The Information - James Gleick [88]
Gödel’s first public mention of his discovery, on the third and last day of a philosophical conference in Königsberg in 1930, drew no response; only one person seems to have heard him at all, a Hungarian named Neumann János. This young mathematician was in the process of moving to the United States, where he would soon and for the rest of his life be called John von Neumann. He understood Gödel’s import at once; it stunned him, but he studied it and was persuaded. No sooner did Gödel’s paper appear than von Neumann was presenting it to the mathematics colloquium at Princeton. Incompleteness was real. It meant that mathematics could never be proved free of self-contradiction. And “the important point,” von Neumann said, “is that this is not a philosophical principle or a plausible intellectual attitude, but the result of a rigorous mathematical proof of an extremely sophisticated kind.”♦ Either you believed in mathematics or you did not.
Bertrand Russell (who, of course, did) had moved on to more gentle sorts of philosophy. Much later, as an old man, he admitted that Gödel had troubled him: “It made me glad that I was no longer working at mathematical logic. If a given set of axioms leads to a contradiction, it is clear that at least one of the axioms must be false.”♦ On the other hand, Vienna’s most famous philosopher, Ludwig Wittgenstein (who, fundamentally, did not), dismissed the incompleteness theorem as trickery (“Kunststücken”) and boasted that rather than try to refute it, he would simply pass it by:
Mathematics cannot be incomplete; any more than a sense can be incomplete. Whatever I can understand, I must completely understand.♦
Gödel’s retort took care of them both. “Russell evidently misinterprets my result; however, he does so in a very interesting manner,” he wrote. “In contradistinction Wittgenstein … advances a completely trivial and uninteresting misinterpretation.”♦
In 1933 the newly formed Institute for Advanced Study, with John von Neumann and Albert Einstein among its first faculty members, invited Gödel to Princeton for the year. He crossed the Atlantic several more times that decade, as fascism rose and the brief glory of Vienna began to fade. Gödel, ignorant of politics and naïve about history, suffered depressive breakdowns and bouts of hypochondria that forced him into sanatoria. Princeton beckoned but Gödel vacillated. He stayed in Vienna in 1938, through the Anschluss, as the Vienna Circle ceased to be, its members murdered or exiled, and even in 1939, when Hitler’s army occupied his native Czechoslovakia. He was not a Jew, but mathematics was verjudet enough. He finally managed to leave in January 1940 by way of the Trans-Siberian Railway, Japan, and a ship to San Francisco. His name was recoded by the telephone company as “K. Goedel” when he arrived in Princeton, this time to stay.♦
Claude Shannon had also arrived at the Institute for Advanced Study, to spend a postdoctoral year. He found it a lonely place, occupying a new red-brick building with clocktower and cupola framed by elms on a former farm a mile from Princeton University. The first of its fifteen or so professors was Einstein, whose office was at the back of the first floor; Shannon seldom laid eyes on him. Gödel, who had arrived in March, hardly spoke to anyone but Einstein. Shannon’s nominal supervisor was Hermann Weyl, another German exile, the most formidable mathematical theorist of the new quantum mechanics. Weyl was only mildly interested in Shannon’s thesis on genetics—“your bio-mathematical problems”♦—but thought Shannon might find common ground with the institute’s other great young mathematician, von Neumann. Mostly Shannon stayed moodily in his room in Palmer Square. His twenty-year-old wife, having left Radcliffe to be with him, found it increasingly grim, staying home while Claude played clarinet accompaniment to his Bix Beiderbecke record on the phonograph. Norma thought he was depressed and wanted him to see a psychiatrist. Meeting Einstein was nice, but the thrill wore off. Their marriage was over; she was