My réseau 

While observing the recent oscillations of my Amazon sales rank, I was reminded that, although Brendan Larvor may well have correctly diagnosed my intellectual style as that of a Parisian intellectual, he neglected to mention that I was lacking the one appendage indispensable to any even modestly ambitious intellectual in the City of Light, namely a réseau.  The word literally means network, as in réseau téléphonique or réseau social (for a number theorist it also means lattice, which is entirely beside the point).  For a Parisian intellectual, though, it’s much more than that; the réseau, which one begins to acquire in a classe préparatoire (if one has not been fortunate enough to attend an élite public high school) and which one consolidates through one’s passage through one or more Grandes Ecoles, provides moral, social, and institutional support, often in intellectual or institutional conflicts with the members of competing réseaux; it arranges invitations, positions, grants, and public appearances, all of which is described by the quaint metaphor of renvoi d’ascenseur — literally “sending back the elevator” (to pick up another member of the réseau), more figuratively “you scratch my back, I’ll scratch yours” — and when the intéllectuel in question is médiatique, in other words the worst kind of Parisian intellectual (e.g. Bernard-Henri Lévy), it’s the réseau that creates the buzz that guarantees that the public will not miss a single one of the intellectual’s words, no matter how absurd — the réseau is the functional equivalent of a public relations operation.

Business, politics, journalism, sports, organized crime:  in France, the basic functional unit is in each case the réseau.  As Bruno Latour wrote a few years ago, « Avoir ou ne pas avoir de réseau:  that’s the question ».  Latour and his collaborator Michel Callon built a whole branch of Science Studies around their notion of actor-networks, and while it’s not all as dismal as the article in the above link, the literary theorists at North American universities should have known better during the “Science Wars” of the mid-1990s than to lend their professional aura to creating a buzz about an interpretation of how science works that is based primarily on the less admirable peculiarities of the Parisian intellectual scene.

But I’m being disingenous.  Of course I have my réseau as well, even several overlapping réseaux.  Chapter 2 hints at how this comes about, referring to

a process that offers valuable insight for a future sociology concerned with the reproduction of the mathematical elite, since the authors in question had without exception spent some or all of their careers studying or teaching at the leading poles of number theory in their respective countries: Oxford, Cambridge, Harvard, Princeton, Bonn, the Ecole Normale Supérieure, Moscow State University, and the University of Tokyo.

I will ignore the thorny question of what I mean by “leading poles” and why some unquestionably great institutions are not on the list, and just mention that I began to join my réseaux by attending two of these “leading poles” as an undergraduate and graduate student, and although I did not have a consistent feeling that I belonged to these réseaux, my subsequent experience has made it clear that I not only fulfilled the requirements to acquire (routinized!) charisma but that the other members of my undergraduate and (especially) graduate réseaux — in other words, the individuals I met while a student — have played a persistent and often unexpected role in maintaining this status.  It may just amount to keeping track of my former professors’ students (and their students, and my fellow students’ students), or to collaborations, or to nothing more than having a name that comes to mind when…  What I’m calling a réseau is the interiorization of the norms and values of the society of mathematicians, especially number theorists, projected onto the individuals who make up that society, with the result that they are (as I see it) not merely a bunch of individual mathematicians but also a social structure that can and should be studied as such.

To get to the point (finally), what I’ve noticed is that most of the positive reviews of MWA have either been written by members of this professional réseau of number theorists, or by members of the philosophy of real mathematics/mathematical cultures/Thales & Friends réseau I have joined more recently; MWA can be seen as a contribution to the literature of this still-diffuse but growing and international réseau.   In addition to Brendan Larvor’s review, I’m specifically thinking of Avner Ash’s review in Harvard Magazine  and Michael Barany’s review on MathSciNet.  I met Barany through one of his articles quoted in MWA and again at Larvor’s Mathematical Cultures 3 in London in 2014; I met Ash, literally, during my first week at Harvard graduate school.  Both reviews are occasionally critical, Barany’s quite sharply so — the criticisms are largely justified and I’ll react to them in future posts — but (as I wrote Ash as soon as I saw what he had written) they are both “dream reviews” and my most serious complaint is that the figure in the illustration accompanying the Harvard Magazine article looks disturbingly familiar and for that reason should not be wearing that ridiculous color combination (but this is by no means the reviewer’s responsibility).

And just to prove that a réseau can be “performative,” here is what happened to MWA‘s Amazon Sales Rank when the Harvard Magazine review went on line.


Of course I’m overjoyed that the reviews are positive (some of the terrific quotes will be posted soon enough) and I’m delighted that the reviewers clearly understood my motivations and objectives, which is unfortunately not always the case (I’ll deal with that one in due time).  But in keeping with the “problematic” subtitle, I have to confess a lingering unease as well, a nagging sense that writing positive reviews of one another’s books is just something one does when one belongs to a réseau.  Note that I’m NOT saying that this is a matter of “sending back the elevator” in the expectation that your réseau-mate will do the same for you when your turn comes.  What I’m saying is that the positive reviews are signs, or symptoms, of a common understanding that one shares with other members of the réseau, and that this is indeed how a sociologically-minded observer can recognize a réseau.

Two more problematic aspects of this otherwise undeniably wonderful situation.  First, the reviews written thus far — positive, hostile, or indifferent — have a common feature that may lead an outsider to suspect that the reviewers and the author all belong to an “old boy réseau” — renewed accusations of insouciant laddishness may not be far behind.  Perhaps more insidiously (or perhaps not) the interconnectedness of the population of reviewers may remind the reader of the circumstance — which is actually the main theme of Chapter 2! — that the system of value judgments, and even of truth judgments, in pure mathematics, unbound as it is by conformity to empirical observation, may to an outsider look uncomfortably like a network effect — or, as Andrew Ross wrote when he was still misled by Callon and Latour,

While the original story of science is still being told in opposition to the humanist tradition of rhetoric, in recent years critics have come to see science itself as just another form of rhetoric; one with particularly aggressive claims on objectivity.

10 thoughts on “My réseau 

  1. Pingback: Networks in action in French economics | Mathematics without Apologies, by Michael Harris

  2. Jon Awbrey

    U Say Réseau, I Say Rousseau,
    Let’s call the whole thing 1.

    Social compacts come and go,
    And may converge to 1 1 day,
    1 that comes and never goes.
    So reap again what u réseau,
    Until u reap what regrows u.


  3. Pingback: You Say “Réseau”, I Say “Rousseau” • 1 | Inquiry Into Inquiry

  4. Pingback: You Say “Réseau” • I Say “Rousseau” • 1 | Inquiry Into Inquiry

  5. Pingback: You Say “Réseau” • I Say “Rousseau” • 2 | Inquiry Into Inquiry

  6. Jon Awbrey

    Readers of Peirce know that the concept of community is integral to his treatment of inquiry, interpretation, knowledge, reality, and truth.  The following statement is a nice résumé of all the main points.

    The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you.  Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of an indefinite increase of knowledge.  (CP 5.311).

    Peirce, C.S. (1868), “Some Consequences of Four Incapacities”, Journal of Speculative Philosophy 2 (1868), 140–157. Reprinted (Collected Papers 5.264–317), (Writings 2, 211–242), (Essential Peirce 1, 28–55).  Online.

    More casual or selective readers may take Peirce for a pioneer in the sociology of knowledge and jump to the conclusion that his social theory is a “coherence theory” or a “consensus theory” of truth.  But a leap like that underestimates the gulf between actual finite communities and what is really a regulative ideal, a community without definite limits capable of an indefinite increase of knowledge.  The relation between the two is like that between an empirical sample and a theoretical population of unknown extent.


  7. Pingback: You Say “Réseau” • I Say “Rousseau” • 3 | Inquiry Into Inquiry

  8. Loïc Merel

    Dear Michael,

    This post meets some of my own observations. I see little remarkable in the parisian réseaux, it’s the same story everywhere, and has always been as part of our primate nature. Not only BHL, but other animals too, understand the “renvoi d’ascenseur”, and game theory has validated this tactic. Your post provokes another reflection. How is it that we, mathematicians, are so often baffled when we realize, sometimes at a late age, that connections are at least as important as competence for success in life? I suspect that the notion (the illusion?) that merit alone suffices is more present in our community than in other parts of academia, let alone the rest of the world.

    Bill Thurston once insisted that we are “deeply social animals”. In my view, this conditions us at several levels. The most obvious is that the connections we make help us in our careers (your parisian réseaux). To paraphrase the latter part of the post, I would say that it is more important for science that our interests are derived from the interests of influential people, which steers our understanding of valuable mathematical research. Thus is undermined the “particularly aggressive claims on objectivity” of maths. I wish to add that mathematics, and perhaps specifically mathematics, are shaped at another level by the social nature of its practitioners. There is a certain tension between mathematics as they are understood by an individual, and mathematics as they are communicated. If there was a single mathematician in the world (let’s say very long lived and dedicated), would mathematics be different? (*) It would seem that the mathematics we know are conditioned by the necessity to be propagated along a social network (the rest doesn’t make it to the limelight). Perhaps a banal observation after all, as we all know (for instance) that the validation of a proof is a social act, but again at odds with the preconceptions I long held.

    (*) Perhaps they wouldn’t. Such a mathematician would need to communicate with himself (i.e. at different time periods). So he would need to make his discoveries transportable across time, so he could recall and use them. Hence a similar filter.

    Liked by 1 person

  9. Pingback: Edward Frenkel’s bela bunda and what it has to do with the Sokal affair | Mathematics without Apologies, by Michael Harris

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