performing Artist’s gender; French Artistes can be patiente or patient or (again copying from the survey) patientæ, patienx, or patiens but they have to be one of those.

I found exactly two tell-tale adjectives in feminine form, applied to the Artiste in the dialogues — and many more in agreement with the number theorist’s designation as théoricien and not théoricienne nor théoricæn. I don’t know how to fix this issue in French, but I don’t even know how to begin to address it in Greek or Chinese, which are the other languages in which you can read the book — if you can read those languages, which I can’t.

mathimatika-horis-apologies-9786185289188-200-1303183

This is the cover of the translation by Βερονα Πετρου, published by Ροπή, in which the Performing Artist is called a ΕΡΜΗΝΕΥΤΡΙΑ ΗΘΟΠΟΙΟΣ.  Although this seems to be a literal translation, and Google translate is of no help in determining whether or not this expression is gendered, when I type ΕΡΜΗΝΕΥΤΡΙΑ on Google, practically all the images that come up are of women.  Moreover, the text is unequivocal.  Here is the Greek version of the French text reproduced above, with the feminine ending circled.

Greek

Greeks must have come up with non-binary rules for adjectives, but I will leave it to Greek readers to help us figure them out.  Meanwhile, there seems to be no way to root out “problematic gendered stereotypes” worldwide, unless we want to imagine the dialogue taking place in the “theater of androids” which — as is recalled at the end of Chapter δ of MWA — was Maurice Maeterlinck’s emergency measure for preserving “the symbol,” “the dream,” and “art.”

Scientists for Palestine at MIT

S4P_MIT

It may not be too late to register for next month’s conference, at MIT, of the Scientists for Palestine network.  This is the third international meeting, and unlike the previous meetings at Cambridge University and at Columbia, this is the first to be co-sponsored by its host university.

Past conferences have focused primarily on physics, but at least one scheduled speaker is a mathematician (topologist Marwan Awartani), and I expect the mathematical sciences will be well represented.  A complete schedule will be posted here when it is made available.

Normally I would have expected the AMS inclusion/exclusion blog to be willing to help publicize such a meeting, since in many respects Palestinians live their entire lives in a state of exclusion.  But I learned that that is not the appropriate venue when my request to publicize last year’s meeting at Columbia was refused:

I’m sorry to say that the Editorial Board had decided that this submission was not quite appropriate for the blog, and I do apologize for not replying to you sooner (before the conference had already happened). Certainly posts on the struggles and successes of Palestinian mathematicians, particular first-person stories of such, are completely appropriate for this blog.  Unfortunately, press releases about conferences, even releases with added introductions and/or commentary, are not appropriate.

Perhaps a mathematician who attended this conference could write a blog post about their experience there, about any Palestinian mathematicians they met, and particularly about any conference talks by mathematicians.   This sort of personal review of a mathematics conference is common on this blog…

Apparently the inclusion/exclusion blog prefers to focus on individual rather than collective exclusion stories.  The present blog reaches a limited audience, but some of my readers have a more extensive presence on social media:  Twitter directed at least 350 visits to my blog over the last two days.  I hope those readers who can do so will help to spread the word.

The soul of a space

The paper Česnavičius and Scholze just posted on arXiv answers several longstanding open questions in fundamental algebraic geometry.  It also introduces a new definition with energetic new terminology:

anima

I don’t pretend to know which of the authors had the idea of returning to Latin roots in order to find the appropriate word to designate the objects that Lurie had chosen to call “spaces,” as well as their cognates in other settings.  Scholze’s terminological innovations have been more than commonly successful up to now, but I predict that “animated sets” will be especially popular.  A whole thesis in philosophy of mathematics — and a second thesis in theology of mathematics? — could be devoted to the last sentence above.

It turns out that the expression “soul of a space” has been popular for some time among interior designers and architects.

Bakliwala

A room designed by architect Vipin Bakliwala

Bakliwala’s reply also deserves our attention:

As architects, it is our duty to induce emotions into a space and create an ambience that brings forth our hidden calm, positive and spiritual side. We strive to expand the brief given by the client and create a space that elevates and improves his life. We struggle to provide an environment which is an enhanced reflection of his thoughts. We call such places soul shelters.  It is that space where the soul remains in its innate nature.

Do emotions inhere more spontaneously in “worldly” point-set “physical” topological spaces or in their animated “calm, positive, and spiritual” ghostly doubles?  Descartes and Spinoza might help us sort this out.

 

UPDATE:  T.G. pointed out that, if I had read past the introduction to the acknowledgments, I would have realized that

The terminology is due to Clausen, inspired by Beilinson; see the acknowledgements, and the first paragraph of section 5.1.

Here is a passage from Beilinson’s article Topological E-factors that sheds some light on his perception of the need for appropriate terminology, and about the desolation of ordinary category theory.

Beilinson

A. A. Beilinson, Topological E-factors, Pure and Applied Mathematics Quarterly 3, 357-391, (2007)

Beilinson, or my imagined recollection of him, expresses a rather different opinion of spaces on p. 202 of MWA.