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 alclass="underline" 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.)