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.

Mathematicians take the lead in coronavirus crisis

Mathematicians in both Britain and France are calling on their respective governments to abandon their present plans, which aim at reaching “herd immunity.”  Here are the first paragraphs of the British petition, which was apparently initiated by a group of applied mathematicians at Queen Mary University of London.

As scientists living and working in the UK, we would like to express our concern about the course of action announced by the Government on 12th March 2020 regarding the Coronavirus outbreak.  In particular, we are deeply preoccupied by the timeline of the proposed plan, which aims at delaying social distancing measures even further.

The current data about the number of infections in the UK is in line with the growth curves already observed in other countries, including Italy, Spain, France,and Germany [1]. The same data suggests that the number of infected will be in the order of dozens of thousands within a few days.

Under unconstrained growth, this outbreak will affect millions of people in the next few weeks. This will most probably put the NHS at serious risk of not being able to cope with the flow of patients needing intensive care, as the number of ICU beds in the UK is not larger than that available in other neighbouring countries with a similar population [2]. Going for “herd immunity” at this point does not seem a viable option, as this will put NHS at an even stronger level of stress, risking many more lives than necessary.

By putting in place social distancing measures now, the growth can be slowed down dramatically, and thousands of lives can be spared.

The complete statement is online.  It already has received more than 500 signatures, and they write

We are still collecting signatures, primarily from UK scientists but
also from leading international experts, mainly in mathematical
modelling, epidemiology, immunology, virology.

If you want to add your signature, you can write to Vincenzo Nicosia at

v.nicosia [at]

While the British statement is politely worded, almost to the point of caricature, Michel Parigot’s op-ed in today’s Libération, entitled Coronavirus:  the population must be locked down now, is extremely direct.  I translate the essential passages:

On Sunday Morning [French Minister of National Education] Jean-Michel Blanquer revealed, with an astounding distance and coldness, what what the government’s strategy had been from the start.  He explained that it is not a question of “preventing the virus from developing … but of ensuring that it develops over the longest possible period”, so that “50% to 70% of the population [are] ultimately infected with the virus “to achieve” majority immunity “.

Behind these figures, people are going to die. The idea is to immunize around 40 million people by exposing them to the virus. With a death rate in the range of 1% to 5%, depending on whether or not there are sufficient care options, that means between 400,000 and 2 million deaths. A strategy of deliberately sacrificing hundreds of thousands of lives when an alternative exists, which the Chinese have already shown is possible, is simply monstrous.

Concretely, Parigot calls on the government to

ban all contacts which are not strictly necessary, and for that to kill the economy [here he quotes an expression that has been circulating in the press], with the exception of strictly necessary economic activities and working remotely. Maximum protection must also be provided to those who provide essential services: healthcare, food (production and distribution), essential infrastructure (water, electricity, internet, etc.). Masks must be worn by anyone who travels. Finally, we must give precise instructions with informative explanations to protect ourselves and others; it’s not enough to recommend “washing our hands as often as possible”.

Parigot’s final paragraph calls on President Macron to lock down the population completely and immediately, and seems to endorse a declaration of martial law if it comes to that.  An article in today’s Le Monde suggests that the French authorities are already thinking along these lines.


(To avoid any misunderstanding, I hasten to add that I can’t imagine that a declaration of martial law by the current US administration would end well; and in view of the violent reaction of the French police to demonstrations over the past 18 months — even as recently as one week ago — I’m not so sure it would work out well in France, either.)



A surprising pattern among world leaders who distribute Fields Medals


The 2014 Fields Medalists in Seoul with former President Park Geun-Hye (now serving a 25-year prison term) and IMU President Ingrid Daubechies

I had been preparing a blog post on the history of holding the International Congress under the patronage of figures of political authority.  This patronage has been symbolized in recent times by inviting important politicians — often heads of state — to place the Fields Medals in the hands of the year’s Laureates.  This has been the consistent practice since at least 2002, when I was in the Great Hall of the People to witness Chinese President and CCP General Secretary Jiang Zemin handing the Fields Medals to Laurent Lafforgue and Vladimir Voevodsky.  Like most of my colleagues I assumed this was a sign of the importance the host country attached to the ceremony, and to mathematics as a whole.  By extension I concluded that an ICM at which the head of state was absent from the opening ceremony was on some level a symbolic failure for the host country’s organizers as well as for the international mathematical community.

On the other hand, as readers of this blog have probably guessed, I was motivated to write about the topic because I wonder whether this kind of high patronage is still a good idea in an age when practically no important political leader in the world enjoys the kind of respect that would do honor to the ideals that motivate the International Mathematical Union, and when so many leaders of major countries (and smaller countries as well) are authoritarians or crooks or both at once.  It turns out that the practice of placing ICM under the sponsorship of the highest political spheres has not been consistent.  The IMU has helpfully made the proceedings of all past congresses available, and the reading of the early pages of the earliest congresses is pleasurable as well as enlightening.  How would I have learned otherwise that the 1920 Congress in Strasbourg cost 83,525 F, and that the most generous sponsor was the Ministry of Foreign Affairs (10,000 F), followed closely by the 7,000 F provided by the Commissariat générale d’Alsace-Lorraine (restored to France only two years earlier) and the 5,000 F donation of Solvay, headquartered (still) in Brussels?  I focused, however, on the congresses at which Fields Medals were awarded, starting with the Oslo congress in 1936, and specifically on whether the honor of presenting the Medals to the winners was entrusted to heads of state, to lesser politicians, to mathematicians, or to other representatives of civil society.

Reports on the opening ceremonies contain gaps, and I am not certain that I am reading them correctly, but I believe that the 1936 proceedings affirms that King Haakon VII of Norway was indeed in attendance, but that it was Elie Cartan who presented the first Fields Medals to Lars Ahlfors and to Norbert Wiener, representing Jesse Douglas who was too “fatigué” to attend.  In Cambridge (Massachusetts) in 1950, it was the turn of Harald Bohr to hand the Medals to Laurent Schwartz and Atle Selberg, and in 1954 in Amsterdam Hermann Weyl transmitted the prize to Kunihiko Kodairo and Jean-Pierre Serre.  Mathematicians — respectively Academician Mstislav Keldysh, Rolf Nevanlinna, Wladislaw Orlicz, Lars Ahlfors, and Beno Eckmann — again did the honors in Moscow in 1966, in Helsinki in 1978, in Warsaw in 1983, in Berkeley in 1986, and in Zürich in 1994.   And it appears that Yuri I. Manin presented the Fields Medals in Berlin in 1998 — but I can’t figure it out from the report on the opening ceremonies, which include lengthy speeches by a series of high officials from various levels of the German government, and this is particularly embarrassing because I was actually in the audience (or maybe I wasn’t) and I don’t remember what happened.

On all the other occasions the prizes were presented by politicians.  Here is a rundown:

1958, Edinburgh:  The prizes were presented by the Right Honorable Ian Johnson-Gilbert, Lord Provost of Edinburgh (not to be confused with Prince Philip, Duke of Edinburgh).

1962, Stockholm:  “The International Mathematical Union considers it a great honour that His Majesty the King has agreed to be present here and to give the Fields Medals to the winners of the Prizes” (ICM Proceedings, p. xl)

1966, Moscow:  Georges de Rham introduced the laureates. “Unfortunately, A. Grothendieck, was unable to come. May I call Messrs. Atiyah, Cohen and Smale to come forward and receive these medals from the hands of Academician Keldysh.”  I have already  mentioned this but I repeat the information because (as I just learned) Академик Мстислав Келдыш is the name of a 6,240 ton Russian scientific research vessel which played a role in the filming of James Cameron’s Titanic.  Not a bad fate for the name of a mathematician!

1970, Nice:  The congress was placed under the highest possible patronage:  “Monsieur Georges POMPIDOU, Président de la République Française, a accordé son haut patronage au Congrès. Monsieur Jacques CHABAN-DELMAS, Premier Ministre, a accordé son patronage au Congrès.”

However, neither the President nor the Prime Minister made the trip to Nice. Instead,

Monsieur Olivier GUICHARD, Ministre de l’Éducation nationale, remet les médailles Fields aux quatre lauréats, qu’il félicite.

The financial sponsorship for the congress was prominently displayed in the Nice proceedings, as it had been in the 1920 Strasbourg proceedings — in other words, I had to skip over the account of financial sponsorship before finding the report on the opening ceremony — and I thought readers might like to see that as well:

Le Congrès a bénéficié de l’aide d’un Comité de soutien pour la diffusion des travaux du Congrès, composé comme suit : Président : M. Georges DESBRIèRE, Vice-Président de Péchiney, Président de l’Association pour le Développement de l’Enseignement et des Recherches auprès des Facultés des Sciences de l’Université de Paris (A.D.E.R.P.). Membres : MM. BAUMGARTNER, Président de Rhône-Poulenc, CHASSAGNY, Prési-dent de l’Union syndicale des industries aéronautiques et spatiales, DELOUVRIER, Président de l’Électricité de France, DONTOT, Président de la Fédération nationale des industries électroniques, FERRY, Président de la Chambre syndicale de la sidérurgie, GALICHON, Président d’Air France, GLASSER, Président du Syndicat général de la Construction électrique, GRANDPIERRE, Président de l’Institut des hautes études scientifiques, HAAS-PICARD, Président de l’Union des Chambres syndicales de l’industrie du pétrole, HOTTINGUER, Président de l’Association professionnelle des Banques, HUVELIN, Président du Conseil National du Patronat Français, LESOURNE, Président de la S. E. M. A. (METRA International), d’ORNHJELM, Président de la Chambre syndicale des Constructeurs d’Automobiles, Ambroise Roux, Président de la Compagnie générale d’Électricité

1974, Vancouver:  H.M.S. Coxeter, President of the Congress,

announced that a telegram would be sent to His Excellency, the Right Honourable Jules Leger, C. C, C.M.M., Governor General of Canada, Patron of the Congress. The text of the telegram is as follows: We much appreciate your agreeing to serve as Patron of the first meeting in Vancouver of the International Congress of Mathematicians. We regret your inability to be present and we convey our warmest wishes for a complete recovery.

At the end of the opening ceremony, Professor Chandrasekharan, chairman of the Fields Medals Committee, made a speech that concluded:

May I offer them our warmest congratulations, and invite them to come forward to receive the medals from the hands of His Honour, the Lieutenant Governor of British Columbia.

1990, Kyoto:  “The winners came forward and received their medals and prize checks from Mr. Kosuke Hori, Minister of Education, Science and Culture.”

The Medals were presented by mathematicians in 1994, and 1998, as I already explained. As you can see, the practice of receiving Fields Medals from high-ranking politicians is not so well established as some of us believed.   And recent history has shown a curious correlation between getting close to the Fields Medal ceremony and being investigated for corruption.  The prime example is that of former President Park Geun-Hye, shown above in Seoul in 2014, charged less than 3 years later with “abuse of power, bribery, coercion and leaking government secrets.”  She will be in jail for a long long time, and although it was no fault of the four Fields Medalists, can they honestly say that it was an honor to accept the medals from an individual who enjoys such a dubious distinction?

The 2018 Fields Medal ceremony narrowly escaped being tainted by the participation of a no less corrupt politician:


Former Brazilian president Michel Temer [here shown in his official portrait] was arrested on Thursday as part of the sprawling five-year Car Wash investigation into political corruption.
Mr Temer was picked up by federal police officers at his home in São Paulo less than three months after he handed over the presidential sash to his successor, far-right former army officer Jair Bolsonaro.  (Irish Times, March 21, 2019)

From France24, May 15, 2019:

Former Brazil president Michel Temer left prison on Wednesday less than a week after returning to a Sao Paulo penitentiary in relation to a wide-ranging corruption scandal that has engulfed several high profile South American politicians.

The 78-year-old left the Military Police Battalion in Sao Paulo at 1.30 pm (1630 GMT) in a heavily guarded convoy as he headed to his home in an upmarket neighborhood in the sprawling city’s west.

His release was ordered by all four judges on the Superior Court of Justice under the writ of habeas corpus, which demands that a prisoner who claims unlawful detention be brought before a court.

However, several conditions were attached, including a freezing of his assets and the seizure of his passport.…

He is suspected of having been at the head of a criminal organization that diverted up to 1.8 billion reais ($460 million) and has been operating for 40 years.

Temer participated enthusiastically in the impeachment of Dilma Rousseff in 2016 and was still President during the ICM in Rio de Janeiro.  In that capacity it was expected that he would hand out the Fields Medals at the opening ceremony.  However (according to a colleague in Brazil with whom I spoke at the time) Temer found a diplomatic excuse to justify his absence at the ceremony, where his presence would certainly have been met with a loud and embarrassing protest — his approval rating had dropped to about 3%, a record low for any sitting President, anywhere in the world, even before his indictment.

It was India’s President, and not the better-known (and more powerful) Prime Minister, who brought the dignity of state to the opening ceremony of the ICM in Hyderabad in August 2010.

The officers of the IMU could have anticipated that the ordinary corruption of state, the ubiquitous kind to which most of us rarely pay attention, would accompany her presence, especially since she had already been under investigation:

From Wikipedia:  Patil was a chairperson of the [Pratibha Mahila Sahakari] bank and also one of its directors, along with many of her relatives. She is one of 34 respondents in an ongoing case [as of 2007, according to Wikipedia] before the Aurangabad bench of the Bombay High Court regarding alleged mismanagement of the bank and misappropriation of funds.… The Reserve Bank of India … revoked the licence of the bank in 2003 after it was found out that the bank had engaged in various irregularities, including illegally waiving interest on loans given to many of Patil’s family members.

At this point in my chronology I was hoping to be able to point to an exception in the person of former King Juan Carlos I of Spain.  While few (probably none) of my Spanish friends are monarchists, they all recognize the role he played at a crucial moment in the consolidation of the still-fragile democracy that was installed after Franco’s death, and for the most part he was comfortable in his role of titular head of state in the system that reserves the actual power of government for the elected parliament.   Moreover, unlike his successor and son, King Felipe VI, he has not intervened pointlessly in the Catalan independence crisis.

Madrid 2006

Overall, then, King Juan Carlos enjoyed broad respect in Spain and did bring a certain dignity to the 2006 ICM in Madrid, as did King Haakon VII in Oslo in 1936 (and even more in retrospect, for his refusal to recognize the Nazi occupation of Norway during the Second World War).  But a week ago this story broke in El País:

This followed the revelation that “A public prosecutor in Switzerland has been investigating a multi-million-euro donation received by Corinna Larsen, a friend of former Spanish King Juan Carlos I, from a Swiss bank account linked to a Panamanian foundation.”  The donation of $100 million to Corinna Larsen — also known as Corinna zu Sayn-Wittgenstein — was apparently a kickback in connection with the construction of the Haramain high speed rail connection between Medina and Mecca, which was completed in 2018 by a consortium of 12 Spanish companies.

I have not found allusions to this story in the English-language press, and perhaps it is because it will have no consequences.  That’s apparently the conclusion of the Spanish Socialist Party (PSOE), the leading force in the current coalition government along with the parties pressing the case (Unidas Podemos etc.).  The PSOE’s reluctance to investigate the economic activities of Juan Carlos is based on their reading of the Spanish constitution, which — as was demonstrated in a similar case two years ago — literally places the King above the law:

“las prerrogativas de inviolabilidad y no sujeción a responsabilidad del Rey, consagradas en el artículo 56.3 de la Constitución, son absolutas, abarcan a la totalidad del periodo en que se ejerce la Jefatura del Estado y tienen efectos jurídicos permanentes”

I am tempted to extend the disgraceful list back to the 2002 ICM in Beijing when I read questions like this:

Why is Xi Jinping afraid to jail Jiang Zemin even though there’s a lot of evidence of corruption against him and his alleged involvement in Beijing blasts to shake Xi’s authority? (Question answered on Quora.)

But I am aware that rivalries among factions of China’s ruling stratum take many unexpected forms and I know too well not to take this kind of comment at face value.

Mathematical platonists like to argue that our work is devoted to the discovery of truths that transcend any merely human laws.  This sheds a novel light on the decision to invite  heads of state who are above the law — whether they enjoy this status by virtue of a political system disposed in their favor, as was at least temporarily the case in 2018, 2014, 2010, and arguably in 2002, or by an exception carved into the law itself, as in the case of Spain’s former King — to lend their aura of inviolabilidad for a moment in order to enhance the solemnity of transfer of the Fields Medal.   Advancing the 2022 Fields Medal ceremony to the week following Donald Trump’s successful evasion of his Constitutional responsibilities, with the help of the (very favorably disposed) US Senate, would have been a perfect illustration of this principle.

But we missed the opportunity and will therefore have to wait another two years for a more exemplary native of the imponderable innermost sanctum of politics, where words like “corruption,”  “grace,” and “raw power” become practically synonymous, to dignify the St. Petersburg ICM with a moment of transcendence.

Colleagues who attended the São Paulo IMU General Assembly meeting, at which St. Petersburg was chosen over Paris as the venue for the 2022 ICM, informed me that the promise that President (for life?) Vladimir Putin himself would be on hand, to present the Fields Medals, was one of the arguments that clinched the decision.  I have just provided a quasi-theological rationale for this thesis but I still find it hard to grasp, and I prefer the materialist explanation:  namely, that  Russia’s team had promised a much more generous budget than the French; the Chambre syndicale des Constructeurs d’Automobile, the Association professionnelle des Banques, and the rest of the list, not to mention Solvay and their 5000 F, carry much less weight in today’s globalized economy than they did 50 or 100 years ago.

It’s all about the Benjamins, in other words; or more precisely, about the николай николаевичи —  the External Goods to which MWA devotes such obsessive attention.  The money for the ICM has to come from somewhere.  Who would seriously argue that private sources like the Union des Chambres syndicales de l’industrie du pétrole are really less tainted than the funds provided by the Russian government  or the St. Petersburg administration?   Besides, the many countries represented at the São Paulo meeting were perfectly aware that xenophobia had been a dominant theme in French elections for over 30 years — remember that at the same meeting they had voted to remove the name of Rolf Nevanlinna, who had presented the Fields Medals just 40 years earlier, from the computer science prize, because of his Nazi sympathies.  And they knew all too well that France’s next presidential elections would be taking place before the 2022 ICM, with unpredictable results.


The candidate elected in 2022 will still be French President in 2026.  But this may be irrelevant.  The rumor is that New York will be bidding for the honors, with External Goods to be provided by the city’s robust financial services industry.  I estimate that something like $30 million would be needed to cover the difference between 10 nights of hotel accommodations for 10000 participants in New York as compared to Paris, under normal circumstances; but maybe New York’s team knows how to transcend normal circumstances.  Most intriguing, of course, is the prospect that the United States will have a very different kind of head of state by then.


Photo September 20, 2018, Union Square, New York




Mathematicians on strike in Paris


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:

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.

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.