“I never want to see another Fourier series as long as I live”


The quotation is taken from a postcard from David Foster Wallace to Don DeLillo, written in 2002, reproduced on p. 274 of Every Love Story Is a Ghost Story: A Life of David Foster Wallace, by D. T. Max, and referring to what he elsewhere called his “wretched math book,” namely Everything and More.   Today’s image is the cover of a special issue of Lettera matematica pristem devoted to mathematics in the work and life of DFW, which has just been published, in Italian and English.   No one has been more adventurous than Italian mathematicians in exploring mathematics as a cultural activity — the last in the series of conferences organized by Michele Emmer in Venice took place this year and the series of volumes (also edited by Michele Emmer) is still available (in some sense) from Springer — but it seems to me that this particular initiative is especially successful.

I’m grateful to Roberto Natalini for inviting me to include my review of Everything and More in this special issue.  Natalini is

Direttore dell’Istituto per le Applicazioni del Calcolo “M. Picone”,
Consiglio Nazionale delle Ricerche

in Rome; but he is also coordinator of the website MaddMaths!,  chair of the EMS committee for Raising Public Awareness;  more to the point, he admits to an “obsession for… many years” with Wallace’s writing.  He and I have something in common:  I proposed to use mathematical ideas (in Bonus Chapter 5) as a scheme for organizing interpretations of the novels of Thomas Pynchon, while Natalini did the same with DFW’s Infinite Jest.  But if you read his essay “David Foster Wallace and the Mathematics of Infinity” in Lettera Matematica Pristem you will agree with me that his analysis is much more substantial than mine.  I limited my attention to conic sections as structural devices in Pynchon’s main novels; Natalini finds cardioids, lemniscates, and Möbius transformations, as well as all the conic sections in Infinite Jest.  He suggests that the two main story arcs (with main characters Hal Incandenza and Don Gately, respectively) form the two branches of a hyperbola (Gately above, Incandenza below), ten years before Pynchon used a similar device (as I claim in Bonus Chapter 5) in Against the Day.  And his proposal to read the fates of the main Incandenza characters in terms of inversion on the Riemann sphere is nothing short of brilliant.

Natalini’s essay originally appeared in a book entitled A Companion to David Foster Wallace Studies, which is as authoritative as it sounds.  My review of Everything and More originally appeared in Notices of the AMS 51(6), June/July 2004:632–638.  Springer, the publishers of Lettera Matematica Pristem, is attempting a kind of inversion of their own; you can read my review for free at the AMS website, but if you want to read it online in the Italian journal you’ll have to pay Springer $39.95,  €34.95, or £29.95.   If you want to make a donation to Springer — and really, they do deserve credit for going to the trouble of publishing Hausdorff’s Gesammelte Werke — save your money for Emmanuele Rosso’s self-referential DFW cartoon.  Or for Stuart James Taylor’s interview with Erica Neely, DFW’s technical consultant for Everything and More which, together with the D.T. Max book cited above, provide insights on DFW’s struggles with the book that I wish I had seen when I was writing my review.

If, on the other hand, you want to see a physical copy of a document that includes my literary reunion with Jordan Ellenberg in Italian, you may have to make the trip to Italy; the Italian edition of Lettera Matematica Pristem doesn’t travel much.  Here is an excerpt from Andrea Piazzi’s translation of my review (I’ve already mentioned, what an honor it is to be translated by the Italian translator of Fantastic Four comics and the cartoons of Will Eisner):

…nel mercatino sotto casa si trovano già titoli divulgativi sull’infinito. Anzi, a quanto pare ce ne sono proprio un bel po’. Uno di questi (Infinity: The Quest To Think the Unthinkable di Brian Clegg) è uscito quasi in contemporanea con E&M e i due sono stati recensiti insieme sul Guardian, dall’autorevole Frank Kermode.
Nonostante la domanda apparentemente illimitata per titoli del genere, una buona parte del sommario sembra essere predeterminata, il che può essere di non poco aiuto a chi fosse interessato a scrivere un proprio libro sull’infinito, oltre forse a dimostrarne di per sé l’esistenza.

Here there is a footnote meant to illuminate the comment about how books about infinity prove the existence of infinity:

4. Il recensore ha consultato cinque titoli divulgativi sull’infinito, tra i quali E&M e il libro di Clegg. I numeri tra parentesi indicano quanti discutono o fanno riferimento all’argomento in questione: il termine greco to apeiron per “infinito” [3], Pitagora [5], l’irrazionalità di √2 [5] e il destino di Ippaso [5]; i paradossi di Zenone [5]; Aristotele e l’infinito in potenza [5]; Archimede e L’Arenario [3]; La Città di Dio di Sant’Agostino [3]; la Summa Theologica di San Tommaso d’Aquino [4]; Nicolò Cusano [4]; le Due Nuove Scienze di Galileo [5]; le coordinate cartesiane [5]; Newton e Leibniz [5]; l’attacco di Berkeley contro gli infinitesimi (“fantasmi di quantità che furono”) [3]; il rifiuto di Gauss di ammettere gli infiniti in atto [5]; i paradossi dell’Infinito di Bolzano [5] e il suo pacifismo [3]; la Sfera di Riemann (con il punto all’infinito) [3]; la fama di Weierstrass come bevitore e spadaccino [3]; la trascendenza di Pi Greco [5]; le Sezioni di Dedekind [4]; il rifiuto dell’infinito da parte di Kroenecker e la sua persecuzione nei confronti di Cantor [4]; la teoria di Cantor degli Ordinali [4], la sua dimostrazione della numerabilità di Q [5], il metodo della diagonalizzazione [5], “Je le vois mais je ne le crois pas” (che Cantor scrisse in francese in una lettera a Dedekind, a proposito della sua dimostrazione della commensurabilità tra la retta e il piano) [5] e l’Ipotesi del Continuo [5]; la definizione di Peano degli interi in termini insiemistici [5]; il Paradosso di Russell [5]; l’Hotel di Hilbert [4]; il Teorema di incompletezza di Gödel [5] e la morte per inedia [5]; la dimostrazione di Cohen dell’indipendenza dell’Ipotesi del Continuo [5].



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