while WN’s Isaac Swift, quite a bit lower on the academic food chain, carps to himself almost nonstop about being “well on your way to everlasting anonymity, never to be quoted and always to be seated somewhere at the back of a conference, assuming you manage to scrounge together the funds needed to attend in the first place,” etc.
Interestingly, though, the most important similarity between the novels concerns the rhetorical problems of audience mentioned supra, while the biggest differences between WN and UPGC concern the ways the two books try to handle those problems. Oddly, the better of the two novels is also the one that seems to be the most confused and confusing about just what its audience is.
The Wild Numbers, translated from the Dutch De wilde getallen and its locale moved from Amsterdam to some nameless U.S. college town, is not the better novel. It’s designed to be sort of a schlemiel-comedy à la Thurber’s “Mitty” or Amis’s Lucky Jim. WN’s Isaac is a mediocrity who at the start of the novel is under-published and reduced to doing scutwork calculations and “refinements” for his superstar colleague Dimitri Arkanov16 and at age thirty-five goes around saying stuff like “I felt old and depressed. There seemed to be no more room for dreams at my age. Everything was measured in terms of success and failure…. I concluded that I was a lesser human being in every respect.” His prospects suddenly change when Isaac stumbles into working on “wild numbers,” which are described in the translation this way:
Beauregard had defined a number of deceptively simple operations, which, when applied to a whole number [integer?], at first resulted in fractions [rationals?]. But if the same steps were repeated often enough, the eventual outcome was once again a whole number [huh?]. Or, as Beauregard cheerfully observed: “In all numbers lurks a wild number, guaranteed to emerge when you provoke them long enough.” 0 yielded the wild number 11, 1 brought forth 67, 2 itself, 3 suddenly manifested itself as 4769, 4, surprisingly, brought forth 67 again.
In an all-nighter of migrainous epiphany, Swift comes to believe he’s found the long-sought answer to the Wild Number Problem, which is apparently a fictional variant of number-theoretic puzzles like the Twin Primes Problem17: “How many wild numbers are there? Are there a finite number that keep coming up, and if so, how many, or are there an infinite number?” Isaac’s proof that the set of all wilds is infinite (a proof that somehow involves FN16’s K-reducibility and calibrator sets as well as what are called “tame” and “pseudo-wild numbers”) appears at first to be sound, and it is confirmed and lauded by Arkanov and submitted to a prestigious journal, catapulting Swift into the mathematical limelight and prompting all sorts of wacky plot-complications before it is finally discovered that the proof doesn’t work after all (but by which time Isaac’s found true love with a caustic divorcée who’s also had horrible career reverses, so everything works out OK in the end).
The major problem with The Wild Numbers looks at first to be artistic but is actually rhetorical. All the book’s math is, as mentioned, made up, which is not necessarily a problem—all sorts of great science fiction, from Asimov to Larry Niven, is replete with fictional math and high tech. What is a problem, though, is that the fictional math in WN is extremely important but also extremely vague, comprising mostly repeated and contextless verbiage—“The trick was to construct a series of infinite sets of pseudo-wild numbers such that their intersection contained wild numbers only”; “If I could only establish its K-reducibility with the aid of a suitable calibrator set!”—without any definitions or even cursory fleshing-out, so that the book’s math-speak ends up most resembling the absurd pseudo-jargon of bad old low-budget sci-fi movies (“Quick, Lieutenant, prepare the antigenic nanomodule for immediate stabilization flux!”). Also vague and kind of bathetic is the novel’s depiction of actual mathematical work, which Isaac Swift appears to undertake only very late at night, bleary and unshaven and trembling with fatigue, “my head buzzing with complicated reasoning that led me around in circles,” “fiddling around with complex equations that only a handful of people understood.”18
Apart from its intrinsic weaknesses, the sketchy made-up math here clearly indicates that The Wild Numbers is meant to appeal mostly to readers with little or no high-math background, an audience that either won’t know that the impressive-sounding terminology is fake or won’t mind that the terms never get connected to each other or anything else. This, too, is not necessarily a problem; many successful books, from Heinlein’s Stranger in a Strange Land to Ellroy’s L.A. Confidential, use sort of perfunctory genre-conventions as scaffolding for what are really complex and essentially human dramas (i.e., for literature). But it is true that a genre book whose particular genre-elements lack technical depth or resonance must depend, for its appeal, on other, more traditionally literary qualities like plot, character, style, etc. And this is a very real problem for WN, because as any kind of literary narrative it is off-the-charts bad, its characters mere 2-D types (the neurotic schlemiel, the kindly mentor, the pompous crank, the vulpine reporter, the fiancée who Doesn’t Understand) and its plot howlingly implausible (e.g., for most of the book, both Isaac and Nobel-laureate Arkanov supposedly fail to spot in Isaac’s proof a basic, freshman-level logical flaw, the eventual discovery of which is sort of the novel’s pie-in-the-schlemiel’s-face climax). Worst, or at least most distracting, is the fact that the author-translator’s English seems rudimentary at best,19 and the actual line-by-line prose of WN is often so stiff and clunky—“My isolated existence was making me lose all sense of measure”; “How the tiny, quivering flame of my intuition was able to withstand the numerous onslaughts of my doubts remains a mystery to me”; “She unzipped her dress, and with a few sexy wriggles, let it slide from her shoulders”—or else riddled with ESL-ish solecisms—“She pouted her lip”; “In the distance, the three white lights of the television mast flashed on and off”; “ ‘I just don’t want to stifle my thoughts to accommodate for the shortcomings of a machine’ ”; “I found back my love for mathematics”—or unintentionally funny—“Her tongue probing deep into my mouth left little room for mathematical reflection”—or just plain bad—“They could not help but open like flowers in the brilliant sunshine of his presence, revealing their innermost secrets to him”—as to make the reader suffer that terrible, embarrassed-for-someone-else feeling on the author’s behalf.20
It is true that Uncle Petros & Goldbach’s Conjecture is also self-translated21 and its prose often awkward or stilted (“The custom of this annual meeting had been initiated by my grandfather and as a consequence had become an inviolable obligation in our tradition-ridden family”; “The next few days I played sick so as to be at home at the usual time of mail delivery”; “I was not made of the same mettle as he—this I realized now beyond the shadow of a doubt,”22 etc.). But here the clunky English is mitigated somewhat by UPGC’s Greco-European setting and the fact that much of its action takes place before 1930. The novel’s framed (or “nested”) structure is itself almost Victorian: the middle-aged narrator, describing in retrospect the history of his childhood relationship with his reclusive uncle, recounts Petros’s own life story in a series of flashbacks “as told to him” by the great mathematician himself. The elaborate set-up and frames notwithstanding, it is Petros Papachristos’s obsessive and tormented career that drives the novel and comprises its heart.
UPGC is about as far from a schlemiel-comedy as you can get. It’s more like a cross between the Myth of Icarus and Goethe’s Werther, and it’s serious as a heart attack.23 Born in Greece around the turn of the century, Petros Papachristos is recognized as a child math prodigy and shipped across Europe to the University of Berlin, where in 1916 he receives his doctorate with a dissertation on “solving a particular variety of differential equations” that earns young Petros early acclaim because of its applications in WWI artillery targeting. It is also at U. Berlin that Petros has his first and only love affair, with his German-language tutor (a young lady by the rather unsubtle name of Isolde), who to
ys with his affections and then elopes with a Prussian officer. In not its best moment, UPGC tries to establish this (wince) Isolde as Petros’s initial motive for tackling the Goldbach Conjecture:
In order to win her heart back, Petros now decided, there could be no half-measures… he should have to accomplish amazing intellectual feats, nothing short of becoming a Great Mathematician. But how does one become a Great Mathematician? Simple: by solving a Great Mathematical Problem! “Which is the most difficult problem in mathematics, Professor?” he asked [his U. Berlin adviser] at their next meeting, trying to feign mere academic curiosity.
Etc., whereupon Petros devotes the remainder of his professional life to the G.C., that Everest of unsolved problems. His twenty-year labor—which ends in failure and devastation—combines periods of seclusion in Germany with extended trips to Cambridge and Vienna, in which latter there are scenes of Papachristos rubbing elbows with some of twentieth-century math’s most important historical figures. The use of this Forrest Gump-ish device—i.e., of inserting actual famous mathematicians into the fiction’s plot and dialogue—implies that UPGC is written for readers who are at least familiar enough with higher math to know who Hardy, Ramanujan, Gödel, and Turing are; but many of the celebrity-scenes themselves are cheesy and kind of irritating. The complex and sensitive G. H. Hardy readers know from his Apology, for instance, gets reduced in Doxiadis’s novel to a sort of gouty old curmudgeon who spouts inanities like “Don’t you forget it, Papachristos, this blasted Conjecture is difficult!”
Its treatment of the “real” Hardy is a good example of UPGC’s particular rhetorical problem: the readers who will actually know who Godfrey Harold Hardy is are also the readers most likely to be put off by the way the book portrays him.24 And Doxiadis’s novel runs into this sort of logico-rhetorical problem again and again, because its big weakness as genre fiction is its weird, ambivalent confusion about just what kind of audience it’s for.
As with Schogt’s WN, there’s no better instance of this confusion than the way pure math is rendered here, although in UPGC the math is 100 percent real and intricately connected to the book’s characters and themes. Petros’s Herculean labors on his proof are recounted to the reader in the form of fireside declamations to his nephew (i.e., the narrator as a child), who’s enough of a mathematical ephebe that Petros can plausibly keep stopping to deliver quick little mini-lectures on the history of number theory, from Euclid’s reductio proof of the infinity of primes to the major theorems of Fermat, Euler, and Gauss on primes’ distribution and succession, to the Goldbach Conjecture and Petros’s own analytic attack thereon via “the Theory of Partitions (the different ways of writing an integer as a sum).”
It gets more complicated, though, because the narrator as a grown man (i.e., the one narrating the flashbacks with Uncle P.) now has an extensive math background, and he himself laces the novel with explanatory asides on everything from Cavafy poems to the Riemann Zeta Function. The problem is that Doxiadis’s decisions about what needs explicating and what doesn’t are often so inconsistent as to seem bizarre, a clear sign that he’s confused about audience. It’s not just that there are long and irrelevant footnotes on, e.g., Gödel’s method of suicide, Poincaré’s theory of the unconscious, or the novel properties of the number 1,729.25 It is that the narrator of UPGC will sometimes take time carefully to define very basic terms like “integers” (“the positive whole numbers 1, 2, 3, 4, 5, etc.”) and “primes” (“integers that have no divisors other than 1 and themselves, like 2, 3, 5, 7, 11”), or to include patronizing asides like “It should be pointed out to the non-specialist that mathematical [text]books cannot normally be enjoyed like novels, in bed, in the bathtub, sprawled in an easy chair, or perched on the commode”—all of which clearly imply a non-math audience—while on the other hand, UPGC is also studded with rarefied technical phrases, such as, e.g., “n’s ratio to the natural logarithm,” “Peano-Dedekind axiomatic system,” “partial differential equation in the Clairaut form,” and (no kidding) “The orders of the torsion subgroups of Ωn and the Adams spectral sequence,” that are tossed around without any kind of explanation, which (especially together with the à clef appearances of Gödel, Littlewood, et al.) seems to presume a highly math-literate reader.
And if all the narrator’s strange elementary definitions are disregarded as mere slips or snafus, and one decides that UPGC’s actual intended audience is one with a solid high-math background,26 there remains an equally strange inconsistency. This lies in the narrative’s discussions of the Goldbach Conjecture itself, and of its history in the early twentieth century. For one thing, UPGC makes hardly mention at all of the crucial distinction between Euler’s “strong Goldbach Conjecture” (see FN7 supra) and the Conjecture’s equally famous “weak” version, which states that all odd numbers > 9 are the sum of three odd primes. Nor, despite all the detailed descriptions of Petros’s labors and all its long excursuses on pre-WWII number theory, does the novel ever once mention Euler’s phi function (a.k.a. “totient” function) or the ingenious “sieve”-type methods that real mathematicians were using to attack the G.C. in all its forms and extensions in the 1920s and 1930s. In fact, even though UPGC gives us page after page on Petros’s anxiety about Ramanujan’s work on the G.C. (which was in reality very slight), there’s no mention of any of the actual important published results of the time—e.g., Schnirelmann’s 1931 proof of the upper limit of primes an even integer can be the sum of, Estermann’s 1938 proof that almost all even numbers are the sums of two primes,27 etc. Strangest of all: though Doxiadis’s narrator spends a lot of time discussing the difference between algebraic and analytic number theory (as well as tracing out Gauss’s “asymptotic” hypothesis of the Prime Number Theorem, and Hadamard and Vallée-Poussin’s 1896 proof of the P.N.T. using analytic tools), there is not one reference in the book to I. M. Vinogradov, the Russian mathematician who in 1937 revolutionized analytic number theory by introducing a powerful method for getting very accurate estimates of trigonometric sums and using it to prove the weak G.C. for sufficiently large numbers.28 Historically, it is Vinogradov who would have been Petros’s real rival, the “unique intellect” he really feared; and it is not Gödel’s but Vinogradov’s Theorem that might plausibly have caused Papachristos to despair.29
The thing to realize here is that none of these omissions would necessarily matter had not Doxiadis chosen to make UPGC so dependent on actual number theory and real historical characters. As it stands, though, UPGC again shoots itself in the same rhetorical foot: the audience knowledgeable enough to appreciate all the “real” math and history woven into this novel is also the audience most likely to notice the strange absence in the book of so much really real historical work on the Conjecture. Here once again, then, is a form of the weird, contradictory-looking problem (viz., that what are necessary conditions for liking the novel are also sufficient conditions for disliking it) that pretty much destroys this book, whose author can’t decide whom he’s writing for.
It would be unfair to Doxiadis, though, not to acknowledge that both his novel and its flaws are far more interesting than Schogt’s WN, and moreover that UPGC does include some moving and rather lovely passages—
The loneliness of the researcher doing original mathematics is unlike any other. In a very real sense of the word, he lives in a universe that is totally inaccessible, both to the greater public and to his own immediate environment. Even those closest to him cannot partake of his joys and his sorrows in any significant way, since it is all but impossible for them to understand their content.
—as well as at least one subtheme of genuine insight and originality, one that manages to go beyond anything Hardy had to say about the tragedies of math. This particular thematic line concerns Petros’s ambition and his place in the mathematical community; and its allegorical touchstone appears to be not Icarus but Minos, the Cretan king who (recall) so coveted a certain great white bull, which the god Poseidon had conjured out of s
ea-foam to help him win the throne, that Minos broke his sworn promise to return it via religious sacrifice and instead kept the bull for himself.30
It is true that doing original math is “lonely.” But it is also true that professional mathematicians compose a community. The reality that Petros never seems to recognize is that the “fame and immortality” he craves will depend entirely on the value of his work to other mathematicians. The role of professional community is so important in nearly all branches of scientific endeavor, in fact, that most Science readers can already probably affirm and appreciate what Lewis Hyde’s The Gift tries to convey to its own more general audience:
[T]he task of assembling a mass of disparate facts into a coherent whole clearly lies beyond the powers of a single mind or even a single generation. All such broad intellectual undertakings call for a community of scholars, one in which each individual thinker can be awash in the ideas of his comrades so that a sort of “group mind” develops, one that is capable of cognitive tasks beyond the power of any single person.
Notwithstanding all the narrator’s heavy declarations that “Uncle Petros’ sin was Pride” and his retreat into paralyzed seclusion “a form of burnout,” “scientific battle fatigue,” it emerges in UPGC that the real cause of Petros’s tragedy is his progressive withdrawal from the professional community as his ambition to solve the Conjecture becomes a rapacity that transforms his colleagues into first rivals and then enemies. The novel’s middle sections trace this progression out nicely. It starts in Cambridge, when Petros rejects an offer of professional collaboration with Hardy and Littlewood because he fears that “their problems would become his own and, what’s worse, their fame would inevitably outshine his,” and determines instead to work on the G.C. alone, withdrawing to Munich. There, over years of seclusion and nonstop work, privacy becomes secrecy, and Petros’s fear and suspicion of other mathematicians approaches “the point of paranoia. In order to avoid his colleagues’ drawing conclusions from the items he withdrew from the library, he began to… protect the book he really wanted by including it in a list of three or four irrelevant ones, or he would ask for an article in a scientific journal only in order to get his hands on the issue that also contained another article, the one he really wanted,” etc. (Q.v. here also Petros’s aforementioned “wild joy” at the death of Ramanujan.)