Category Archives: Values

Mathematicians as beneficiaries, and their patrons

What follows are the uncorrected notes for a presentation by videolink at the first workshop on Ethics in Mathematics, held in Cambridge April 20-21, 2018.

It’s a humbling experience for me to be asked to speak at this meeting, alongside some authentically legendary figures. Maurice Chiodo and Piers Bursill-Hall have assembled a stellar lineup in a remarkably short time. This is certainly a tribute to their energy and initiative, but the fact that so many speakers have agreed to participate is also a sign that Maurice and Piers have identified a need whose urgency is increasingly recognized across the profession. I do hope this week’s meeting will be remembered as the start of a genuine international movement to place ethics at the center of our work as mathematicians.

It’s a special honor to be invited to participate in a conference on mathematics and ethics that is taking place in Cambridge, home of G. H. Hardy, a mathematician whose commitment to pacifism and social justice is well-known even beyond the profession. Since mathematicians are constantly being asked why our work is useful, it’s appropriate to recall that Hardy once wrote that

A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.

Hardy was thinking particularly of military applications of science, as well as of the mathematical economics of his time. Had he lived a few years longer he would have witnessed the growth of mathematical game theory, whose destructive consequences in both domains have been developed assiduously by the RAND Corporation, which figures prominently in the biography of John Nash, among other mathematical heroes.

I consider Hardy a precursor of current proposals for mathematicians working on various applications to adopt “Hippocratic Oaths,” the ethics of abstaining from doing harm. In an article published last year entitled Do Mathematicians Have Responsibilities?, I mention some of the more recent applications of mathematics that are “useful” in Hardy’s sense, but my focus is different.

While pure mathematicians in particular may have wondered whether much of their work would ever be socially useful, it was generally believed that at least it caused no harm. Events of recent years have called that belief into question.  The sophisticated and often opaque derivatives developed by financial mathematics magnified the effects of a downturn in sectors of the US housing market into a global financial crisis whose consequences are still with us. Edward Snowden’s revelations in 2013 served as a reminder that contemporary cryptographic techniques based on number theory can also be used to facilitate general surveillance by governments. The rapid growth of Big Data has made it possible for commercial as well as public actors to track individual behavior with increasing precision, with grave implications for privacy.

In each of these applications of mathematics one finds the same three features: an approach to human activity that is purely instrumental; a disdain for democratic decision-making; and the empowerment of experts on the basis of their mathematical training. And in each case, a few mathematical scientists have pointed out that the power of mathematical technology imposes social responsibility on those who develop it, beyond putting trust in experts.

In this brief presentation I want to stress the second and third features, because they make it clear that the call to “do no harm,” important though it is, does not fully discharge our social responsibilities as mathematicians. The fact is that our very expertise, as academics and researchers, contributes to the reproduction of the social order that makes the abuses not only possible but often inevitable. We perceive the universities and research institutes in which we work as protected spaces and spaces to be protected, and this is true as far as it goes. But the primary function of the university is to reproduce existing relations of power and influence. In this sense, Hardy’s refuge in pure mathematics is itself part of the problem. Indeed, A Mathematician’s Apology fairly reeks of the elitism that, even in its current attenuated form, is an essential aspect of the image, or the brand, that distinguishes universities like Cambridge and Oxford and Harvard and Columbia and endows their professors with the expert status that so often serves to undermine the democratic process.

Let me add right away that I am fully aware of the dangers of this kind of talk in the face of climate denial and right-wing populism more generally. Nevertheless, I remain convinced that the primary role of the expert in public policy is to be mobilized in support of dominant interests, in the spirit of Margaret Thatcher’s There is no alternative. The article I just quoted has a good illustration of this in connection with the current massive growth of artificial intelligence, and the feverish promotion of the Internet of Things as a technological inevitability and a promising investment opportunity. The ethical implications of these developments seem to have been entrusted, in particular by the EU, to the AI industry itself:

In connection with [the risks of AI], it was announced that Facebook, IBM, Amazon, Google, and Microsoft had just formed the “Partnership on AI” for the purpose of “conducting research and promoting best practices.”

Since then Apple has joined (the big five + IBM) and there are now representatives of civil society (ACLU, EFF, and Center for Democracy and Technology, among others). Of course the relative weight of the corporate and civil partners in defining “best practices” remains to be seen.   My point, however, is that the vision of democratic decision-making still places the expert at the center.

By the way, I have not come to you today with an alternative and more democratic model. The problem is a profound democratic deficit in the society at large. That’s not a problem for this gathering to solve; but in my opinion it is inseparable from any serious reflection on the ethical obligations of mathematicians or any of our fellows in the elite sphere we inhabit.

My aim was rather to make a few remarks about research funding, and I will quote from my article in the Times Higher Education Supplement to indicate how difficult it is to avoid tainted sources.

[Tom Leinster’s] question hasn’t gone away: should we cooperate with GCHQ? The problem is that research funds have to come from somewhere; the survival of number theory depends on it. 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. Henry VIII was a morally ambiguous character, to say the least, and a pioneer in eavesdropping as well as cryptography; but neither Hardy nor his friend Bertrand Russell refused his fellowship at Trinity on that account.  

It would be nice if the State could provide its own kidneys and impose an impermeable barrier between the budgets for research that is socially progressive, or at least innocuous, and the military and surveillance functions about which the less we know, the better. But States don’t work that way, and for the most part they never have. The only alternative to public funding, from whatever the source, is private philanthropy. America’s great private universities are monuments to the past and present generosity of some of our wealthiest citizens. That is not, however, what is most appealing about them. I find it demeaning to have to express gratitude for my research funding to practices of which I otherwise heartily disapprove — like hedge fund management, for example, or data mining — but that have given a few people the status of Ultra-High Net Worth Individuals … and thus in the position of being able to function publicly as philanthropists. Or to despots like the Emir of Kuwait, whose Foundation used to sponsor a generous lecture series at Cambridge.

It seems that anywhere you turn, you’re going to be someone’s kidney. But feeling demeaned is beside the point. As …Cathy O’Neil… put it in January 2014, “We lose something when we consistently take money from rich people, which has nothing to with any specific rich person who might have great ideas and great intentions.…” One of the things we lose: control of how decisions are made: “…the entire system depends on the generosity of someone who could change his mind at any moment.”

The more basic problem is that the very existence of UHNWI entails the concentration of power beyond the control of democratic oversight. Among billionaire patrons, Jim Simons stands out for his commitment to the values of working mathematicians — which is natural, given that he was a distinguished geometer before his management of the wildly successful hedge fund Renaissance Technologies made him an UHNWI. But the same high-frequency trading algorithms that fueled Simons’s philanthropy gave us Breitbart, courtesy of Robert Mercer, Simons’s former colleague at Renaissance. Mercer was much in the news earlier this year after it was revealed that, through his connection to Cambridge Analytica, he used psychologically targeted advertising on social media to intervene in the Brexit and Trump elections, possibly tipping the balance in both cases. Mercer has come to personify the sinister side of the UHNWI phenomenon, but even outspoken liberal billionaires like Facebook’s Mark Zuckerberg and Google’s Sergei Brin, who have been subsidizing pure mathematics indirectly through their cosponsorship of the extravagant Breakthrough Prizes, have built their fortunes on mathematical techniques that are no less threatening to privacy than GCHQ surveillance.

I could continue for quite a long time expressing my regret that the need to sustain our research places us in the uncomfortable position of dependence on ethically dubious sources of funding. In the interest of full disclosure, and to highlight the paradoxes of my own position, I ought to mention that this afternoon I will be heading to a conference in the Bavarian Alps, sponsored by the Simons Foundation! The first part of today’s presentation, however, was meant as a reminder that as researchers and academics our very salaries are being paid by institutions whose primary function is the preservation of the status quo. Insofar as the possibility of the most visible aberrations (Cambridge Analytica, NSA undermining of encryption standards, credit default swaps, drone guidance systems and so on) are built into the normal functioning of the status quo, and are justified by an ideology of expertise that is maintained by our universities and research institutes, our very existence as experts guarantees that our profession provides no refuge of ethical purity.

Interjection: How, by the way, did Trinity get to be so rich? I don’t know the answer; instead, I offer this bit of information as an ironic metaphor for our defense of ethics from our perches within the power structure:

At what is today Columbia University, there was a medal issued at graduation every year by the Manumission Society — many of whose members were slaveowners — for the best essay each year that opposed the slave trade (from a report by Eric Foner on Columbia’s website, as quoted in The Trinity Tripod of Trinity College, Connecticut, dated February 11, 2014)

(Of course, Columbia was hardly alone; Harvard, Penn, Dartmouth, William and Mary, and other leading universities of the time had interests in the slave trade.)

As I wrote in the THES piece:

[T]he immense privilege of devoting our lives to the research projects we have chosen freely imposes on us the obligation to speak out when our work is used for destructive ends, or when the sources of our funding do not share our values.

By “speaking out” I don’t mean simply reacting to abuses. I mean actively anticipating possible uses of our work, including our teaching of students, for purposes of which we do not approve. Here I would add that we are no less obligated to acknowledge the role of our institutions, and of our expert status within and through these institutions, in preserving existing power relations that are incompatible with democratic ideals.

The privilege of devoting our lives to our freely chosen profession makes us beneficiaries in the sense described in a recent book by my Columbia colleague Bruce Robbins. A great many people need to perform less rewarding work, or are rewarded less well for what they do, in order to provide us the means to pursue our professional goals.

Nevertheless, I want to conclude by stressing the importance of defending these benefits. I’m sure that each of you has been asked at one time or another some version of “how is what you do useful?” And if you are a pure mathematician you might have resorted not to Hardy’s definition of “useful” but rather to Hardy’s argument that mathematics is an art form, and therefore deserves to be pursued for its own sake. I suspect such an answer provides little defense against accusations of self-indulgence, irresponsibility, and a lack of due regard for the taxpayer’s money. Faced with such accusations — usually by individuals whose own position within the power structure leaves them open to challenge — I like to reverse the terms of the question: if mathematics is not to be pursued for its own sake, then for the sake of what? For profits, or Facebook “likes,” or to give Britain a leg up in the international marketplace? This should immediately pose the question of democracy, which in the present context includes the right to adhere to values that are not determined by the market and its ideologues and functionaries. All work should ideally be for its own sake. But this is an idea I am struggling to articulate, and I hope to have made some progress if and when we meet again.



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.)

The belief that there are natural laws of finance

I continue the discussion of Frédéric Lordon’s Jusqu’à quand, which contains an explanation of the practices that made the 2008 crash inevitable that has yet to be translated into English although it is more specific and complete than Margot Robbie in a bubble bath or celebrity chef Anthony Bourdain making fish stew.  Here is a quotation that grapples directly with the most dangerous of the many illusions promoted by the manufacturers of mathematical models, namely that the objectivity of such models can be separated not only from the empirical observations needed to confirm and perfect them but also from need for a conceptual framework in which the question of the model’s objectivity can be raised.   Lordon argues that quantitative (probabilistic) models of finance are meaningless if there is no reason to believe that finance is governed by natural laws:

Obviously the most devoted partisans of quantitative finance will argue that any imperfection is transitory and remind us how the development of science is progressive but irresistible; even if today’s models still make a few mistakes, there is no problem that won’t eventually give way to hard work and research.  There are nevertheless reasons to think that this optimism will come up against a fundamental and insurmountable obstacle, rooted in the very question of knowing whether it is possible, and if so how far, to grasp financial risk through the calculus of probabilities.    Transcribing risk in the language of probability is such a common practice that it is never called into question.  The modelers, who consider the question trivial, are thus barely aware of the — absolutely non-trivial — theoretical choices they undertake when they make the hypothesis that the prices of financial assets are governed by this or that probabilistic law. … Of all the tools offered by the calculus of probability, the so-called “Gaussian” law is the one most commonly used … because it’s the simplest to manipulate.  But Gaussian laws have the unfortunate property of considering large price variations as events of minuscule probability… even though they are frequently observed in financial reality.  [Thus there is a competition to find the most realistic law…]  But the more frenetic the search for the “right hypothesis” becomes, the more one loses sight of the essential point…:  the belief that one will someday find the “right probability density” amounts to the belief that there are natural laws of finance.  This belief can be given the name of “objective probabilism” because it presupposes that there objectively exists a certain law of probability — “we’ll find it in the end” — that governs the price of assets.

Lordon finds more credible an “alternative approach,” which he associates with the name of André Orléan, according to which

“the” probability density doesn’t fall from the sky of “objective natures” but is rather the endogenous product of the interaction of financial operatives.  … It’s the radical modification of the configuration of interactions between operatives, expressed notably by the brutal variation of the degree of heterogeneity (or homogeneity) of behaviors, that produces the regime shift, and the qualitative transformation of the relevant probability density.

Students of dynamical systems will recognize the similarity to the language of René Thom’s catastrophe theory.  Lordon continues:

If one is absolutely set on maintaining the notion of law to describe the phenomena of finance — and the observation can be extended to all the phenomena of economics — one must bear in mind that the laws in question are not natural and invariant but rather temporary, variable, and contingent.   If one wishes, one can therefore preserve the general probabilistic framework but only after amending it substantially… where quantitative finance believes firmly in an objective probabilism, what one could even call a transcendent probabilism, there is in reality only an immanent probabilism:  the laws of probability do not fall to earth from a heaven of ideas, they emerge from below, shaped by the concrete interactions of agents — another way to rediscover that God doesn’t exist.

The last few words notwithstanding, here we see Lordon on the road to Spinozism.  We will not follow him there, but rather draw the conclusion that, if “There is no alternative,” the formula associated with Margaret Thatcher, it’s because the decision-makers, the Powerful Beings, as they are called in MWA, have contrived to make alternatives impossible.  It’s certainly not because alternatives are mathematically unthinkable.


The alternative is to change the frame

Lordon at Bourse du Travail

Frédéric Lordon at the Bourse du Travail, Paris, April 20 (March 51), 2016

In their haste to titter about the drama to which Guido Menzio was subjected the other day at Philadelphia International Airport — the University of Pennsylvania economist was pulled off his flight and briefly questioned by the FBI, before he was allowed to reboard, because he had been spotted scribbling differential equations in his note pad — the journalists (and the FBI agents as well, apparently) neglected to ask the obvious question:  were his equations blueprints for what Warren Buffett called “financial weapons of mass destruction?”

The answer:  apparently not.  Menzio, who is linked to the author of this blog by seven degrees of separation, Menzio

is a specialist in the equilibrium of job search models, not in financial derivatives.  The journalists nevertheless squandered an opportunity to remind their readers that economics can be no less life-threatening than suicide bombers and that a quantitative comparison of their relative dangers is urgently needed.

I first encountered Frédéric Lordon’s elegantly ironic prose in the pages of Le Monde Diplomatique, probably in 2004, when he was already writing about the destructive effects of finance, long before the crash of 2008 showed him in retrospect to have been a prophet.  As the warning signs of the coming catastrophe accumulated in 2007, Lordon was there to point them out;  when the crash finally did arrive, I immediately turned to the book Lordon had completed, a few weeks before the Lehman Brothers collapse, for an explanation of what had brought the world’s economy to the brink of disaster.  Lordon’s book contained an introduction to what was then the arcane superstructure of MBSs, SPVs, CDOs, and CDSs that the “mad mathematicians of Wall Street” had erected on what would soon be the smoking ruins of what is politely called the “real economy,” and although MWA didn’t cite Lordon explicitly, I regret not including his book in the bibliography, since Chapter 4 could not have been written without it.

My next post will translate an excerpt from Lordon’s 2008 book of particular relevance to mathematics and mathematicians.  The witty and multiply-talented Lordon has since gone on to write many articles in Le Monde Diplomatique as well as many books, including what must be the only comedy in rhyming alexandrine verse (since made into a film) about the subprime crisis:

Le banquier

Monsieur le Président, votre haut patronage
Nous offre l’occasion de multiples hommages.
A votre action d’abord qui fut incomparable
Et victorieusement éloigna l’innommable.
Mais à votre sagesse nous devons tout autant
La grâce que nous vaut le parfait agrément
De vous entretenir et d’avoir votre oreille,
Pour éloigner de vous tous les mauvais conseils.

Le quatrième banquier

Nous savons le courroux qui saisit l’opinion,
Tout ce que s’y fermente, toute l’agitation.
Nous entendons la rue rougeoyant comme forge
Vouloir nous châtier, nous faire rendre gorge.
Le peuple est ignorant, livré aux démagogues,
Outrance et déraison sont ses violentes drogues.
Il n’est que passion brute, impulsion sans contrôle,
Un bloc d’emportement, et de fureur un môle.

Le troisième banquier

Mais nous craignons surtout que des opportunistes,
Sans vergogne excitant la fibre populiste,
Propagent leurs idées, infestent les esprits.
Ils ne nous veulent plus que raides et occis.
Même les modérés sont assez dangereux.
Incontestablement ils semblent moins hargneux,
Et s’ils n’ont nul projet de nous éradiquer,
Ils ne veulent pas moins nous faire réguler…

In recent years he had switched his attention (and his academic affiliation) to philosophy and was calling himself a Spinozist — the only one of his books translated into English is entitled Willing Slaves of Capital:  Spinoza and Marx on Desire.   But when le peuple began their nightly occupations of the Place de la République in Paris, calling themselves Nuit Debout,

Nuit Debout - 1.jpg

Nuit Debout by day, March 49, 2016

Lordon was acknowledged as an intellectual reference — a maître de penser, according to Le Monde.  The image at the top of this post is a screen capture of his (seated) intervention at a mass meeting around the corner from the Place de la République devoted to the “next step.”  The passage that starts at about 7’05” is particularly recommended.  I translate the climax (from 7’50” to 8’20”):

When the liberals say TINA, There Is No Alternative, it is objectively true.   But it is a conditional truth.  Yes, it is objectively true that, when one has set up the frame of all the neoliberal structures I just mentioned, there are no longer alternatives, and the frame is designed precisely to rule them all out.  However, if there are no longer alternatives within the frame, there is always the alternative of changing the frame.

Nuit Debout - 1 (1)

Nuit debout at dusk, March 64, 2016

Economics as theology, as viewed by Chinese astrologers



Chinese armillary sphere, Ming Dynasty, from Wikimedia Commons

Readers who recall Joseph Stiglitz’s quip that “economics is really a religion” will not be surprised to find a scholar of Chinese religion drawing parallels between the dismal science’s contemporary prestige and that of imperial Chinese astrology, on the basis of the common dependence of the two disciplinary practices on sophisticated mathematical models.  Not that imperial China had a monopoly on astrological economics:

…take the extraordinary success of Evangeline Adams, a turn-of-the-20th-century astrologer whose clients included the president of Prudential Insurance, two presidents of the New York Stock Exchange, the steel magnate Charles M Schwab, and the banker J P Morgan. … when Adams was arrested in 1914 for violating a New York law against astrology, it was mathematics that eventually exonerated her. During the trial, her lawyer Clark L Jordan emphasised mathematics in order to distinguish his client’s practice from superstition, calling astrology ‘a mathematical or exact science’. Adams herself demonstrated this ‘scientific’ method by reading the astrological chart of the judge’s son. The judge was impressed: the plaintiff, he observed, went through a ‘mathematical process to get at her conclusions… I am satisfied that the element of fraud… is absent here.’

I’m quoting from an article by Alan Jay Levinovitz on the website (one of whose senior editors owes me a letter, if I’m not mistaken).   The common origins of mathematics and astrology are addressed at some length in Chapter 8 of MWA, but not to make a point about superstition.  The deference granted economics on the grounds of its sophisticated mathematical models, in spite of its “unearned empirical authority,” deserves sustained analysis as well as critique.   I refer you to the references in Levinovitz’s article.  Here are a few choice quotations:

The historian Caley Horan at the Massachusetts Institute of Technology described to me how computing technology made financial astrology explode in the 1970s and ’80s. ‘Within the world of finance, there’s always a superstitious, quasi-spiritual trend to find meaning in markets,’ said Horan. ‘Technical analysts at big banks, they’re trying to find patterns in past market behaviour, so it’s not a leap for them to go to astrology.’ In 2000, USA Today quoted Robin Griffiths, the chief technical analyst at HSBC, the world’s third largest bank, saying that ‘most astrology stuff doesn’t check out, but some of it does’.

Modern governments, universities and businesses underwrite the production of economic theory with huge amounts of capital. The same was true for li production in ancient China. The emperor – the ‘Son of Heaven’ – spent astronomical sums refining mathematical models of the stars. Take the armillary sphere, such as the two-metre cage of graduated bronze rings in Nanjing, made to represent the celestial sphere and used to visualise data in three-dimensions. As Morgan emphasises, the sphere was literally made of money. Bronze being the basis of the currency, governments were smelting cash by the metric ton to pour it into li. A divine, mathematical world-engine, built of cash, sanctifying the powers that be.

‘I’ve come to the position that there should be a stronger bias against the use of math,’ [NYU economist] Romer explained to me. ‘If somebody came and said: “Look, I have this Earth-changing insight about economics, but the only way I can express it is by making use of the quirks of the Latin language”, we’d say go to hell, unless they could convince us it was really essential. The burden of proof is on them.’

and a reminder that Stiglitz’s joke was already the title of a book long before the 2008 crash:

Romer is not the first to elaborate the mathiness critique. In 1886, an article in Science accused economics of misusing the language of the physical sciences to conceal ‘emptiness behind a breastwork of mathematical formulas’. More recently, Deirdre N McCloskey’s The Rhetoric of Economics (1998) and Robert H Nelson’s Economics as Religion (2001) both argued that mathematics in economic theory serves, in McCloskey’s words, primarily to deliver the message ‘Look at how very scientific I am.’


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.

Alain Badiou bows down to mathematics


S’il existe une authentique Internationale, aujourd’hui, c’est bien celle des mathématiciens.

Alain Badiou, Éloge des mathématiques

When Alain Badiou, who is proud to call himself a Communist, claims that mathematicians represent the only authentic International (with a capital “I”), you know that, whatever the problem, he sees mathematics as part of the solution.   Badiou has written in Éloge des mathématiques that “the fundamental relation between philosophy and mathematics is a relation of reverence, if I may say so.  Something in philosophy bows down to mathematics.”

What, according to Badiou, is the purpose of philosophy?

I believe that philosophy has no other goal than this:  to allow anyone to apprehend, in the field of [his or her] vital experience, what is a happy orientation.  One could also say this:  to place at everyone’s disposal the certainty that the true life [vraie vie], that of a Subject freely oriented according to a true idea, is possible.

Mathematics contributes to this goal because the mathematical Subject’s orientation is free but disciplined:

…by virtue of their aesthetic force and of the invention they require, mathematics forces one to become a Subject whose freedom, far from being in opposition to discipline, demands it.  Indeed, when you work on a mathematical problem, the invention of the solution — and thus the creative freedom of the spirit — is not some sort of blind wandering, but is rather determined like a path always bordered in a way by the obligations of global coherence and of the rules of proof.  You accomplish your desire to find the solution not against rational law, but together with its help and its prohibitions at the same time.  Now that is what I began to think, in the first place with Lacan:  desire and law are not in opposition, they are dialectically identical.

Badiou’s secret mathematical love formula:  Desire = Law.  (Maybe someone can suggest a symbol for identity that is more dialectical than =?)  In a different formulation:

 Is there a happiness greater than [the pleasures that one finds in commerce]?  There’s the great question of philosophy.  Our societies, domesticated by Capital and fetishism of goods, answer:  no.  But philosophy, tenaciously and since the beginning, has labored to make us think that it exists.

For Badiou, although mathematics is not for everyone, it does offer a “model, limited but convincing, of the possible dialectical relation between the finiteness of the individual who works and strays, and the infinity of the Subject who has understood a universal truth.”

I have underlined many more sentences in my copy of  Éloge des mathématiques and could go on quoting them, explaining both my agreements and disagreements.  But the few passages translated above should give a sense of his aims.  Readers who are only familiar with philosophy of mathematics in the analytic tradition will probably find this all baffling, but you should bear in mind that Badiou sees philosophy not as a series of footnotes to science but rather, in the spirit of the ancient Greeks, as an accompaniment in the search for happiness and the vraie vie.   Mathematics plays a central role because, as Badiou sees it, philosophy only became possible with the development of systematic mathematical reasoning.

Here is the list of Badiou’s New York appearances last December (and a few from previous years).  Can you find the word “mathematics?”

Alain Badiou, “The Fundamental Contradictions of the Contemporary World”

Monday, December 15, 2014 – 6:00pm

Location: East Gallery, Buell Hall (Maison Francaise)

Event Category: Talks

Eminent French philosopher Alain Badiou will deliver a public lecture on the topic of the fundamental contradictions of the contemporary world.
Alain Badiou is a philosopher, playwright, novelist and political activist. Heis professor emeritus at the École Normale Supérieure in Paris and continues to teach seminars at the Collège International de Philosophie and the European Graduate School. Trained as a mathematician, Alain Badiou is one of the most original French philosophers today. His philosophy seeks to expose and make sense of the potential of radical innovation (revolution, invention, transfiguration) in every situation. In addition to several novels, plays and political essays, he has published a number of major philosophical works, including Theory of the Subject, Being and Event, Being and Event II: Logics of Worlds and Being and Event III: The Immanence of Truths (forthcoming).

Below is his December program in NYC:

December 13th, at 6pm

He will be at the Miguel Abreu Gallery for the book launch of the English translation of Gilles Châtelet’s To Live and Think Like Pigs, for which he wrote the foreword.

Miguel Abreu Gallery, 36 Orchard Street, New York, NY 10002.

(Gilles Châtelet obtained a Ph.D. in mathematics before he went on to a career in philosophy; more about him in future posts.)


December 13th, at 7 pm:

He will participate in a lecture-performance entitled “A Dialogue Between A Chinese Philosopher And A French Philosopher” at The Educational Alliance.

The Educational Alliance, Manny Cantor Center, 197 East Broadway, New York, NY 10002


December 15th, at 6 pm: 

Badiou will give a presentation entitled “The fundamental contradictions of the contemporary world”, at the Maison Française of Columbia University.

Maison Française of Columbia University, 515 West 116th Street, New York, NY 10027

December 16th, at 6 pm:

On the occasion of the US publication of his book, The Age of the Poets: And Other Writings on Twentieth-Century Poetry and Prose, he will give a talk about “Literature and Onthology” at the Maison Française of NYU.

Maison Française of NYU, 16 Washington Mews, New York, NY 10003


December 17th, at 7 pm:

He will be at the Jack Tilton Gallery to lead a discussion entitled “Some considerations about contemporary art”.


Literature and Philosophy: Roman/Romanesque

Alain Badiou in dialogue
with Emily Apter

Thursday, December 10, 2015, 7:00 p.m.

A New French Philosophy Event, co-sponsored by the departments of French and Comparative Literature

ALAIN BADIOU is a philosopher, playwright, and author. His books include Logics of Worlds; Being and Event; Theory of the Subject; The Century and a host of treatises and manifestos on aesthetics, Arab Spring, love, and, most recently, mathematics.

EMILY APTER teaches in the departments of French and Comparative Literature at NYU. She co-edited a collection of Badiou’s essays on literature with Bruno Bosteels (Verso, 2014), and is currently completing a book on “unexceptional politics.”