When Gödel did the political math

I spent much of the past week coughing when I should have been sleeping, the only boon of which is that I managed to read Jordan Ellenberg’s lively and instructive How Not to Be Wrong: The Power of Mathematical Thinking. I came across an alarming politics-related anecdote about Kurt Gödel, the mathematician who famously demonstrated that in any formal axiomatic system of arithmetic, there will be some true theorems that can’t be proved to be true.

Apparently, when Gödel was studying for the U.S. citizenship test in 1948, he found what seemed to him a fatal flaw. “The document,” Ellenberg writes, “contained a contradiction that could allow a Fascist dictatorship to take over the country in a perfectly constitutional manner.” For better or worse, the exact nature of this flaw has been lost to posterity, but Gödel was apparently so upset that he couldn’t help but talk about his concern with the judge who examined him on behalf of the Immigration and Naturalization Service, despite the advice of colleagues Albert Einstein and Oskar Morgenstern, who thought he should keep his worry to himself. Years later, in 1971, Morgenstern wrote down his memory of the exchange:

The examiner turned to Gödel and said, Now, Mr. Gödel, where do you come from?

Gödel: Where I come from? Austria.

The examiner: What kind of government did you have in Austria?

Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship.

The examiner: Oh! This is very bad. This could not happen in this country.

Gödel: Oh, yes, I can prove it.

The examiner, Morgenstern remembered, “was intelligent enough to quickly quieten Gödel and broke off the examination at this point, greatly to our relief.”

Ellenberg’s source is a webpage at Princeton’s Institute for Advanced Study, a page that unfortunately no longer exists, but there’s an account of Gödel’s immigration exam on page 7 of the spring 2006 issue of the institute’s newsletter, and the writer Jeffrey Kegler has put together a synopsis of the documentary evidence and has shared a scan of Morgenstern’s memorandum.