It surely says something about the slanted, flickering halos we place atop the figures of twentieth-century "genius" that Rebecca Goldstein's wonderful new study of the life and mind of Kurt Goedel doesn't get around to the math that made him famous until around page 150. This is no fault of Ms. Goldstein, who artfully and engagingly carpenters a stage of historical and philosophical preconditions that led to the eventual discovery of "incompleteness."

Goedel, Escher, Bach. Einstein, Goedel, Heisenberg. The umlaut hovers over that "o" like the twin theorems over the head of the agape initiate. What's an obscure Austrian name doing in troikas of such forbidding company, anyway? Goedel is the third tenor, the "other guy." There never was a Philip Glass opera called Goedel on the Beach. No taut, world-traveled Michael Frayn duologue ever clocked in as Vienna. A poster of the ferrety logician's hand imperceptibly tracing itself will not become a staple of the computer desktop background. And when tortured prodigies of number theory do gain some measure of popular recognition, they get Ben Affleck as their confidant in the suburbs, not the nimbus-domed author of the most famous equation in history.

The man in the street may have heard of Kurt Goedel, but that man is on wobblier footing than when terms like "relativity" or "uncertainty" or "fugue" are invoked. Like each of these schema-altering concepts, Goedel's theorems have been misunderstood and misappropriated by all the usual suspects in cerebral larceny: postmodernists, creationists, people who think "It all depends on what you mean by genocide" is a moral argument. "Incompleteness," then, also seems to be referring to Goedel's legacy, which is... what, exactly?

In 1930, at the age of twenty-four, a University of Vienna graduate student quietly, and to yawning initial reception, established the following: 1. There are provably unprovable but true propositions in any formal system that is consistent and contains arithmetic; 2. The consistency of such a system cannot be proven.

These discoveries may look bite-sized enough to fit comfortably inside a nutshell, but they shook modern epistemology, in all its kingdoms of infinite space, to the core and blew the living daylights out of regnant Continental notions about objective reality. Not bad for a pre-doc.

Goedel's proofs scuppered the positivism of the famed Vienna Circle, which was embodied most charismatically by Ludwig Wittgenstein, actually more of a tangential member. Founded on the Protagorean, or Sophist, idea that "man is the measure of all things," the Circle held that nothing beyond sensory experience was truly "meaningful." Touch, taste, smell, etc. -- that's all we should ever bother to work with as everything else is metaphysical bunkum. In Goedel's opinion, which was fundamentally Platonic, man was not the measure of all things. There was indeed a pure absolute reality, albeit one which could only be apprehended through the tenebrous lenses of probability and presupposition. Nothing wrong with them, however, since they formed the bases of a priori reasoning and hence all mathematics. (When Einstein later formed his peripatetic friendship with Goedel at the Institute for Advanced Research at Princeton, the physicist confessed to sharing this belief in a "higher," semi-translucent realm. Einstein dubbed it the "out yonder.")

The positivists' favorite mathematician, the one they believed they could trust not to futz with their worldview, was the formalist David Hilbert. This was because his bete noire, like theirs, was intuition, that unreliable gatekeeper of the "out yonder." Hilbert's desire was to create what he called "consistent formal systems" which would drain mathematics of any descriptive relation to external phenomena: numbers, sets of objects, etc. Like the recent ads for Las Vegas, "What happens here, stays here," formalism decreed that mathematical systems should only consist of stipulated rules governing symbols that were internally "meaningful" (having semantic value within the system, but no mundane representation to upset the positivists.) Simple enough, except that no math is an island; even in formalism, to get from one system to the next requires a point of origin, a hub system from which all others can be then be accessed. Axioms and the rule of inference, which logically allows any pre-proven theorem to act as "given" in the proof of a new one, traditionally served as the bridges for convenient systems-hopping. But what happens when an axiom is divested of its real-world significance? Where one used to rely on a fingers-crossed "best guess" assumption, now the spadework had to be done using the "provability" of symbols worth nothing outside their own domains.

The hub was arithmetic. The first challenge was proving its consistency, i.e. showing that no logical contradictions could be found in the stuff everyone learns in grade school. A contradiction proves anything; it's the anarchist monkey wrench tossed into a well-oiled machine. The second challenge was proving arithmetic complete, that its logic was tautologous. Accomplish these two things, and formalist revolution could begin.

Goedel stopped the revolution in its tracks. Through metamathematical legerdemain, he was able to use the very syntax (the rules) of a uniquely designed, number-based formal system to both compute and comment upon the meaning (semantic value) contained therein. The numbers he used symbolized starting-point logical propositions that, although not actually paradoxical, were weird and entendre-loaded enough to be saying something about themselves. E.g., "This very statement is not provable in this system." When this self-cannibalizing logic worked itself out, Goedel had produced contradictions of Russian doll-complexity, one integument of meaning masking another.

Goldstein elegantly compares Goedel's winning style of being able to have his cake and pop out of it too to the dramatic conceit of the "play within a play." Specifically, the kind where the characters of the one become "actors" within the other and then use that medium say relevant things about their character selves. She cites Leoncavallo's opera I Pagliacci as she might have done the season of Seinfeld where George and Jerry work on a television series a lot like the one Jason Alexander and the real Jerry Seinfeld had been appearing in. And while I suppose Hamlet technically doesn't qualify because the "players" in Shakespeare's tragedy were all out-sourced allegorizers, Tom Stoppard's paradox-loving comedy Rosencrantz and Guildenstern Are Dead most certainly does. The syntactic-semantic barbershop pole around which Rosencrantz and Guildenstern coil their celebrated "question game?" Very Goedelian. Indeed, the filiations between mathematics and literature were never more finely exampled, especially at the self-referential and meta levels. Goedel's theorems are said to consist of a logical "double speak." Letting aside the coincidence of another "Goldstein" who factors significantly in 1984, is Orwell's novel of thwarted political revolution itself not brokered upon a clever plot involution? Winston Smith is handed a book encoded within a book: a fabricated essay theorizing the motives of a factitious society, stuck between the pages of that society's updated "formal system" of grammar. Elsewhere we hear of the "Alice-in-Wonderland" model Goedel braided around Einstein's field equations for relativity; or the "rigorous rule-bound logic" he admired in Kafka's writing.

Actually, Kafka affords an easy segue into the kind of psychic distress that would come to define Goedel's life following his annus mirabilis. Goldstein uses a good chunk of her book exploring the logician's chronic bouts of paranoia and delusion. His fear of being poisoned by refrigerator fumes and food ultimately led to his demise: the medical record indicated "malnutrition and inanition" as the causes of death. A no less acute, if slightly more justified, sensitivity lay in Goedel's hearing his unorthodox ideas -- which only grew more unorthodox and less remunerative as he got older -- ridiculed in public. This led to reclusiveness and the mournful, too-familiar symptoms of a heavyweight intellectual losing his shit. Some of these read like plagiarism of Bellow's Herzog: the tranches of go-where notes; the unpublished papers and unposted letters; the mounting agoraphobia and anthrophobia.

We know from Douglas Hofstatder that an overactive imagination can produce "swirly, twisty, vortex-like" patterns of rational and creativity marvels. But we also know from the historian Richard Hofstatder that there's a much darker side to this synaptic industry. In his classic essay "The Paranoid Style in American Politics," this second Hofstatder made an observation by no means exclusive to styles American or political: "The paranoid spokesman sees the fate of conspiracy in apocalyptic terms; he traffics in the birth and death of whole worlds" [Italics added].

The cartel ran out for Kurt Goedel at a rather unripe age.

So we get Noam Chomsky once running into the "greatest logician since Aristotle" and asking him what he was working on. The MIT linguist "received an answer that probably nobody since the seventeenth-century's Leibnitz had given: 'I am trying to prove that the laws of nature are a priori.'" Yeah, any day now.

A less melancholy anecdote involves Goedel's precarious navigation of the a posteriori laws of naturalization. Having obsessed over his US citizenship exam, he uncovered a "logical contradiction" in one of the clauses of the Constitution, a loophole he believed could eventually be exploited for the purpose of transforming democracy into dictatorship. The incompleteness of "It can't happen here" would have to wait, however, if the ÈmigrÈ wished to remain here. Einstein and the economist Oskar Morgenstern agreed to calmly distract their friend from bringing up this alarming matter before the New Jersey justice, who, having presided over Einstein's own case, turned out to be a lot more sympathetic than Goedel was distracted:

"'Up to now you have held German citizenship.'
Immediately, Goedel corrected the judicial error: 'Austrian citizenship.'
Duly corrected, the judge continued.
'In any case, it was under an evil dictatorship. Fortunately, this is not possible in America.'"

The look on the Bavarian sage's face at this moment should have been photographed and sold as the pop art complement to the shots of him on the bicycle or sticking out his tongue.

Ernest Gabor Straus once wrote that "Goedel had an interesting axiom by which he looked at the world; namely, that nothing that happens in it is due to accident or stupidity. If you really take that axiom seriously all the strange theories that Goedel believed in become absolutely necessary." And Goedel's silly-to-sinister regard for the status quo becomes explainable, if not quite excusable. Try to avoid wincing through the chapter in which he travels back to Nazified Vienna preoccupied only with his "rights" as a certified academic. Possessing a Wodehouse-like obliviousness to current events -- even after being roughed up by a gang of brownshirts for his ostensible resemblance to a reviled race -- Goedel had to take an enormously detoured return trip to the lush and secure quandrangles of Princeton. What news of home did he bring with him for his info-starved fellow exiles? "The coffee was wretched."

In that same letter, Straus indicates that the normally indulgent and avuncular Einstein was given -- just once -- to write his daily walking partner off as "completely crazy." "Well, what worse could he have done?" inquired Straus. "He voted for Eisenhower."

From Plato's disciple to Plato's Republican.

I began by alluding to the fetish our culture seems to have for slowly morphing eccentric geniuses into genius eccentrics. If there is a "strange axiom," or telos, which guides these fantastic anomalies of the species, "legend" occurs somewhere between awe and condescension, between the whispered campus rumor and the Time magazine cover story. It's a real credit to Goldstein that her book does not contain a passage of greater endeavor than the one in which, drawing on all her skills of characterization as a novelist, she hazards this cant-free, and un-Hollywood portrait of the logician as a young man:

"When the random permutations of genetic blending produce an offspring whose intelligence far outstrips that of his parents that child faces a special sort of predicament: he both recognizes his utter dependence, being after all only a child; and he also clearly perceives the sever limits of his own parents' understanding. Most people come to the latter recognition only during adolescence, when the normal reaction is an explosive mixture of hubris, contempt, and outrage (how can they be so dumb?). But the reaction of a young child is more likely to be blind terror (how can they be trusted to take care of me?) It would be comforting, in the presence of such a shattering conclusion, especially when it's reinforced by a serious illness a few years later, to derive the following additional conclusion: There are always logical explanation and I am exactly the sort of person who can discover such explanations. The grownups around me may be a sorry lot, but luckily I don't need to depend on them. I can figure out everything for myself. The world is thoroughly logical and so I is my mind -- a perfect fit."