Both Flesh and Not: Essays

RHETORIC AND THE MATH MELODRAMA

MATH’S CULTURAL STOCK HAS risen hard in recent years, no doubt driven by the same booming and metastatic Knowledge Economy that’s turned yesterday’s non grata nerd into today’s cyber-tycoon. Call the phenomenon “Geek Chic” or “Hip(2b)²” or whatever you will: abstract tech is now sexy, the mathematician a viable commercial hero — see for example the success of recent films like Good Will Hunting and π.

Or a better instance of math’s new cachet here is Amir D. Aczel’s Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem, which made nonfiction bestseller lists in 1996 and transformed Princeton’s Andrew Wiles into a weird kind of horn-rimmed pop icon, and in the wake of which has appeared everything from Paul Hoffman’s The Man Who Loved Only Numbers and Sylvia Nasar’s A Beautiful Mind¹ to David Berlinski’s Newton’s Gift and Charles Seife’s Zero: The Biography of a Dangerous Idea.

Though fiction, Philibert Schogt’s The Wild Numbers and Apostolos Doxiadis’s Uncle Petros & Goldbach’s Conjecture both draw heavily on Aczel’s Fermat’s Last Theorem (as well as on G. H. Hardy’s A Mathematician’s Apology²). And there are other, rather striking similarities between these two novels. Both are set in the world of academic mathematics and feature characters whose specialty is number theory,³ higher math’s most purely abstract branch. Both novels revolve around their protagonists’ quests to solve famous and long-standing number-theoretic problems. And both WN and UPGC have been translated by their own authors from foreign-language originals.

The facts of these two novels’ close resemblance and near-simultaneous release here in the States, as well as the vigor with which their U.S. publishers are hyping them,⁴ appear to signal the inception of a whole new commercial genre — the “Math Melodrama,” as it were. This is a development that should come as no surprise, given the success of some of the other titles mentioned supra, not to mention the commercial success in recent years of other nascent tech-intensive genres (the cyberpunk of Neuromancer et seq., the Clancy-style technothriller, the plucky-young-hackers-thwarting-evil-monolithic-institutions of Sneakers, Hackers, The Matrix, etc.).

As exemplified by WN and UPGC in fiction and Fermat’s Last Theorem and A Beautiful Mind in non-, the Math Melodrama can be roughly characterized as combining the “Vocational Travelogue”⁵ charms of genre authors like Arthur Hailey and Michael Crichton with some of the weightier allegorical functions that other genres and their heroes often serve — the Western sheriff as emblem of Apollonian order, the Noir private eye as existential hero, the plucky young hacker as Odyssean trickster. The Math Melodrama’s own allegorical template appears to be more classically Tragic, its hero a kind of Prometheus-Icarus figure whose high-altitude genius is also hubris and Fatal Flaw.⁶ If this sounds a bit grandiose, well, it is; but it’s also a fair description of the way Math Melodramas characterize the project of pure math — as nothing less than the mortal quest for Divine Truth. What’s odd here is that whether a particular reader accepts this characterization or sees it as pretentious and silly will often depend less on the qualities of the Math Melodramas themselves than on certain biographical facts about the reader himself, namely how much knowledge and experience of higher math he happens to have.

This sort of oddity is, in fact, a frequent problem in reviewing or assessing “genre fiction,” which is a type of narrative it’s usually fair to call “the sort of thing someone who likes this sort of thing is apt to like." The evaluative criteria tend to be rather special for genre fiction. Instead of the basically aesthetic assay the reviewer gets to make of most literary fiction—“Is this piece of fiction good?”—criticism of genre fiction is ultimately more rhetorical—“To whom will this piece of fiction appeal?” In other words, as is the case with all but the broadest and coarsest genre fiction, the central questions about novels like WN and UPGC concern what rhetoricians call “audience”: What is the intended audience for these books? And is this audience apt to find the novels satisfying on the same terms by which it finds other Math Melodramas satisfying? And if not, are there other audiences whom these books are more likely to satisfy? And so on. One reason this is a problem for reviewers is that book reviews are usually supposed to be short, clear, and relatively simple, and rhetorical criteria tend to yield very complex, sometimes even paradoxical conclusions. In the case of The Wild Numbers and Uncle Petros & Goldbach’s Conjecture, the paradox is that the type of audience most likely to accept and appreciate these novels’ lofty, encomiastic view of pure math is also the audience most apt to be disappointed by the variously vague, reductive, or inconsistent ways the novels handle the actual mathematics they’re concerned with.

To put it in a simpler, more book review-ish way: neither of these novels is very good (one, in fact, is downright bad); but the precise ways in which they’re not very good will vary directly with how much an individual reader already knows about the extraordinary field these two books are trying to dramatize.⁷

Not just professional mathematicians, but just about anyone lucky enough ever to have studied higher math understands what a pity it is that most students never pursue the subject past its introductory levels and therefore know only the dry and brutal problem-solving of Calc I or Intro Stats (which is roughly analogous to halting one’s study of poetry at the level of grammar and syntax). Modern math is like a pyramid, and the broad fundament is often not fun. It is at the higher and apical levels of geometry, topology, analysis, number theory, and mathematical logic that the fun and profundity start, when the calculators and contextless formulae fall away and all that’s left are pencil & paper and what gets called “genius,” viz. the particular blend of reason and ecstatic creativity that characterizes what is best about the human mind. Those who’ve been privileged (or forced) to study it understand that the practice of higher mathematics is, in fact, an “art”⁸ and that it depends no less than other arts on inspiration, courage, toil, etc…. but with the added stricture that the “truths” the art of math tries to express are deductive, necessary, a priori truths, capable of both derivation and demonstration by logical proof.⁹

It may be that mathematics is not generally recognized as one of the arts precisely because so much pyramidal training and practice is required in order to appreciate its aesthetics; math is perhaps the ultimate in acquired tastes.¹⁰ And it’s maybe because of math’s absolute, wholly abstract Truth that so many people still view the discipline as dry or passionless and its practitioners as asocial dweebs. Some readers of Science will probably know all too well the frustration of trying to describe the beauty and power of Gauss’s differential geometry or the Banach-Tarski Paradox to someone who remembers only the drudgery of factoring quadratic equations or the terror of a trig midterm. In fact, the weird fear and distaste that low-level math provokes in so many¹¹ is part of what makes the emergence of the Math Melodrama exciting: if the genre can find ways to vivify pure math and communicate the discipline’s extraordinary beauty and passion to the average reader,¹² both readers and math itself stand to gain.

The ways in which Schogt’s and Doxiadis’s novels go about trying to humanize and animate math are also kind of similar. Besides both struggling to solve classic problems in number theory (the actual Goldbach Conjecture in UPGC, in WN a fictitious conundrum called “Beauregard’s Wild Number Problem”¹³), the books’ protagonists also both conceive of their projects almost wholly in terms of personal achievement, glory. WN’s Isaac Swift, a once-promising student whose pro career has stagnated, spends much time fantasizing about solving the Wild Number Problem and having “an international symposium held in my honor… and, now that I was not just a mathematician, but a famous mathematician, women would suddenly find me attractive, not just eccentric or at best amusing.” And UPGC’s Petros Papachristos, while already a number-theorist of substantial reputation who holds an endowed chair at U. Munich, nevertheless “sought in mathematics a great, almost transcendent success, a total triumph that would bring him world fame…. And to be complete, this triumph should be exclusively his own.” Despite their different stations and attainments, the two protagonists suffer almost identically (and at great length) from the insecurity of measuring themselves against their colleagues and the fear that someone else will solve “their” problem first (Petros actually rejoices when Srinivasa Ramanujan¹⁴ dies young of tuberculosis, simply because Ramanujan’s “unique intellect was the only force he considered capable of purloining his prize”). Both protagonists’ work is characterized as an anxious race against the clock and calendar; both novels make much of the fact that pure math is a “young man’s game” and that the vast majority of important mathematicians do their best work before thirty-five.¹⁵ And both heroes brood and expound at great length about the particular despair of being a good but not immortally great mathematician, i.e., a mathematician brilliant enough truly to appreciate the genius of Riemann, Euler, Poincaré, et al. but not brilliant enough to be their equal. As UPGC’s Petros tells his nephew:

Take Hardy and Littlewood, top-class mathematicians both of them. They possibly made the Hall of Fame — a very large Hall of Fame, mind you — but even they did not get their statues erected at the grand entrance alongside Euclid, Archimedes, Newton, Euler, Gauss… That had been my only ambition and nothing short of the proof of Goldbach’s Conjecture, which also meant cracking the deeper mystery of the primes, could possibly have lead me there. [sic]

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 toys 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 Ω_n 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 sea-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.)

The real Minoan-type crisis, though, comes about halfway through the novel, when Petros achieves an important “intermediate result” in his progress toward the Conjecture — a “deep, pioneering theorem… which opened new vistas in the Theory of Numbers”—and has to decide what to do. Petros’s internal debate about whether to publish the result (which is really a Hyde-vs.-Minos argument about membership in a community) is probably the novel’s best moment:

Undoubtedly, its publication would secure him recognition in the mathematical world much greater than that achieved by his method for solving differential equations. In fact, it would probably catapult him to the first ranks of the small but select international community of number theorists, practically on the same level as its great stars….

By making his discovery public, he would also be opening the way into the [Goldbach] problem to other mathematicians who would build on it by discovering new results and expand the limits of the field in a way a lone researcher, however brilliant, could scarcely hope. The results they would achieve would, in turn, aid him in his pursuit of the proof to the Conjecture. In other words… he would be acquiring a legion of assistants in his work. Unfortunately, there was another side to this coin: one of the new unpaid (also unasked for) assistants might conceivably stumble upon a better way to apply his theorem and manage, God forbid, to prove Goldbach’s Conjecture before him….

He didn’t have to deliberate long. The danger far outweighed the benefit. He wouldn’t publish.

From here on, the die is cast. And because he is not a king, it is not his community but Petros himself who receives the inevitable punishment for this “hoarding of the general benefit.”³¹ What happens is that “his” unpublished result is independently discovered by another mathematician, a development Petros finds out about only years later, from Hardy, who “expressed his amazement that Petros had not been aware of this, since its publication had caused a sensation in the circles of number theorists and brought great acclaim to its young author.”³²

As UPGC’s plot unfolds, this sort of Aesopian, reap-just-what-you-sow punishment gets inflicted on Petros again and again, worsening as each ego-blow increases his alienation and paranoia and sends him deeper into a kind of professional solipsism. Far more than any supposed misreading of Gödel’s First Incompleteness Theorem, it is this solipsism that leads to Petros’s “failure”—as both a mathematician and a person — and he ends up rather like Milton’s Satan, not just alone but Alone, sustaining himself on the sort of megalomaniacal self-pity that creative people everywhere know and dread: “I, Petros Papachristos, never having published anything of value, will go down in mathematical history — or rather will not go down in it — as having achieved nothing. This suits me fine, you know. I have no regrets. Mediocrity would never have satisfied me. To an ersatz, footnote kind of immortality, I prefer… total obscurity!” Despite the confused and confusing math-labyrinth it’s hidden inside, the embedded story of Petros’s fall is a kind of monstrous gem, one in whose facets readers of many different backgrounds and tastes might see parts of themselves reflected. Apparent implication: if math can be art, so sometimes can genre.

— 2000