Category Archives: Ethics

Time to move on

wainua               Figure 6.1 (Clairaut's diagram)

Snail image:  Creative Commons licence courtesy of Te Papa; Clairaut’s love formula from Chapter 6 of MWA

My tireless editor Vickie Kearn at Princeton University Press has brought me the welcome news that Mathematics without Apologies will be coming out in a paperback edition next spring.   I started this blog for two reasons, and one of them — to clarify my intentions in writing the book — will vanish when I add two or three pages to the preface of the new edition.   The new pages — I have already written them — will devote one paragraph or so to each of four topics, provisionally under the headings charismamemoirsutility, and ethics; each paragraph will address some of the points raised by comments on this blog as well as in some of the more negative reviews.

My other reason  for starting this blog was to find some outlet for the wealth of material that I was not able to incorporate in the book.  Most of this material has remained untapped while I composed comments on current events or new findings, and I was idly wondering when I would get around to sifting through the 7 GB  or so that is gathering nanodust on my computer’s hard drive.  My Eureka! moment came when I realized that I had already devoted a considerable amount of my free time to writing the book during the better part of three years.  Perhaps I didn’t really want to return to the old material?  With the new preface, I can finally declare the book finished and move on to something else.

Will it be another book, maybe one that will win me the mythical seven figure advance?  Or will there be another blog, or the same one under another name?   That’s for the future to decide.  Meanwhile, this one will remain visible, but with no new entries.

My thanks to the regular readers and occasional visitors who helped keep the blog from slipping into solipsism.  And my special thanks to authors of comments who, by disagreeing, often sharply, with opinions expressed here, demonstrated that the meaning of mathematics is still a matter of controversy.


This was supposed to be the last entry, but I’m now thinking I should include part of the new preface material — or all of it, if PUP allows it.  Meanwhile, in order not to let anything go to waste, here is the post on which I was working when I realized that this blog had reached the end of its natural life…




I Cunfirenti

This was originally going to be an appendix to the playlist near the end of Chapter 8:  an exploration of the attitude to mathematics in the genre of organized crime ballads.  The deeper meaning of Rick Ross’s 2009 single Mafia Music was exposed even before it was released,  but I was unable to find an interpretation of the unexpected appearance of mathematics in the middle of this rap à clef:

I thought about my future and the loops I could pin.
Walked out on a gig and I turned to da streets,
Kept my name low key, I ain’t heard from in weeks.
I came up with a strategy to come up mathematically,
I did it for da city but now everybody mad at me.

Apart from Rick Ross, Gödel is the only person Google finds who can “come up mathematically.”  My guess is that Ross’s strategy (unlike Gödel’s) involves money.  But Ross is not really a gangster, and Mafia Music is not really a mafia song at all; in fact, by naming names the song breaks what I’m told is the most fundamental of all the rules of the Italian Malavita, namely the rule of omertà, the iron law of silence.

Now it struck me when I saw this that the mathematical profession has its own version of omertà, probably not very different from other forms of academic rules of silence, having to do with forms of behavior that straddle the line that divides the unpleasant from the unethical.  The behavior protected by mathematical omertà differs from other varieties in that it tends to inspire less literary commentary.  Instead it consists in scandalous rumors whispered in corridors when they are not being shouted across barroom tables, but that must under no circumstances be mentioned in public.  (There was a scurrilous exception in a well known literary magazine a few years ago, but I will not dignify it with a link.)

I am particularly sensitive to this rule just now, because in the past few weeks I was shocked to learn of abuse of power by several colleagues I would not have believed capable of such behavior (and by a few others I can easily believe capable of anything).  Whether being the repository of such confidences is one of the perks of my charisma, or whether it’s the abusers who feel newly entitled as a result of their own charisma, the mildest punishment I could expect if I chose to betray the dark secrets of the mathematical profession is not to be privy to such secrets in the future.  Breach of Mafia omertà is treated more harshly than that.  Many of the songs on the delightful album La Musica della Mafia are devoted to the many kinds of punishment the gangster ethic  —

Laws that don’t forgive those/Who break their silence

reserves for traitors — cunfirenti, in Calabrian dialect.  For example, the song entitled I cunfirenti promises that they will find “their final resting place in concrete walls” (‘Mpastati ccu cimentu e poi murati).

The album’s title is imprecise; it’s not a collection of songs of the Sicilian mafia but rather the ballads of their Calabrian declension, the ‘Ndrangheta, who deserve to be better known, and not only for their songs:

Its success at drug smuggling catapulted the ‘Ndrangheta past its more storied Sicilian rival, the Cosa Nostra, in both wealth and power. Italian authorities now consider the ‘Ndrangheta to be Europe’s single biggest importer of cocaine.

What I find most charming about this collection is the contrast between the lively rhythms of many of the songs and the uniformly grim, often bloody, content of the lyrics.  For example:

Malavita, malavita
Appartegnu all’Onorata
Puru si c’impizzu a vita
Eu nun fazzu na sgarrata

Which means

Malavita, malavita!
I am one of the honorable society.
And even if it costs me my life,
I will never surrender.

If you’re looking for mathematical content you have to skip to the last verse:

Ed eo chi tingu sangu ´nta li vini
Su prontu d’affruntari mille infami
A chista genti ci rispunnimu
Pidi sunu pronti centu lami

Which means

And I who have blood flowing through my veins
Am ready to face 1000 traitors
As they know all too well
That 100 sharpened knives are ready for them.

French expert committee resigns in protest

The members of the French Scientific Evaluation Committee in mathematics and computer science (CES 40) resigned unanimously on June 1 to protest “the confiscation of scientific choices by a purely administrative [i.e., bureaucratic] management.”

The role of the CES 40, and of similar committees in other disciplines, is to evaluate research proposals submitted to the Agence Nationale de la Recherche (ANR), which then decides which projects to fund.  The ANR (not to be confused with absolute neighborhood retract) was created in 2005 in emulation of the NSF, in order to shift priorities from long-term funding of laboratories and research teams to short-term funding of specific projects, “in a context of budgetary constraints [i.e. austerity],” according to Wikipedia.  Former French President Nicolas Sarkozy (currently under investigation for illegal campaign funding) explained the motivations of the move with his characteristic disdain for the scientific community:

Je souhaite qu’à cette nouvelle génération soit inculqué non plus le réflexe du financement récurrent mais la culture du financement sur projet, la culture de l’excellence, la culture de l’évaluation.

The text of the protest letter is copied below, and can also be read here, with comments, as well as on the website of the Société Mathématique de France.

Le Comité d’Evaluation Scientifique en mathématiques et en informatique de l’Agence Nationale de la Recherche démissionne en bloc pour protester contre la confiscation des choix scientifiques par une gestion entièrement administrative

Le 1er juin, à l’issue de trois jours d’évaluation scientifique, le comité en mathématiques et en informatique (CES 40) a décidé unanimement de ne pas transmettre ses conclusions à l’ANR. Ses membres refusent de servir de caution scientifique et déclineront toute sollicitation ultérieure de l’ANR dans les conditions actuelles.

Le comité conteste l’opacité du processus de sélection. A ce jour, le nombre de projets financés est déterminé en proportion du nombre de projets soumis, sans que les comités aient la maîtrise du seuil d’acceptation, ou la connaissance de l’enveloppe budgétaire attribuée. Or, loin d’être uniquement des informations financières ou administratives, ce sont des éléments scientifiques essentiels sans lesquels les comités ne peuvent élaborer une proposition cohérente.

L’addition des contraintes budgétaire et administrative conduit mécaniquement à un taux d’acceptation trop faible pour être incitatif. Or, la constitution d’un dossier de qualité exige un temps important, que de moins en moins de collègues accepteront d’investir au vu du taux de succès qui a cours. Cela s’est traduit par une diminution de plus de 20% du nombre de projets soumis dans le CES 40 qui entraîne à son tour une baisse du nombre de projets financés. L’ANR manque donc l’occasion de soutenir un nombre important de projets à fort impact.

Le comité s’inquiète aussi de la perte annoncée de son indépendance, puisque son président sera désormais employé par l’ANR.

Les membres du comité demandent à la direction générale de l’ANR la mise en place un nouveau mode de fonctionnement. Ils souhaitent un meilleur contrôle du processus de sélection, de manière à mettre en œuvre une politique scientifique cohérente qui respecte les spécificités de chaque discipline, au service de la stratégie nationale de la recherche.

Les membres du CES 40, unanimes :
– Christophe BESSE, Président du CES 40, Professeur de Mathématiques, Université Toulouse 3
– Marie-Claude ARNAUD, Vice-Présidente du CES 40, Professeur de Mathématiques, Université d’Avignon
– Max DAUCHET, Vice-Président du CES 40, Professeur émérite d’Informatique, Université Lille 1
– Mourad BELLASSOUED,  Professeur de Mathématiques, Université de Tunis El Manar
– Oliver BOURNEZ, Professeur d’Informatique, Ecole Polytechnique
– Frédéric CHAZAL, Directeur de Recherche en Informatique, INRIA Saclay
– Johanne COHEN,  Chargée de Recherches en Informatique, CNRS, Université Paris Sud
– François DENIS, Professeur d’Informatique, Université Aix-Marseille
– Bruno DESPRES, Professeur de Mathématiques, Université Paris 6
– Arnaud DURAND, Professeur de Mathématiques, Université Paris Diderot
– Alessandra FRABETTI, Maître de Conférence en Mathématiques, Université Lyon 1
– Jin Kao HAO, Professeur d’Informatique, Université d’Angers
– Tony LELIEVRE, Professeur de Mathématiques, Ecole des Ponts ParisTech
– Mathieu LEWIN, Directeur de Recherche en Mathématiques, CNRS, Université Paris Dauphine
– Gaël MEIGNIEZ, Professeur de Mathématiques, Université Bretagne Sud
– Sophie MERCIER, Professeur de Mathématiques, Université de Pau et des Pays de l’Adour
– Johannes NICAISE, Professeur de Mathématiques, Imperial College Londres
– Lhouari NOURINE, Professeur d’Informatique, Université Blaise Pascal
– Jean-Michel ROQUEJOFFRE,  Professeur de Mathématiques, Université Toulouse 3
– Alessandra SARTI,  Professeur de Mathématiques, Université de Poitiers

Mathematics, morality, and crossing the finish line

Perelman

Andrei Yafaev is in New York and he thought I might like to watch a Russian television documentary about Grisha Perelman, which you too can watch on YouTube.   It’s in Russian but English subtitles have been added.  It has so far been viewed 268,517 times, so I’m probably not telling you anything most of you don’t already know; but it has a few provocative moments.

The documentary insists repeatedly that Perelman was “impeccably honest,” [безукоризненно честен] even as a child.    And this is depicted, for the Russian audience, as a characteristic of mathematicians.   Perelman’s “teachers insisted that mathematics is not only the Queen of the Sciences, but also the most moral science.”  Alexander Danilovich Alexandrov, Perelman’s thesis advisor, is quoted (at 32’02”) as saying “I’m not interested in geometry, I’m interested in morality [нравственность].”  Anatolii Vershik follows with a claim (at 32’12”) that mathematicians “have a very clear sense of right and wrong.”  Here “right and wrong” is a translation of истинность; this should ring a bell for those of you who have seen Ed Frenkel’s Rites of Love and Math, where the love-making and seppuku are both performed under the sign of истина, which is translated “truth.”  So we see Mikhail Gromov claiming (at 34’51”) that “mathematicians don’t care about money and prizes” — though he admits that money is convenient:  if you break your glasses you can replace them.

Perelman — a “national hero,” according to Fyodor Bogomolov — is unusual only for taking his impeccable honesty, his attachment to  истинность, to extreme lengths; his refusal of the Fields Medal and of the Clay Millenium Prize are the best-known examples of this.  But the documentary takes a strange detour near the end:  having spent 40 minutes depicting Perelman as a supreme exemplar of mathematical morality, suddenly the narrator remarks (at 39’17”) on how “strange” it is that he “rejects an ethical rule [главное этическое правило] of mathematics” [even a “main ethical rule” in the Russian original] in insisting that Richard Hamilton was equally deserving of the Prize.   And here Jim Carlson, speaking for the Clay Mathematical Institute, informs the viewer that “according to an unspoken rule the prize goes to the one who crosses the finish line.”  (The Russian version has Carlson attributing this to “mathematical sociology” —  questionable translations in both directions.)

This is weird in more ways than I can count, but I’ll just mention a few of them whose weirdness is independent of the Russian context.  Most obviously, the Clay Mathematical Institute is giving out its own prizes, and surely it can make up its own rules.  Next, the idea that there are “unspoken rules” governing the awarding of prizes in mathematics is completely new to me.  It’s hard, of course, to apply the methods of sociology to the study of “unspoken rules,” since by definition nobody is talking about them — but even if (as is likely) Carlson used “unspoken” as a poetic synonym for “hardly ever spoken,” or “spoken about in whispers,” one wonders:  how high up do you have to be in the hierarchy (oppressive or not) to have heard the faint whispering about these unspoken rules?

And then there is the principle itself, which seems to me to leave little scope for formal appreciation of those who point out where there are finish lines, so that others can exemplify an ethical rule by collecting prizes for crossing them.  I have a few people in mind, mathematicians whose names are most familiar in adjectival form.  Does anyone know where one might fruitfully whisper about this principle, and to whom?

 

Is the mathematical hierarchy oppressive?

After many interruptions I finally finished reading all the comments on Piper Harron’s blog, especially the long exchange (62 comments) entitled “Why I do not talk about math.”  This extended dialogue is deeply educational, and not only for those interested in mathematics.  Repeatedly contributors attempt to demonstrate their good intentions in the name of an abstract universalism, and Harron replies, politely but firmly, pointing out how the form as well as the content of their intervention reflects a position of privilege that is not necessarily conscious.  The entire exchange serves to reinforce the point of Harron’s title, as I understand it, namely that the process of repeatedly pointing out the effect of what (in a different post) Harron calls “oppressive hierarchies” eventually becomes tiresome, if not oppressive.

Harron’s comments overlap with the subject of Chapter 2 of MWA, entitled “How I acquired charisma.”  The chapter is primarily an extended reflection on the hierarchical structure of contemporary mathematics, interspersed (for narrative purposes) with an ideal-typical Bildungsroman whose anti-hero — who for the sake of convenience was chosen to bear a strong resemblance to the author of the book —is conducted, through the apparently natural workings of this hierarchical structure, to a middle-management position (routinized charisma) within the hierarchy.  The original purpose of the chapter was not mainly to engage in social criticism — that’s the focus of (parts of) Chapters 9, 3, and 4 — but rather to formulate a philosophical thesis, a tentative answer to the question formulated by KD on Harron’s blog:

I have always wondered exactly who gets to decide what is “important” or “interesting.”

I take sociology to be the discipline whose role is to answer questions like this, to study how collective decisions by groups of human beings come to be construed as objective and natural, and the chapter has a number of references to the sociology of science, and a handful of references to the much smaller literature in sociology of mathematics.

KD’s question, however, is political rather than sociological, with the implication that those who “get to decide” are exercising power from which those who don’t “get to decide” are excluded.  In the context of Harron’s blog, it is understood that this exclusion is not legitimate — or rather, since legitimacy as such can only be determined within the social order, that the order itself deserves to be called into question; in other words, as Harron writes, “We Need a Revolution. Period.

In a chapter of The Princeton Companion to Applied Mathematics entitled “Mediated Mathematics:  Representations of Mathematics in Popular Culture and Why These Matter,” Heather Mendick has written about how this exclusion is reflected in popular culture:

…popular culture can include some and exclude others.  For example, while society confers on all a responsibility to become mathematically literate, it suggests that only a special few possess mathematical “ability.”  It overwhelmingly depicts this ability as belonging in white, male, middle-class, heterosexual bodies.

Popular culture is not exactly a mirror of the reality of the profession, but it’s uncomfortably close.  Harron wrote an unconventional thesis in part because she sees this exclusion as rooted in the norms of contemporary mathematical practice; as she wrote

I just think our criteria for “new” “contributions” are seriously flawed and counterproductive and marginalizing. any mathematician who cares about “diversity” needs to be willing to shatter current paradigms.

I have been unhappy with the use of the word “diversity” in this context ever since I learned how it entered American jurisprudence in Christopher Newfield’s book Unmaking the Public University:

…in [Justice Lewis] Powell’s diversity framework, diversity was the expression of an institution’s freedom to choose particularly attractive individuals, and was about ensuring this freedom for powerful institutions like… Harvard College.…Diversity acquired social influence not as a moderate mode in which to pursue racial equality but as an alternative to that pursuit.

But Harron, whose blog is called The Liberated Mathematician, obviously doesn’t have Powell’s framework in mind when she uses the word diversity, so I will leave that discussion for later.  Instead I will engage in utopian speculation, in order to address what I see as the more subversive implications of Harron’s call for “power^people.”  Suppose one could magically do away with all the barriers to participation in mathematics of underrepresented populations, all the forms of exclusion, that are conventionally seen as political.  Would mathematics still be hierarchical?  And if so, would it still be oppressive?

A long tradition sees mathematics, and the sciences more generally, as necessarily hierarchical.  MWA quotes Max Weber on p. 10:

“Democracy should be used only where it is in place,” wrote Max Weber in the  1920s.  “Scientific training …is the affair of an intellectual aristocracy, and we  should not hide this from ourselves.”

And just last year, Alain Badiou wrote

The mathematical aristocracy at the creative level is… the most restrictive of all possible aristocracies.  (Badiou, Éloge des mathématiques, p. 23)

Chapter 2 of MWA exhibits the operations of hierarchy both symbolically (the IBM Men of Modern Mathematics poster, as well as Figures 2.1, 2.2, and 2.3) and materially (the role of the journal system in what Terry Tao called “certifying… significance” and “designation”, see p. 36).

Are these practices a relic of a more aristocratic period in the life of our species, and can we look forward to a future mathematics that is more inclusive, in the vision expressed by David Pimm and Nathalie Sinclair and quoted on p. 33 of MWA:

Asking “[I]n  what sense … can mathematics be considered a democratic regime…” open to all,  Pimm and Sinclair quote  … Henri Poincaré to the effect that “only  mathematicians are privy to the aesthetic sensibilities that enable” the decision of “what is worth studying.”  The article, published in a journal for educators, is  motivated by the “view that mathematics can do something for me in a  humanistic sense that repays the careful attention and deep engagement it may  require; one that may expose students to a fundamental sense and experience of  equality … and provide them with another sense of human commonality.”

Or is it the case, as Chapter 2 suggests, that “the content of mathematics is bound up … with a hierarchical charismatic structure”;  so that if Weber’s “intellectual aristocracy” lose control of the editorial boards of the “great journals” will mathematics be voided of its content and collapse into a sort of intellectual gray goo?

Philip Davis and Reuben Hersh, in The Mathematical Experience, famously claimed that “the typical working mathematician is a Platonist on weekdays and a formalist on Sundays.”  I would consider substituting “social constructivist” for “formalist” in that sentence; that would make clearer the unsettling radicalism implicit in Harron’s critique.  For my part, while my (routinized) charismatic bargain leaves me the freedom to be a social critic on the weekends, when I write things like this blog entry and Mathematics without Apologies, on weekdays I carry out my middle-level managerial tasks of maintaining the charismatic hierarchy — writing letters of recommendation, sitting on hiring committees, refereeing journal articles, all the “Traditional Rituals” (in the language of sociologist Bernard Gustin) without which the system would not be a system.  I’m a gatekeeper, in other words.  Not only that, I fulfill my functions with sincerity and commitment, and that should go without saying, otherwise my charisma would be unceremoniously withdrawn.

So am I contributing to the preservation of an oppressive system?  It’s easy to point to out that our professional autonomy is conditioned by one might call its limited sovereignty, the fact that (but this is one of the themes of Chapter 3) that we are dependent on Powerful Beings for the external goods without which the profession ceases to exist.  The Elsevier boycott of 2012 brought home to me just how little leverage we have, as mathematicians, over the profession’s material conditions, even those one might expect to be most dependent on our charismatic consent.  Our professional associations enjoy a fair amount of moral authority but lack the personnel, the organizational structure, the money, and the executive power to put up substantial resistance to the Powerful Beings on whom we depend.  Rereading the comments on Piper Harron’s blog, it occurs to me that the people to whom they are addressed, namely her readers, are not in a position to do much of anything about the issues raised there, beyond trying to answer questions like the one in this post’s title.

You should not be reading this!

SKMBT_36160209112200

Jean-Michel Kantor is concerned that “the American intellectual world is … closed to European (French /CNRS) ideas,” and that readers of this blog, especially American intellectuals, have not had the opportunity to read what Michael Blay has written about blogs and other forms of electronic communication.  The proof that you are closed to French/CNRS ideas is that you are still reading this blog, and even the quotation on the back cover of Blay’s book has not yet convinced you to stop.  At Kantor’s request, I am therefore making the pages he selected from the book available so you can decide whether or not to overcome your click-addiction and devote fingers like the ones (presumably Kantor’s) pictured in the photocopies to slower and more ethical activities.

SKMBT_36160209112200

And if your fingers are not yet convinced of the virtues of slowness and don’t have time to read the three pages in French, here is a key excerpt, with (absent) punctuation as in the original:

“[…] choose slowness in order to recover the viewpoint of an actor of your existence by escaping the supposed virtues of the ever-faster and of acceleration that dispossess each of you of your existence by reducing it to unreflected behavior that is to say to ideologically conformist and learned behavior, to behaviors by means of which the totality of existence can enter into the productive field;”

Beneath the excessively long jargon-and-banality-packed phrasing — a clear sign that the author chose something other than slowness in pasting together this pamphlet — the reader may recognize one of the recurring themes of this blog, and of MWA:  namely, the resistance to reducing mathematics to its function in “the productive field.”  Although Blay concludes with a conclusion with which I believe I am in agreement, I am unable to detect anything resembling a persuasive argument in this excerpt, and, unlike Kantor, I remain convinced that it is possible to reason within the frame of a 250-1000 word blog entry.  For all I know, Blay may even agree with me.

Hollywood verdict: Quants not guilty

 

gavel_41

And so, by implication, are the mathematics professors who taught them how to model financial derivatives.  The parties responsible for the collapse of 2008 are clearly designated in The Big Short and they are bankers and investment brokers, with a strong supporting cast in the ratings agencies and the financial media; government regulators are guilty primarily of crimes of omission.   I only remember seeing one quant:  Ted Jiang, in a brief appearance by Stanley Wong, presented by the Ryan Gosling character as Yang, who doesn’t speak English (though in fact he does) and whose role in the film is to project the nightmare stereotype of the “math guy” whom one could not imagine possessed of human agency, much less of being able to be guilty of anything.

The distribution of responsibilities on view in The Big Short is consistent with what I’ve seen in other films on the (continuing) financial crisis; the “math guy” is never the culprit.  Thus the quant played by Zachary Quinto has a substantial part in advancing the plot of Margin Call, released in 2011, but his role is purely technical; the unethical means to which his firm resorts to escape being brought down in the unfolding disaster are entirely the responsibility of the bankers.  Quants are hardly visible at all in the other films I’ve seen, but I confess I haven’t seen them all and my impression is open to correction.

Insofar as Hollywood shapes mass consciousness, the bottom line seems to be that we’re not guilty.  Good.  Does that mean we’re off the hook?  The next time the system collapses, will it be enough to follow Daniel Stroock’s lead and protest that “others were supposed to man the brakes?”  I think we can do better, and it would be wise to get started sooner rather than later.

Added January 14:  I neglected to mention that Stroock’s “batfish” article in Technology Review was taken up by the international press.  On December 9, 2007 it was cited by the Financial Times in an article entitled

Does not compute: How misfiring quant funds are distorting the markets

that concluded

Whether quants have a future, however, depends on how far investors burnt by the losses of August and the subsequent flight to less risky-looking assets can share Mr Stroock’s confidence.

In May 2008 El País cited Stroock’s “batfish” piece in an article entitled “This robot will make me a millionaire”;  the Madrid daily identified Stroock as a defender of automated trading.  (That’s the quotation that eventually led me to the Technology Review exchange.)  A few months later the Lehman Brothers collapse settled the debate for most purposes.

 

Batfish in Gotham (where is Laurent Schwartz? part 2)

Batfish

When I started this blog I took pains to explain that what some of the blurbs called the author’s “erudition” was in fact a kind of optical illusion facilitated by the Internet.  (See the answer to question 5.)  Just yesterday I found this in an article about translation:

Any translator of [German author W.G.] Sebald can spend days skipping from one website to another and feel very erudite, but with scant practical results.
In my case the practical results were considerable:  69 pages of endnotes and a 25-page bibliography.  But erudition is much more than that.  In the process leading up to the writing of MWA, I had the privilege of meeting genuinely erudite people.  They know things before they look them up.  Big difference.  It means, specifically, that their writing is not marred by gaps and glaring omissions.
I can illustrate this by pointing to a particularly glaring omission in MWA. Early in Chapter 4 MWA quotes a Le Monde interview in which former French Prime Minister Michel Rocard accuses mathematics professors of “crimes against humanity” for teaching their students how to make “a killing on the stock market” [coups boursiers].  The interview was published in early November 2008, six weeks after Lehman Brothers filed for bankruptcy, setting off a recession from which Europe, at least, has yet to recover.  Rocard said at the time that

ce qui frappe, c’est le silence de la science [what’s striking is the silence of science].

A few days later, science responded in the persons of Jean-Pierre Kahane, Denis Talay and Marc Yor, but Le Monde “n’a pas jugé bon” to print their response; it was finally made public the following May in Images des mathématiques.  Every word in their answer to Rocard is worth reading.  It was quoted briefly in Chapter 4 and I won’t repeat what I wrote there.  It suffices to mention that they distinguished between the responsibility of mathematicians, which is to develop quantitative models that are “indispensable to deal with risks of an increasingly complex world”; that of the quants, who apply the models they learn from the mathematicians; that of the traders and bankers who used these models to create the dangerous derivatives that brought global finance to the brink of collapse; and that of the politicians, whose task it is to make such abuses impossible, but who failed in that task and thus “are much more guilty than the mathematicians…”

Au fait, le pouvoir politique n’a-t-il pas été bien plus coupable que les mathématiciens en n’imposant pas aux institutions financières de réelles contraintes sur leurs risques ?

And one more quotation in the same vein:

Exprimés sous forme de modèles mathématiques et d’équations, les risques deviennent, au moins en partie, objectifs et quantifiables. Le pouvoir politique dispose alors d’informations utiles pour que la minimisation des risques, plutôt que la maximisation des profits, soit un objectif prioritaire.

At the time I was convinced that concerns must have been expressed in print before the crash, but I had no idea where to look.   I confess I didn’t try very hard.  Just this week, though, I found a pair of articles in MIT’s Technology Review, dating from November-December 2007, that a truly knowledgeable author would not have failed to cite.
 The first article, entitled The Blow-Up, by Bryant Urstadt, was a Featured Story that reported on the implications of the collapse of the subprime market during the summer of 2007.  “Is Subprime the Canary in the Mine?” was the title of a conference attended by “200 of the smartest people on Wall Street” that August.  We learned the answer to that question just over a year later, but at the time only “the most pessimistic” quants
imagined that the collapse of the subprime market could lead to a shortage of credit as banks dealt with defaults. That would chill the economy, causing worldwide job losses, still more defaults, decreased spending, and withdrawals from the stock market, culminating in a global recession, or worse.
The most pessimistic of the quants were far from pessimistic enough, it turns out.   The second article, by the eminent MIT probabilist Daniel W. Stroock, did not address that question, however.  Instead, Stroock, who identified himself as a teacher of quants, reacted to one passage in the Blow-Up article:

The events of August were outliers, and they were of the quants’ own making.…To begin with, quants were indirectly responsible for the boom in housing loans offered to shaky candidates.

Stroock disagreed; he considered the role of quants “closer to that of the sweepers who used to clear the ticker tape off the floor of the stock exchange than to that of a traditional investment banker.”

The role that so-called quants play in the financial world is analogous to the role batfish play in keeping coral reefs tidy. Just as batfish do not construct the reef but are essential to its health, quants do not create the structure financial markets depend on but do preserve the conditions that make markets function. So it would be misleading to suggest that quants were responsible for this summer’s meltdown in the subprime-mortgage market or for the broader troubles that followed….

Readers of MWA will recognize Stroock’s batfish as the genteel cousins of the flesh-eating Wall Street piranhas that make an appearance on p. 101; as Stroock goes on to explain:

By scrutinizing financial data, quants spot arbitrage opportunities and alert their employers to act before others have a chance to do the same.

Stroock concludes that quants are not responsible

for the mess in which the financial world finds itself. Quants may have greased the rails, but others were supposed to man the brakes.

Who, one is entitled to wonder, are these “others?”  When Kahane, Talay, and Yor wrote their response to Rocard, the crash had happened and it was too late to pass the buck:

Les scientifiques ont un devoir d’alerte quand ils peuvent mettre en évidence un danger collectif. A cet égard, les mathématiciens ont une responsabilité particulière.  [Scientists have a duty to sound the alarm when they can make a collective danger visible.  In this respect (with regard to finance, that is) mathematicians have a special responsibility.]

Have mathematicians been exercising this responsibility in the drafting of regulations to prevent future abuses like those that caused the crash of 2008 — or at least to make sure there is someone to “man [sic] the brakes?”  Have the teachers of quants been sounding the alarm?  Are they making sure their students receive the ethical training to sound the alarm when their employers are unable or unwilling to do so?  Have codes of professional responsibility been drafted so that quants can recognize an ethical problem when they see one?
These are sincere questions (even though I’m pretty sure I know the answers).  My knowledge of the relevant literature is severely deficient, whatever may be claimed regarding my supposed erudition.  Worse, although the Black-Scholes equation is displayed in all its enigmatic majesty on p. 85, and although I did more or less manage to follow its derivation on Terry Tao’s blog, my command of the underlying concepts has always been shaky at best.  It’s not that I’m incapable of learning the basics of stochastic differential equations.  It’s because the theorems of financial mathematics are about money, which, frankly, is something whose appeal I have never understood.

At this point, many of you are probably asking why I am presuming to talk about these matters, since I obviously lack the necessary professional qualifications.  I will answer with an autobiographical digression.  The incidents described in the first of the excerpts (the one that starts “Now you’re in for it”) really took place.  At the European Congress of Mathematicians in Barcelona I really did experience a sense of dread and foreboding when a speaker said something on the order of “Thank God for Finance Mathematics” because it “providentially brought so many undergraduate and masters’ students to our departments’ lonely corridors” (as you can read in the excerpt).  At that moment, in 2000, I had a premonition that the whole scheme would collapse; that no one would “man [sic] the brakes” and governments would be forced to bail out the too-big-to-fail banks, as in the Savings and Loan crisis of the 1980s; and that mathematicians would be blamed.  Naturally, out of a minimal sense of professional responsibility, I resolved then and there that, together with like-minded mathematicians, I would teach myself what those providential students were learning, and explain the dangers to anyone who would listen.

 

I didn’t find any like-minded mathematicians at the time.  I actually bought a few texts on financial mathematics and tried to read them, but all that talk of money and investments, from the very first pages, clouded my understanding.  And so, because I failed in my mission to make myself an expert, I decided I had no standing to speak out.  What I learned from the crisis that started in 2008, with no end in sight, is that one can’t wait for the experts to speak out.  Chapter 4 is my penance.  What have the experts learned?
IMAGE CREDITS:
Bat Fish
By Rein Ketelaars (Flickr: DSCN1938.jpg) [CC BY-SA 2.0 (http://creativecommons.org/licenses/by-sa/2.0)%5D, via Wikimedia Commons