Category Archives: Images

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 do so 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 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”

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




The soul of a space

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


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

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


A room designed by architect Vipin Bakliwala

Bakliwala’s reply also deserves our attention:

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

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


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

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

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


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

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

Videos of the 2018 Mazur conference


The videos filmed and (barely) edited by filmmaker Oliver Ralfe were recently put online on the IHES YouTube channel.   Only about half of the events were filmed, but these include all the panel discussions (listed on the right hand side of the poster).   Here is the complete playlist:



Manjul BHARGAVA ‘Coming soon’



Poetry Panel



Persi DIACONIS – Barry Mazur as an Applied Mathematician



Philosophy/Law/Physics Panel



Jordan ELLENBERG – Heights on Stacks



History of Science Panel



Haruzo HIDA – Galois Deformation Ring and its Base Change to a Real Quadratic Field



Glenn STEVENS – Modular Symbols, K-theory, and Eisenstein Cohomology



Alexandra SHLAPENTOKH – Defining Valuation Rings and Other Definability Problems in Number Theory



Akshay VENKATESH – Derived Hecke Algebra for Weight One Forms and Stark Units



Wei ZHANG – Selmer Groups for Rankin-Selberg L-functions of GL(2)xGL(3)

Not about Fibonacci

quadrivium - 1

Arithmetic, geometry, and music in Giovanni Pisano’s pulpit (1301-1310), Duomo di Pisa

Pisa is the international symbol of improbable constructions and therefore a fitting location for this week’s workshop.  Pisa is also a fitting location for meditating on the eternal and impossible question:  do we engage in mathematics because we find it beautiful, or do we find mathematics beautiful because of our programming?  Are Pisa’s medieval arcades beautiful because we are used to them or do we admire Pisa for the beauty of its medieval architecture?

In addition to the Roman sarcophagi that littered Pisa’s underworld and were recycled in medieval times to house the remains of political and military citizens “di primario spicco,” Pisa’s Camposanto contains the gigantic (5.6 x 15 m) 14th century fresco Il trionfo della morte which might have served as a reminder of the urgency of completing the program of this week’s workshop, but which is undergoing restoration and is therefore not visible to the public.  It seems to me the workshop provides a striking illustration of the complex interplay between freedom and inevitability in the design of a mathematical theory, in this case the mod p Langlands program, whose ultimate goals are being defined, democratically as far as I can tell, through workshops and conferences like this one.

Pisa’s medieval walls are also decorated with a variety of political statements.  Someone found it worth his or her while to design a stencil to celebrate an American mathematical personality:

Kaczynsky - 1

Seen on a wall in central Pisa. The caption reads “strike where it hurts the most.”


Some cold mathematical humor

Voltaire - 1

What could Duchamp and Man Ray have had in mind when they aspired to “introduce a cold mathematical humor into life?”  I’ve been looking for examples in the dada canon, and no doubt readers will be able to point to more cogent examples, but the only one I managed to find in the Dadaglobe Reconstructed exhibition at the Kunsthaus Zürich is item 5 on the above contribution by Egidio Bacchi.

All human unhappiness stems from an incomprehensible truth:  2+2 = 4.  Why?

If it weren’t the case, then we would have enough wealth to sleep with the most beautiful woman of our country.

Items 2 and 6 are rather worse.   The exhibition, which is a genuine reconstruction of

the more than two hundred artworks and texts that were sent to Tristan Tzara in 1921 by artists from all over Europe

for a book project that was never completed,  will be closing in Zürich on Sunday and will be moving in June to the Museum of Modern Art in New York.  I don’t expect MOMA’s curators, any more than their colleagues in Zürich, will want to draw any more attention to this specimen of Dada’s last gasp.

Since the Zürich dadaists were in communication with Filippo Marinetti, the Italian futurist and future fascist — even going so far, according to Wikipedia, as to reproduce excerpts from Marinetti’s poem Zang Tumb Tumb in the first issue of the journal Cabaret Voltaire  — I worried that Bacchi was aiming at the kind of cold humor later popularized by Mussolini:


Mussolini joking with il federale Gazzotti in the Roman Forum, May 30, 1936

It was therefore a relief to see that Bacchi, who made his name as an art critic rather than as an artist, is identified as an antifascist, even  a “dangerous antifascist” according to one source.

I made the mistake of going back to Cabaret Voltaire a second time, when the humor was warmed-over rather than cold — a cook was serving what he claimed were roasted 50-franc notes to members of the audience, who were eating them.

Big Dada: A statistical found object at Cabaret Voltaire

Voltaire - 1

Here’s one even Jordan Ellenberg may not know.  There really is a Cabaret Voltaire in Zürich, right on the same corner as the original one, and while this year Zürich is celebrating the 100th anniversary of Dada, mostly at the Cabaret Voltaire, a few years ago there really was an exhibition with the title Dada x Statistik, and you can read about it on the city’s website.   The exhibition was held, naturally enough, at Cabaret Voltaire, where you can buy the exhibition catalogue (which features a lot of statistical diagrams and not so much Dada, as far as I could tell upon perusing it quickly while waiting for the show to start); but maybe it was at the city statistical agency as well, because the pretext for this exhibition was apparently that Dada and Zürich statistics are roughly the same age, and the two institutions are “a stone’s throw” from one other, according to the website:

Dass Statistik Stadt Zürich und Cabaret Voltaire gemeinsam eine Ausstellung realisiert haben, mag ungewöhnlich sein, überraschend ist es nicht. Beide prägt eine ähnlich lange Geschichte. Statistik Stadt Zürich ist das älteste städtische Statistikamt der Schweiz. Eine fast ebenso lange Geschichte hat der 1916 im Cabaret Voltaire begründete Dadaismus. Die beiden Institutionen liegen räumlich nur einen Steinwurf voneinander entfernt. Was lag also näher, als gemeinsam ein Projekt zu realisieren?

I don’t find this convincing enough to translate.  The catalogue had a slightly more plausible explanation:  the statistical agency and the dadaists have in common a propensity to collect a lot of stuff.   The Cabaret Voltaire’s website is not much more convincing (what does it mean to “bring the ideas of Dada into a connection with the morality and ethics of statistics and to create an instructive and entertaining third term”?).  But it does explain that 2013 was the “International Statistical Year”:

Dada x Statistik ist eine Zeitreise über die letzten 100 Jahre der Stadt Zürich. Mit situativen Interventionen und Exponaten wird das Arbeiten, Wohnen und Leben der Dadaisten um 1916 erfahrbar. Mit statistischen Daten und Prognosen wird zudem bis ins Jahr 2023 geblickt und so indirekt auch Dada in die Zukunft projiziert.

Dada x Statistik bringt die Ideen von Dada mit Moral und Ethik der Statistik in Verbindung und schafft ein lehrreiches wie unterhaltsames Drittes.  Dazu werden alle Räumlichkeiten sogar die Toiletten des Cabaret Voltaire bespielt.

Kuratoren von Dada x Statistik sind Adrian Notz vom Cabaret Voltaire und Statistik Stadt Zürich. Die Ausstellung ist ein partnerschaftliches Projekt, das im Rahmen des Internationalen Jahres der Statistik 2013 durchgeführt wird.

The big surprise, for me, was that the catalogue made no reference whatsoever to Big Data, although the pun is obvious; is it because the expression Big Dada is protected by a copyright since 1997?

The performance had nothing to do with statistics — unless that “instructive and entertaining third term” is now permanently installed at Cabaret Voltaire.   One of the performers, playing the part of André Breton, spoke this sentence twice:

And the wind gave way to mathematical illusions.

If this is a direct quotation, it’s unknown to Google, in English, French, or German, and I would be (moderately) grateful if someone could provide a source.  It turns out that both dada and surrealism were pursued by individuals who had studied mathematics, including  Tristan Tzara and Hans Bellmer; the Larousse Encyclopedia’s entry for dada alludes to the intention of Duchamp and Man Ray to “introduce a cold mathematical humor into life.”  And one recalls that, in the mid 30s, Max Ernst sketched and Man Ray took pictures of the objets mathématiques that they discovered during a visit to what the Centre Pompidou calls the Institut de Raymond Poincaré.

Given the widespread belief that nothing of world-historical importance, other than banking, has happened in Zürich since the First World War, and that the original Cabaret Voltaire was the center of the Zürich avant-garde at the time, I was expecting the present-day Cabaret to be a crass attempt to turn the subversion and anarchy of those pre-revolutionary days into a reliable revenue stream, an exercise in sanitized nostalgia for the TripAdvisor generation.  And perhaps it was, but I was surprised to observe that the standing-room crowd was uniformly hip (with at most one exception).  Maybe it’s because so many of them were American; the performers were from New York and Los Angeles, none of them could pronounce either the French names or the German names correctly, and it didn’t matter.  This naturally raises a paradoxical question.  The Breton character quoted a question Breton posed in 1922:

…among the objects said to belong to modernity, is a top hat more or less modern than a locomotive?

I ask:  is today’s Cabaret Voltaire hip because it attracts a hip crowd, or is the crowd hip because they’re at the Cabaret Voltaire?

Programming began in Mesopotamia

Plimpton322 - 1

This is a picture of Plimpton 322, a relatively late (less than 4000 years oldOld Babylonian cuneiform tablet that just happens to be located in Columbia’s Rare Books and Manuscript Library.  It may be the most famous of all mathematical tablets, because it contains a list of Pythagorean triples, including (in sexagesimal notation) (1:22:41, 2:16:01, 1:48).  Eleanor Robson’s “reassessment” seems to be the most influential recent analysis of the tablet, but since that link is behind Elsevier’s paywall, you may prefer to read her article in the February 2002 American Mathematical Monthly.


I took that picture, and here is another picture of the tablet in my very own gloved hands,

Plimpton in gloves

taken two weeks ago by a visiting colleague.

I had been thinking about Babylonian mathematical tablets in connection with an article I’m currently writing.  The title of this post is suggested by the following quotation from an article (unpublished, I believe) by Jim Ritter, entitled Translating Babylonian Mathematical Problem Texts:

A good interpretive level would be one which would use only the cognitive tools used in Ancient Mesopotamia, which would apply to all mathematical problem texts and which would remain as close as possible to the formal structure of the text. Such an approach was first suggested for Babylonian mathematical texts as early as 1972 by the pioneer of computer algorithmic, Donald Knuth (KNUTH 1972 and 1976), an algorithmic approach based on sequences of arithmetic and control commands. Unfortunately for Assyriology, the paper was published in a computer science journal and so remained unknown there in general until this approach was independently rediscovered in the late 1980s (RITTER 1989b).19 The advantages in this approach are major. First of all, the problem texts as they have come down to us are algorithmic in nature. There is no need to move beyond what is actually written and the same approach applies to the whole corpus. Moreover the dual nature of the commands in the text—calculational (arithmetic operations) and control (initialization, storage, parallel computing)—parallel exactly the dual nature of modern programming. Perhaps most importantly, this interpretation is minimal in the sense that it does not block an algebraic or geometric further development if the reader or translator so desires.






Image from Plimpton 322, in the collection of Columbia University, via Wikimedia Commons

Coincidence? Or secret signal?


When N. H. Abel’s portrait stared back at me through the window at [REDACTED] airport I was briefly under the impression that at least one airline was ready to celebrate our vocation’s romantic imagery.  Then I leafed through the on-board magazine and leaned that Abel was only one of Norwegian Air’s tail fin heroes and had been spotted exercising this function as early as 2011.    One reads:

The word “halehelt” (tail fin hero) was placed number six on the Top Ten Words of 2012 list, developed by the Language Council of Norway and NHH – the Norwegian School of Economics.…

The solution was to involve people in local elections to find Norwegian’s next tail fin heroes. The portrait of the local tale fin hero, voted for by local citizens, would grace the tail fin of one of Norwegian’s new aircraft. The concept was developed by ad agency Kitchen, while our task was to make sure we created engagement around the campaign in earned media.

Heroes are Scandinavian and include Henrik Ibsen, Kirsten Flagstad, Fridtjof Nansen, H.C. Andersen, and many other more or less familiar figures.  Greta Garbo is on the way but not, apparently, Sophus Lie.

It should be obvious to readers that the story is merely an excuse to display the above photo; and while I’m at it, here’s a completely unrelated photo that I forgot to include in an earlier post on Cédric Villani’s ubiquity in French media:


Nevertheless it’s fair to ask:  what was the likelihood that I would see precisely this and no other portrait on my sole Norwegian Air Shuttle flight?   Between 1 and 2%, judging by the list.

Global warming equations in the Paris metro

RER Gare du Nord - 3

(added June 24, 2020)


These photos were posted in 2015.  Maybe you would be interested in reading something more recent and timely?


If you didn’t make it to the COP21 meeting in Paris in November you missed the opportunity to be placed under house arrest; but you also missed the exhibit of climate change equations still on display at the southbound RER B platform in Gare du Nord.  The explanation, such as it is, can be read on this panel:

RER Gare du Nord - 8

The man in red has nothing to do with the climate meeting; he is standing there to prevent passengers from falling onto the tracks during rush hour and to help them onto the train at all times.

If you need to get to the IHES from the north of Paris, you’ll almost certainly stand on this platform, and you’ll have enough time between trains to take your own snapshots.  For those of you who won’t have that opportunity, here is a more or less complete collection.

RER Gare du Nord - 1RER Gare du Nord - 2RER Gare du Nord - 6RER Gare du Nord - 5

The equations are not labelled individually, and apart from the green poster pictured above, the only explanation is to be found on this one:

RER Gare du Nord - 7

If you’re really curious about global warming, you’d do better to read Ivar Ekeland’s new book, entitled Le syndrome de la grenouille. I’ll be providing a complete report in a later post.