Category Archives: External goods

The inevitable questions about automated theorem proving


The author and René Guitart at the conference Alain Badiou:  l’hypothèse du contemporain, IRCAM, June 7, 2019, still from

I’ve been saying for some time that most articles about controversies regarding the AI future of mathematics focus primarily on two questions — “Is it good or bad?”  and “Will it work or not?” — while neglecting to reflect on the presuppositions that underlie these questions — what is the good of mathematics, and work to what end? — not to mention what should always be the first question to be addressed to any significant social development — cui bono, in whose interest?  Within the limitations imposed by this conventional frame of reference, last week’s article in Quanta by Stephen Ornes was a good one.  It provided a clear introduction to the subject matter for the well-informed amateurs as well as professionals who read Quanta, recalled the history of attempts to automate proofs — with a helpful reminder that these attempts were originally motivated by the need for computer scientists to verify the reliability of their programs, a theme treated in depth by Donald MacKenzie in his classic Mechanizing Proof — and surveyed some of the most ambitious contemporary projects and their applications within mathematics.

When I agreed to be interviewed for the article it was in the hope of nudging the discussion in the direction of the questions that are typically neglected.  In responding to Ornes’s first message I made only one request:

If you decide you do want to use one or more quotations from me, I would want at least one of them to address this point:  that what pure mathematicians find valuable about what we do is precisely that it provides a kind of understanding whose value is not determined by the logic of the market.
Note my abusive and rather underhanded implicit definition of the pure mathematician as one whose values conform to an impossibly unrealistic ideal.  The impulse to cash in must surely be alive in my professional community as it is in every other corner of neoliberal civilization.  And yet, if the products of our imagination cannot provide an escape from the market, what can?
The sentence quoted above was in the last draft of the article that Quanta showed me, but it did not make the final cut.  (And the editors also disregarded my invitation to use the photo reproduced above, which better conveys my mixed feelings about the whole business than the photo they did use.)  The article’s only hint of the cui bono question was a brief allusion to Christian Szegedy’s group at Google Research.  I don’t know what was in the back of Google’s mind when they decided to sponsor research into automating mathematical proof.  Their business is computing:  maybe they are simply looking to improve software verification, like the original proof automaters.  Or maybe they really are interested in mathematics as such; but I would not count on them to care about “a kind of understanding whose value is not determined by the logic of the market.”  To a very great extent, Google and its Silicon Valley companions are the market.  If Google’s aim is to reproduce what drives us to invent things like homotopy theory and pseudodifferential operators, it can only be because they think they can bottle it and sell it back to us, just as they have done with our search histories and the keywords they extracted from our gmail.
Whether or not you find that “evil” depends on your frame of reference.  Just yesterday I received a notification of an NSF Program Solicitation entitled “National Artificial Intelligence (AI) Research Institutes”:
Artificial Intelligence (AI) has advanced tremendously and today promises personalized healthcare; enhanced national security; improved transportation; and more effective education, to name just a few benefits. Increased computing power, the availability of large datasets and streaming data, and algorithmic advances in machine learning (ML) have made it possible for AI research and development to create new sectors of the economy and revitalize industries. Continued advancement, enabled by sustained federal investment and channeled toward issues of national importance, holds the potential for further economic impact and quality-of-life improvements.

The 2019 update to the National Artificial Intelligence Research and Development Strategic Plan [1], informed by visioning activities in the scientific community as well as interaction with the public, identifies as its first strategic objective the need to make long-term investments in AI research in areas with the potential for long-term payoffs in AI. The President’s Council of Advisors for Science and Technology has published Recommendations for Strengthening American Leadership in Industries of the Future [2], including AI, and calls for new and sustained research in AI to drive science and technology progress. The National AI Research Institutes program enables longer-term research and U.S. leadership in AI through the creation of AI Research Institutes.

This program is a joint government effort between the National Science Foundation (NSF), U.S. Department of Agriculture (USDA) National Institute of Food and Agriculture (NIFA), U.S. Department of Homeland Security (DHS) Science & Technology Directorate (S&T), and the U.S. Department of Transportation (DOT) Federal Highway Administration (FHWA). New to the program this year are contributions from partners in U.S. industry who share in the government’s goal to advance national competitiveness through National AI Research Institutes. This year’s industry partners are Accenture, Amazon, Google, and Intel Corporation.

This program solicitation invites proposals for full institutes that have a principal focus in one or more of the following themes, detailed in the Program Description:

• Theme 1: Human-AI Interaction and Collaboration
• Theme 2: AI Institute for Advances in Optimization
• Theme 3: AI and Advanced Cyberinfrastructure
• Theme 4: Advances in AI and Computer and Network Systems
• Theme 5: AI Institute in Dynamic Systems
• Theme 6: AI-Augmented Learning
• Theme 7: AI to Advance Biology
• Theme 8: AI-Driven Innovation in Agriculture and the Food System

(Emphasis added.)  I’d guess Automated Theorem Proving fits best with Theme 1.  So the researchers quoted are unwittingly (or maybe wittingly) contributing to a logic of national competition.  This sort of language always strikes me as ironic, given the international nature of projects like proof automation, and given my own failure to muster much enthusiasm for French national competitiveness during my years teaching in Paris, in spite of frequent exhortations from the authorities using identical language (but in French, of course).

I shouldn’t complain that Quanta did me the honor of giving me the last word but when I read it in the draft —
Even if computers understand, they don’t understand in a human way.
— I couldn’t believe that I had actually written anything so imprecise.  And I’m still pretty sure I never did; but unfortunately I did speak those words at this roundtable.  The thought is hardly original to me; mathematicians have been saying this in various ways for years, at least since the Appel-Haken solution of the Four-Color Problem.  I tried to add some content by revising the sentence to restore the context in which it was spoken:
Even if we do want to attribute understanding to computers, it won’t be the kind of understanding we attribute to human beings.
This amendment, too, was included in the last draft I saw, but the sentence reverted to the shorter version.  I should not have been surprised:  the published sentence is meaningless but is admittedly more journalistically effective.  On this blog I’m not constrained by a word limit, so let me revise the sentence one more time:
Even if we do want to attribute understanding to computers, it won’t be the kind of understanding we currently attribute to human beings.
The word “currently” reflects my expectation that the industrial version of proof automation, which is where I suppose this is all heading, will lead not only to a reconsideration of the purpose and nature of mathematical proof — hardly for the first time — but also to a new adaptation of human understanding to the needs of machines.  This is in line with the industrial imperative Shoshanna Zuboff sees in what she calls surveillance capitalism:

With this reorientation from knowledge to power, it is no longer enough to automate information flows about us; the goal now is to automate us.

(S. Zuboff, The Age of Surveillance Capitalism, p. 15.)  On Zuboff’s telling, Google, naturally, was the pioneer in this process.

Challenges the math community faces in the future

These are the notes I prepared for the “Global panel” at the CARTOON conference on May 30, 2020.  There is only time to discuss a small fraction of this material, which itself is a minuscule selection of the massive literature inspired by thoughts about what our life, academic or otherwise, will be like if and when the pandemic is brought under control.

I expect to add resources and references as the summer progresses.


We have all been reading about the difference between “getting back to normal” and “adjusting to the new normal.”  There turns out to be fairly broad agreement that not only were some features of the “old normal” highly undesirable — like inequality, pollution, xenophobia, dependence on fossil fuels, austerity in public services, or the gig economy, or the for-profit health care system in the United States — but that the current crisis provides a once-in-a-lifetime opportunity to eliminate or at least to attenuate some of these undesirable features.

In the face of the coronavirus, a small window has opened in our societies to gain scope for action. It is important to keep this window open a bit.

(Bernd Scherer, Director, Haus der Kulturen der Welt)

Or, to quote Juliette Binoche, Iggy Pop, Vaughan Jones, Béla Tarr, Madonna, and Tim Gowers, among many other celebrities, it is time

to leave behind the unsustainable logic that still prevails and to undertake a profound overhaul of our goals, values, and economies.

In that spirit, I’m going to focus on the challenge to the mathematics community of using the current opportunity to address some aspects that need to be reconsidered of the system that makes our profession possible.  I will divide these artificially into four groups:  relations with the broader society, relations with universities and higher education, relations within the profession, and relations with ourselves.


Relations with broader society

The crisis has revealed something we already suspected:  that we are not essential workers.  This has two sides:  on the one hand, our mathematical activities are not necessary for the basic functions of civilized society; on the other hand, our material circumstances are safer and much more comfortable than those of nurses, sanitation workers, transport workers, food handlers, and so on.  What we owe in exchange for our comfort is a serious reflection on what is the “essence” of our work, with regard to the broader society.

Serious reflection on our essence requires in the first place speaking out about the ethical challenges posed by the many spectacularly problematic applications of mathematics — financial engineering, Cambridge Analytica, algorithmic weapons of math destruction, surveillance, as well as strictly military applications.  That doesn’t mean we necessarily have to refuse funding from the Heilbronn Institute, as Tom Leinster argued a few years ago; but it does mean owning up to what accepting such funding entails.

One direction I strongly advise avoiding is to reduce our essence to the market value of applications of mathematics, in scientific modeling or commercial innovations.  The argument can and should be made that these applications depend in multiple ways on a robust community of pure mathematicians, but promising spinoffs and startups in exchange for support of our profession is a toxic habit of concession to neoliberal thinking, and that habit clouds our thinking at every level.  For many reasons we should take advantage of the crisis to seal the collected thoughts of Margaret Thatcher and Ronald Reagan in a time capsule and bury them permanently in a toxic waste dump.

I will return to the essence of our work at the end.  In the meantime, avoiding the neoliberal reading of our essence as far as the broader society is concerned means taking on the neoliberal model of the university.  To quote the petition Refonder l’Université et la Recherche pour retrouver prise sur le monde et nos vies (more than 7000 signatures since March 20, including mine):

Le corollaire de l’autonomie du monde savant est son engagement sur un principe : sa responsabilité vis-à-vis de la société.  L’usage politique, technique et industriel des travaux scientifiques doit se décider dans un cadre pluraliste et démocratique, en accord avec l’intérêt commun.


Relations with universities  

In the neoliberal model the university provides the service of enhancing the student’s market value, and we, as teachers, are service workers.  This vision has the merit of relieving our fear of being seen as social parasites.  But the relief is short-lived, because the model of university education built on massive student debt is not sustainable, and other models are actively being discussed.  In March Stefan Collini wrote this in the Guardian:

The “marketisation” of universities in the past decade has changed their ethos as well as their funding. Older notions of an academic community, or a scholarly career, have been replaced by economic analyses that look to reduce unit costs per output. Replacing permanent staff with cheaper, disposable temporary ones reduces the power of academics and increases that of managers.

The rich Ivy league and similar universities have already announced hiring freezes; Johns Hopkins has gone even further, sending signals that even tenure may not guarantee the expected level of material comfort for much longer.

Suddenly anticipating losses of over $350 million in the next 15 months, the university imposed a hiring freeze, canceled all raises, and warned about impending furloughs and layoffs. Most extraordinarily of all, it suspended contributions to its employees’ retirement accounts.

(François Furstenburg, Chronicle of Higher Education)

The Times Higher Education Supplement has this headline story:

            Mergers and ‘FE future’ predicted for some English universities 

While many universities would need “pretty big cuts in teaching and research staff” as a result of the coronavirus crisis, such action would not be enough to save some institutions, which would be forced to merge as a condition of receiving extra funding…

Sir Steve Smith, vice-chancellor of the University of Exeter, adds

The future prosperity of the UK depends on having a strong university research base, which is subsidised by international student income.

Lurking in the background in this and similar articles is the prospect that the existing system of higher education will be replaced by one where universities become content providers to fit the respective business models of leading national industries — Silicon Valley in the US, for example.

The promise of freedom of subjective development and the democratization of knowledge was, however, increasingly functionalized through business models that use the orientation of citizens on the internet to collect data and sell them as goods for digital capitalism.

(Bernd Scherer, loc. cit)



A few of the sponsors of the 2020 WICHE Conference on Educational Technology

Some of the initiatives to preserve what we see as the values embodied by universities focus on protecting the most precarious university workers.  Among them are colleagues who have undergone the full academic apprenticeship process but who have not acquired the professional stability that is one of the chief attractions of the academic life.   I am one of 2800 signatories, including only 25 mathematicians, of the Covid-19 Academic Solidarity Statement, which

calls on universities to protect the lives and livelihoods of its contingent academic workers, including non-tenure track (NTT) teachers and graduate students. … Signatories to the statement further pledge not to accept speaking invitations during the 2020-21 academic year at institutions that have extended tenure clocks for their tenure-track faculty, but have not similarly extended contracts for all currently employed NTT teachers and graduate students.

(All eight Ivy League universities, including my own, are on the list of institutions whose invitations are to be refused, along with many others, public as well as private.  See also the long list of Related Campaigns, mainly by graduate workers and non-tenure-track faculty.)

It usually comes as a surprise to our colleagues in the humanities that mathematicians can be uniquely effective in campaigns in defense of progressive values.  A good example is Tim Gowers’s pledge in 2012 to boycott Elsevier, which inspired the Cost of Knowledge statement that quickly collected over 10000 signatures (17000 by 2018).


Relations with the profession

And with inevitable pressure on the job market as a result of the collapse of public budgets as well as the economy more generally, the priorities of the profession will come into question in a way that has not been seen since the 1950s — except in Russia, where mathematics has not recovered and may never recover from the collapse of the USSR.  Even before the financial crisis of 2008 the internal contradictions of the model of the reproduction of the humanities through graduate programs were widely recognized (as early as 1970, according to Christopher Newfield).  In mathematics, the imbalance between entering graduate classes and the job market (but why do we accept the “job market” as a fact of nature?) has been mitigated by the possibility of employment in the toxic “old normal” industries I already mentioned.

A recent Intercept article by Naomi Klein spells out how the tech industry, in partnership with local governments, plans to cash in on installing “smart” technology in the wake of the crisis.  She quotes Eric Schmidt:

Congress should meet the president’s request for the highest level of defense R & D funding in over 70 years, and the Defense Department should capitalize on that resource surge to build breakthrough capabilities in A.I., quantum, hypersonics and other priority technology areas.

Jobs in these sectors may well help PhDs in mathematics and the sciences survive the loss of stable university positions.  And this need not be a social and political disaster — if these developments are placed under democratic control, so that the benefits do not all accrue to Silicon Valley billionaires and the power is not designed to favor autocracy.  To quote Klein again:

Will that technology be subject to the disciplines of democracy and public oversight, or will it be rolled out in state-of-exception frenzy, without asking critical questions that will shape our lives for decades to come? Questions like, for instance: If we are indeed seeing how critical digital connectivity is in times of crisis, should these networks, and our data, really be in the hands of private players like Google, Amazon, and Apple? If public funds are paying for so much of it, should the public also own and control it? If the internet is essential for so much in our lives, as it clearly is, should it be treated as a nonprofit public utility?

However, even if one’s conscience is willing to forget that the expansion of employment opportunities for mathematicians to develop the tools of speculative finance and monetization of personal data that are at least partially responsible for the conditions that made the present crisis much worse than it had to be, there’s no guarantee that these industries will be able to absorb the surplus of mathematics PhDs when the crisis is over.


Relations with self

If you want to continue in this profession, your main task is to ask yourselves what you find important and valuable about the mathematical vocation, and then to acknowledge that much of this is likely to come under attack, precisely for the reasons that you find it appealing, and that preserving what is important and valuable is really up to you.  Ultimately this means placing the economic model and political justifications that sustain higher education, including those discussed above, under scrutiny; drawing the appropriate conclusions; and then doing whatever is necessary, as indicated by these conclusions, in order to preserve whatever drew you to the mathematical life in the first place.

In other words, if the values of mathematics are important to you, you will have to become activists.  If you have been reading or rereading Camus’ The Plague, you will have seen that there was “no great merit” in doing what Tarrou chose to do, “because they knew it was the only thing to do and not to have decided to do it would have been incredible.”

Humanistic scholars are much more skillful than we are in finding the language to justify their activism.

In a time in which public education must struggle to establish itself as a public good, it is incumbent upon faculty to clarify in what senses higher education is a value in our public worlds and why it should be supported. The answer provided by the recent AAUP statement …  relies on a notion of progress that is hardly explained, and given that experts have surely led us astray (experts in neoliberalism, technologies of indefinite detention, nuclear war), we would have to know which version of expert knowledge is advanced and judge whether its advancement is really a public good. Since we need to know and evaluate the direction and aim of such an “advancement,” we would have to rely on those humanistic disciplines explicitly devoted to critically interrogating the problem of value, justification, and the various senses of the public good.

(Judith Butler, Academe)


This text predates the COVID-19 crisis but the conclusions remain valid, and they challenge us to explain how the values that motivate us as mathematicians — the values that arise authentically from our practice, not those that are assigned to our work by the market — contribute meaningfully to “various senses of the public good.”  I think we can meet the challenge, but more of us will have to put more effort into our explanations than most of us have done so far.

Mathematicians have made considerable progress in recognizing ethical challenges within the profession.   The AMS has gone so far as to institutionalize the language of inclusion and exclusion in its publications.  But the scope for inclusion will be severely diminished if we don’t  find the language to address the challenges to the profession within the broader society.


1-minute summary

Forget everything you think you know, look for allies outside of mathematics, figure out what is most precious and hold on to it, and be prepared to fight to preserve it, because I guarantee there are political and economic forces that will take it away from you if left unopposed.



SOME CHOICE QUOTATIONS (some behind paywalls)

Once hard decisions have been made about academic offerings, high-level estimates of required faculty can be calculated with existing load levels, class sizes, and student-to- faculty ratios. Each of these items should next be analyzed as part of the second key question: How productive can our faculty be?

…Many argue that the traditional professorial model of tenure, lighter teaching loads, long vacations, and sabbaticals was formed when salaries were lower in higher ed but has been maintained even though salaries have risen.

(Chronicle of Higher Education, How to Address the Elephant in the Room: Academic Costs)


Faced with an education minister, Jean-Michel Blanquer, who has been bypassed by events, teachers have themselves invented new practices, working school by school and class by class. Away from the education authorities and the school inspectorates, the great majority of teachers have taken it upon themselves to choose and organise the details of the return to school.

…what this flurry of initiatives and mobilisation, and this capacity for self-organisation and innovation, have also shown is the extent to which a health crisis has ended up revealing the dangerously archaic nature of our political system.

(MediapartHow virus crisis is changing the face – and politics – of French society)


This crisis affords a rare chance to make personnel changes that have historically been resisted by strong campus cultures of inertia or by union agreements.

…Be prepared for big-change efforts and major cost-cutting (both administrative and academic), and invest in strategic differentiation to advance your college’s long-term health as well as survive this short-term crisis. In general, you will want to strive to cut more rather than less, and if things turn positive, you will be in a position to re-invest according to your strategy.

(Chronicle, Under Covid-19, University Budgets Like We’ve Never Seen Before )


The real Fields Medal curse?


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

(This is a revised version of a post published on March 12, under a much longer title.  The revision takes into account the later dramatic developments in the case of retired King Juan Carlos I of Spain.  If  you missed János Kollár’s article about the curse that, according to two economists, afflicts Fields Medalists with an alarming loss of productivity, you probably have the time to read it now.  It’s very entertaining and I guarantee it will take your mind off the pandemic and your lockdown for a few minutes at least.)

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 Kodaira 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.

The case of Moscow was a bit ambiguous.  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!

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).

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 before I revised this post the following 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.

When I originally wrote this post I had not found allusions to this story in the English-language press.   The Spanish Socialist Party (PSOE), the leading force in the current coalition government along with the parties pressing the case (Unidas Podemos etc.).  was reluctant to investigate the economic activities of Juan Carlos, 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”

Ultimately King Felipe VI, son of Juan Carlos, renounced his inheritance and cut off his father’s stipend in a belated recognition that the individual standing in the middle of the above photo, and many other photos during his long reign, did not in retrospect lend dignity to the ceremony (and many other ceremonies) to the extent that the (figurative) crown on his head must have led the organizers to expect.

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

This is only apparently a sex scandal


From the cover page of the report

The news that several departments at Harvard, including the mathematics department, maintained connections with Jeffrey Epstein for many years after his conviction in 2008 “on charges related to soliciting minors for prostitution” has provided an opportunity for expressions of Schadenfreude on the part of several of my French colleagues.  Last September, after Harvard President Lawrence S. Bacow described Epstein’s actions as “utterly abhorrent . . . repulsive and reprehensible,” Harvard undertook a systematic review of Epstein’s donations to Harvard.  The report on that review can now be consulted online.

Attentive readers will have understood that the true scandal is not that one particular philanthropist turned out to be repulsive and reprehensible.  Dig into the backgrounds of the founders and funders of our most cherished institutions of higher learning and you will see that reprehensible actions are a frequent feature of their biographies.  Nor is it that the sexual exploitation of minors is one of the reddest of red lines, and that few of even our most intrepid colleagues would want to be caught red-handed on its wrong side.  What is really scandalous about the new story is that it is just the latest version of the old story, that the pursuit of the values of our profession, the internal goods in the language MWA borrowed from Alasdair MacIntyre, remains dependent on the continuous supply of external goods from benefactors who, practically without exception, have all crossed red or reddish lines in order to attain the status of Ultra-High Net Worth Individuals that allows them to play the role of benefactors in the first place.

Reddish lines have been shading redder in recent years.  Institutions have been cutting their ties with the intermediaries who brought them the embarrassing associations with Epstein; they have de-Sacklerized at an accelerating rate from one month to the next.  The to which I alluded in an earlier post

One veteran colleague likens mathematical research to a kidney; no matter where it gets its funding, the output is always pure and sweet, and any impurities are buried in the paperwork. Our cultural institutions have long since grown accustomed to this excretory function, and that includes our great universities.

— is growing increasingly unacceptable to mathematicians, as it is in the wider culture.  Can our profession every hope to be free of association with scandal?

Update:  you really should read the Vox article about the MIT Media Lab, specifically these two segments:

The argument that anonymous donations from bad people are good, explained

Who would you rather have $5 million: Jeffrey Epstein, or a scientist who wants to use it for research? Presumably the scientist, right?


“Everyone seems to treat it as if the anonymity and secrecy around Epstein’s gift are a measure of some kind of moral failing,” Lessig writes. “I see it as exactly the opposite. … Secrecy is the only saving virtue of accepting money like this.”

This from the former director of the Edmond J. Safra Center for Ethics at Harvard University.  After 5000 years of ethical reflection, is this the best we can do?

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.

Number theory, GCHQ, and kidneys

If you can get past the paywall you can read some of my thoughts on research funding in an article published on March 8 in the Times Higher Education Supplement .

If not, here is a “fair use” excerpt:

Mathematicians have been reluctant to recognise that if our work interests generous donors, it is often precisely because it is “useful” according to a definition that Hardy proposed near the beginning of the First World War: “its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life”.

We will have to overcome this reluctance and draw uncomfortable conclusions. Wherever you turn as a mathematician, you’re going to be someone’s kidney: practically every potential source of research funds is tainted in some way.

(I’m afraid you’ll have to find a way to read the article if you want to know what that kidney is doing in that last paragraph.)

Sen. Al Franken to address Atlanta Joint Mathematics Mtg


The AMS Committee on Science Policy (CSP) will be hosting a panel discussion at next month’s Joint Mathematics Meeting in Atlanta.  Karen Saxe, who worked for Senator Al Franken as the 2013-2014 AMS/AAAS Science and Technology Policy Congressional Fellow, invited the Minnesota Senator (and former Saturday Night Live cast member) to speak to the panel, and he obliged by sending a video to be played at the meeting.  Here is the full CSP panel program:

AMS Committee on Science Policy Panel Discussion 

Friday, January 6, 2:30 pm — 4:00 pm

Place:              Atlanta Marriott Marquise, Atrium Level, Room A704   

Title:                “Grassroots Advocacy for Mathematics and Science Policy”

Organizers:      Jeffrey Hakim, American University ( )
Douglas Mupasiri, University of Northern Iowa ( )
Scott Wolpert, University of Maryland ( )

Moderator:      Karen Saxe (, Director, AMS Washington Office

Panelists:         Catherine Paolucci, Office of Senator Al Franken (

Douglas Mupasiri, University of Northern Iowa (

Scott Wolpert, University of Maryland (

Description:     The AMS Committee on Science Policy has organized this panel to discuss ways to engage with elected officials in addressing policy issues of concern to the mathematics community, including research funding and education.  Panelists will discuss the importance of grassroots advocacy and building relationships with legislators to further goals.

The video is about three minutes long, and those of you who cannot attend will be able to watch it at the AMS website — details to be supplied later.   In the meantime, if you’re wondering what “Grassroots advocacy for mathematics” looks like, Karen directed me to this blog post about a recent (Capitol) Hill Visit by a Villanova student delegation, organized by the Association for Women in Mathematics.

Speaking of Washington, I found the following quotation from Nietzsche’s Transvaluation of all Values in the chapter on Sade and Nietzsche of Horkheimer and Adorno’s Dialectic of Enlightenment:

The weak and unsuccessful must perish; this is the first proposition of our philanthropy.  And they should even be helped on their way.

Also this quotation from Sade’s Justine:

How in truth can  you require that he who has been endowed by nature with an eminent capacity for crime… should have to obey the same law that calls all to virtue or to moderation?

If these sentiments remind you of individuals, living or dead, who have been mentioned in the news recently, you will be relieved to see that, more than one month after national elections, the officials entrusted with the business of the Republic appear not to be guided by Sadist ethics.


Urgent news from Leicester

Tim Gowers has once again done the university community a great service by using his blog to publicize the impending decimation of the University of Leicester’s mathematics department.  More like a double decimation:  of the department’s 23 full-time staff, 5 are slated to lose their jobs, with the research staff shrinking by close to 30%.  Rather than repeat the details, which you can find presented with Gowers’s customary clarity on his blog, I am using this space to encourage readers and their friends to sign the protest petition.  The petition already has over 2500 signatures, many of them alerted to the situation (as I was) by reading Gowers’s account.

Leicester is being cut back across the board, but the cuts in mathematics are particularly severe.  For a crash course in the neo-liberal conception of the university, you can read the relevant chapter in Wendy Brown’s Undoing the Demos, featured in an entry on this blog last year.

This blog has been suspended but it will be revived occasionally for urgent news items like this one.

UPDATE:  Vladimir Tasić points out that this sort of thing is happening with increasing frequency in Canada as well.


Four scientific societies react to the resignation of French experts

I am told that the previous post on the resignation of the ANR evaluation committee for mathematics and computer science was widely shared on Facebook, notably by researchers in the social sciences.  Today the Société Mathématique de France published a joint statement signed by the presidents of four professional organizations, as well as the text of a motion in support of the resignation, voted by the SMF at their national meeting last week.

The joint statement is reproduced below (in French).

Déclaration des sociétés savantes françaises de mathématiques et d’informatique

Société Française de Statistique (SFdS),

Société de Mathématiques Appliquées et Industrielles (SMAI),

Société Mathématique de France (SMF),

Société Informatique de France (SIF).

Mise  en  garde  sur  l’inadéquation  du  modèle  de  sélection  de  l’ANR  pour  les mathématiques et l’informatique.

Les sociétés savantes de mathématiques, statistique et informatique (SFdS, SMAI, SMF, SIF) alertent  les  pouvoirs  publics,  l’Agence  Nationale de  la  Recherche  (ANR)  et  la  communauté scientifique  sur  la  démobilisation  massive  des  mathématiciens  et  informaticiens  constaté  ces dernières années dans les appels à projets de l’ANR.

Cette démobilisation  apparaît comme une conséquence  du choix de l’ANR de ne pas tenir  compte  des  spécificités  disciplinaires  et  de  ne  pas  impulser  une  dynamique  qui soit réellement au service du développement de la science et de l’innovation en France.

Les  mathématiques,  les  statistiques  et  l’informatique  sont  fortement  moteurs  et  vont l’être  de  plus  en  plus  de  façon  directe,  transversale  et  interdisciplinaire  dans  tous  les changements  en  cours  concernant  le  développement  technologique,  les  enjeux  du numérique  et  la  capacité  d’innovation  en  France  et  à  l’international.  Pourtant,  le conseil  de  prospective  de  l’ANR  n’intègre  aucun  mathématicien  ni  informaticien  en son sein.

Le  Comité  d’Evaluation  Scientifique  de  l’ANR  en  mathématiques  et  informatique (CES 40) a  constaté  une  forte  baisse  du  nombre  de  projets  soumis  en  2016, conséquence immédiate d’une perte de la motivation des  collègues face au très faible  taux  d’acceptation  des  années  précédentes.  Il  souligne    également  la difficulté  de  mobiliser  les  collègues  pour  expertiser  des  projets  trop  souvent rejetés.

Or le nombre de projets soutenus est calculé par l’ANR proportionnellement au nombre de projets soumis. Cette année, nos deux disciplines auront donc encore moins  de  projets  acceptés,  amorçant  un cercle  vicieux  qui  met  en  danger  la vitalité de nos communautés.

En outre, les modalités d’élaboration du taux d’acceptation de l’ANR ne sont pas discutées  de  façon  ouverte  ni  diffusées  à  la  communauté  scientifique  (toutes disciplines  confondues).  Ce  taux est  déterminé  par  l’ANR,  de  façon  opaque  et  sans   aucune   concertation   avec   les   comités   après   leur   travail   d’évaluation scientifique. Il est fixé pour chaque défi, sans aucune considération disciplinaire qui permettrait  de  dégager  une  vision  pour  le  développement  de  la  science  et leur impact économique et sociétal. Les comités doivent aujourd’hui travailler en «aveugle», sans aucune information sur la politique de répartition des moyens, et sans prise en compte des critères scientifiques pour le classement final.

Les quatre sociétés savantes signataires  demandent donc que les comités scientifiques soient pleinement associés aux modalités d’élaboration des taux d’acceptation, qu’une enveloppe budgétaire soit décidée en amont du travail des comités et que le conseil de prospective de l’ANR soit plus représentatif pour les mathématiques et l’informatique. Porteuses  des  attentes  de  leur  communauté,  elles  souhaitent  rencontrer  le  ministère dans les plus brefs délais.

GÉRARD    BIAU,    Président    de    la    SFdS,

FATIHA    ALABAU,    Présidente    de    la    SMAI,

MARC    PEIGNE,    Président    de    la    SMF,

JEAN-­MARC    PETIT,    Président    de    la    SIF.