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.

richardelguru says

“…is [there] any limit to my shameless self-promotion!”

I’ve got to know: is there?

🙂 🙂 🙂 🙂 🙂 🙂

Leo Buzalsky says

I’m more curious if there is a limit to you making notes about your “shameless self-promotion”? 🙂 🙂 🙂

Mano Singham says

Self-promotion does not come easily to me. And yet people in the publishing industry tell me that I have to suppress my distaste and do it relentlessly if I want to make my writings better known. So I try to balance the self-promotion with a self-deprecatory, semi-facetious comment to the effect that I am aware of what I am doing and that it can be grating to the reader!

Right now I am preparing a book proposal to send to agents and publishers and this requires self-promotion. As a result, I am finding it harder to write the proposal than it was to write the book itself!

machintelligence says

I have no problem with you touting your books. For truly it is written: if a man tooteth not his own horn, who will toot it for him?

Brian English says

I’m pretty sure you can pay people to toot your horn.

Brian English says

I read a popular (i.e. paperback) book about Goedel that seemed part hagiography, part (attempted) corrective regarding Goedel’s status as a philosopher. The gist of the philosophical argument attributed to Goedel was that he was a platonist/idealist (mathematical objects exist, there is a real true circle, there is a real true pi, etc in some other ‘dimension’ that we dimly grasp when see a circle, or whatever) and he was motivated to find a floor with Principia Mathematica because if it was shown to be consistent and whatever, then it would be a blow to platonism. By using his superb logical abilities, he worked out his consistency theorems, which did for Principia et al, but also had the virtue (to some) of showing idealism, (at least with mathematical objects) to be philosophically respectable. I’m not a philosopher, but I find platonism a bit absurd, but it’s interesting how Goedel was motivated to refute logicism (assuming the book is correct about his motivation).

mnb0 says

“I try to balance the self-promotion with ….”

Better still: every time you commit self-promotion you must tell us a bit of what we can expect from your book.

https://en.wikipedia.org/wiki/Teaser_campaign

hyphenman says

So, Mano, when will we be able to pre-order your book?

I’ve been checking

Mac’s Backs—our local independent bookstore (note to other readers: when you do pre-order your copy, please do so from an independent bookstore and notthe ever-evil Amazon)—once a week for your book to come up.Please be sure to (shamelessly) announce the pre-publication availability date and when you’ll be signing copies here in Cleveland.

Cheers,

Jeff

Mano Singham says

Jeff,

I haven’t even got a publisher yet. I will definitely tell readers when it can be ordered.