Mathematical logician Kurt Gödel was a prodigy who by 1931 at the age of just 25 had already published his landmark incompleteness theorems. Many people are familiar with Gödel’s name but have only a vague idea of why he is such an important figure. This brief biography gives a summary account of it.
In 1931, Gödel published results in formal logic that are considered landmarks of 20th-century mathematics. Gödel demonstrated, in effect, that hopes of reducing mathematics to an axiomatic system, as envisioned by mathematicians and philosophers at the turn of the 20th century, were in vain. His findings put an end to logicist efforts such as those of Bertrand Russell and Alfred North Whitehead and demonstrated the severe limitations of David Hilbert’s formalist program for arithmetic.
By the age of 25 Kurt Gödel had produced his famous “Incompleteness Theorems.” His fundamental results showed that in any consistent axiomatic mathematical system there are propositions that cannot be proved or disproved within the system and that the consistency of the axioms themselves cannot be proved. In addition to his proof of the incompleteness of formal number theory, Gödel published proofs of the relative consistency of the axiom of choice and the generalized continuum hypothesis (1938, 1940). His findings strongly influenced the (later) discovery that a computer can never be programmed to answer all mathematical questions.
I discuss and explain Gödel’s theorems and their implications for the search for scientific truths in my forthcoming book The Great Paradox of Science. (Regular readers of this blog are no doubt asking themselves where there is any limit to my shameless self-promotion!) Gödel was also notoriously eccentric and I recounted earlier the amusing story of his naturalization interview before. His life came to a sad end when he died of starvation, convinced that someone was trying to poison him.
What is surprising is that despite his impressive accomplishments, he was turned down in 1938 for an academic job at the University of Vienna. Why didn’t Godel get that job, given that he had already made such major breakthroughs in mathematical logic and was recognized as brilliant? I knew that Godel was one of the many refugees who fled to the US because of the rise of Nazis prior to World War II. I had always assumed that this was because he was Jewish and that the university denied him the job for that same reason, that he was yet another victim of the rising Nazi anti-Semitism that resulted in the exile of so many of Europe’s greatest scientists and mathematicians. But it turns out that he was not Jewish but that he fled the country because he did not want to be conscripted into the German army.
In 1938, Gödel’s application for a paid position at the University of Vienna was turned down. Fearing conscription into the German army, he applied for a visa to the United States. In late 1939, Kurt and Adele fled Nazi Germany, traveling via the trans-Siberian railway and ship to San Francisco, where they arrived on March 4, 1940. They settled in Princeton where Gödel’s position at the Institute was renewed annually until 1946, when he became a permanent Member until appointed to the Faculty.
So if he was not Jewish, why didn’t he get the university job? The problem may have been that he hung out in intellectual circles that had many Jews and thus people may have simply assumed that he was Jewish too.
Unlike many [of the other refugees from Europe who ended up at the IAS], he was not Jewish, although he moved in circles of Jewish intellectuals and was sometimes thought to be Jewish. He had once been attacked as such by a gang of youths while walking with Adele on a street in Vienna. During the 1930s it was not unusual for university students who were Jewish or had socialist leanings to be forcibly removed from classes. Many of Gödel’s contemporaries were fleeing Europe.
So it may be that even if the University of Vienna authorities knew that he was not Jewish, such was the strength of anti-Semitic sentiment that even hiring someone who was simply perceived to be so or hung around with Jews was too much for them.