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In 1947, having left Nazi-occupied Vienna for the quaint idyll of Princeton, N.J., seven years before, the mathematician Kurt Gödel was studying for his citizenship exam and became preoccupied with the mechanisms of American government. A worried friend recalled Gödel talking about “some inner contradictions” in the Constitution that would make it legally possible “for somebody to become a dictator and set up a fascist regime.” Gödel started to bring this up at his actual examination, telling the judge that the United States could become a dictatorship — “I can prove it!” — before his friends (one of whom was Albert Einstein) managed to shut him up so that the naturalization process could go on as planned.
It’s the kind of unruly eruption that Stephen Budiansky showcases to potent and entertaining effect in “Journey to the Edge of Reason,” his account of Gödel’s life and work. Gödel’s “incompleteness theorem,” which he presented in 1930, when he was 24, upended his profession’s assumption that mathematics should be able to prove a mathematical statement that is true. Gödel’s proof landed on a mathematical statement that was true but unprovable.
For interested readers, Budiansky supplies an appendix that moves through Gödel’s proof, step by step, but granular knowledge of formal logic isn’t essential for anyone’s enjoyment of this moving biography. Budiansky — whose impressive and impressively varied output includes a novel, a book about Oliver Wendell Holmes, another about post-Civil War violence and a history of cats — brings a polymath’s interest to bear on a man whose life intersected with the political and philosophical upheavals of the 20th century.
Gödel was born in 1906 to a prosperous German-speaking family in Brünn, in the Moravian part of the Hapsburg Empire. His was a happy childhood, in what the writer Stefan Zweig called “the golden age of security,” before the empire collapsed with World War I. From the age of 4, Gödel was known as “Herr Warum,” or “Mr. Why.” He would later tell a psychiatrist that he was “always curious, questioning authority, requiring reasons.” He experienced this as a delight, not a burden: “The highest aim of my life (conceived in puberty) is pleasure of cognition.”
Budiansky recounts Gödel’s intellectual coming of age in full — his move to Vienna in 1924, where he studied mathematics after deciding that physics was “logically so messy”; his participation in the famed Vienna Circle, which tasked itself with discussing the transformations in scientific thought occasioned by revolutionary ideas like Einstein’s theory of relativity.
Vienna at the time was intellectually exhilarating and politically perilous, a place of astonishing scholarship and higher learning that also functioned as “the world capital of cranks, paranoids, megalomaniacs and conspiracy theorists,” Budiansky writes. Interestingly and also tragically, Gödel himself would come to embody this untenable jumble, swinging between bouts of exacting lucidity and utter delusion.
Not only does Budiansky offer a clear discussion of the incompleteness theorem along with the accolades it elicited; he takes care to embed the proof in the life, avoiding the kind of gloomy interpretations that so often made Gödel feel misunderstood. Gödel had smashed the establishment understanding of mathematics to pieces — or had he? Gödel refused the nihilistic conclusion drawn by some from his work: that because there were truths that weren’t provable, nothing mathematical was truly knowable. He drew optimistic inferences instead, choosing to emphasize that there would always be new mathematical truths to discover. If anything, Budiansky writes, Gödel believed his result “meant that human ingenuity would be required to build new paths to the truths that were out there, waiting to be found.”
It’s this emphasis on the human and humane implications of Gödel’s life and work that gives this book its mesmerizing pull. Budiansky devotes a chapter to his subject’s decision to leave Nazi-occupied Austria — a “year of living indecisively,” Budiansky writes, when the family’s finances were running low. Gödel wasn’t Jewish, and even voted in favor of incorporating Austria into the Reich; but as a groundbreaking mathematician with many Jewish friends, he would have undoubtedly come under the suspicion of a regime ruled by crackpot theories about a “racial value index” and a “glacial cosmogony” filled with “cosmic ice.”
Gödel found a home at the Institute for Advanced Study in New Jersey, where scholars were paid good money to pursue their research interests free from the responsibility of a teaching load — a setup so cushy that the jealous professors at nearby Princeton called it “the Institute for Advanced Salaries.”
Gödel could go for long walks with his fellow institute scholar Einstein, who sponsored Gödel’s citizenship application and called him the greatest logician since Aristotle, but he was wracked by physical ailments and nervous conditions. A doctor told him he had a bleeding ulcer, which he strangely refused to believe, even though he was also a self-medicating hypochondriac. He subscribed to all sorts of conspiracy theories, insisting that “nothing happens without a reason,” and that the reason was almost always a hidden one. The unlimited freedom he had at the institute proved to be double-edged, Budiansky observes. In one sense, it saved Gödel’s life; but it also allowed his consciousness to wander into the darkest places, without the checks on his expansive anxieties that interactions with the ordinary world might have otherwise provided.
“Journey to the Edge of Reason” makes ample and illuminating use of Gödel’s correspondence and journals, including a diary, kept in a special shorthand, that had never been translated before. Budiansky is judicious with interpretations, preferring mostly to let his themes emerge from the absorbing story he tells. Gödel died in 1978, after weeks of starving himself to a weight of 65 pounds. His psychiatrist had been recording Gödel’s spiraling descent into self-loathing and paranoia. But a satisfactory “why” for Herr Warum’s ultimate end remains elusive. The attending physician wrote that the cause of death was “more apathy and resignation than an active volitional suicidal effort.”
The mathematician who cheerfully insisted that his proof opened up space for human creativity had succumbed to the doomed visions of his own despair. It’s an apparent inconsistency that Gödel might have noticed had it been presented to him in the cold terms of formal logic, but as this vibrant biography so beautifully elucidates, the truth of a life can’t ever be proven; it can only be shown.
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