Scientist of the Day - Kurt Gödel
Kurt Gödel, photograph, Vienna, 1925 (Wikimedia commons)
Kurt Gödel, an Austrian-American mathematician, was born Apr. 28, 1906, in Brünn (Brno, the home of Gregor Mendel, in Gödel's youth part of the Austro-Hungarian Empire). He studied at the University of Vienna, where he became interested in mathematical logic, a relatively new discipline, stemming from the work of David Hilbert, that provided an alternative to the philosophical logic of Alfred North Whitehead and Bertram Russell in their Principia Mathematica (1910-13).
Gödel wrote his dissertation in 1929 on the completeness theorem, proving that in first-order logic, which deals with sets of countable objects, all axioms are provable.
However, in 1931, Godel presented two Incompleteness Theorems, in which he showed that in second-order logic, dealing with infinite sets, such as the natural numbers, there will always be propositions that are true but unproveable within that system. This was a profound and unexpected discovery.
Kurt Gödel and Albert Einstein, photograph, undated but ca 1950, New Yorker, Feb. 21, 2005 (newyorker.com)
Gödel had become a Czech citizen in 1918, with the dissolution of the Austro-Hungarian empire after WWI, which he resisted, considering himself Austrian, and by the time of his Incompleteness Theorems, he had traded in his Czech citizenship for Austrian. He finished his habilitation in 1931 and became a privatdozent in Vienna. He survived the initial rise to power of Hitler in 1933, since he was neither Jewish nor German, although he did spend a year at the Institute for Advanced Study (IAS) at Princeton in 1933-34. But when Hitler annexed Austria in 1938, made all Austrians German citizens, and abolished the position of privatdozent, Gödel saw the handwriting on the wall. In 1939, he and his new wife Adele boarded the Orient Express, rode the rails all the way to the shores of the Pacific, took a steamship to San Francisco, and then a train to Princeton, where he was invited to join the IAS. He would remain there for the rest of his career.
Gödel had met Albert Einstein on his trip to Princeton in 1933, and once Gödel settled back in at the IAS in 1939, the two became fast friends, and used to walk together to and from work. Einstein was 27 years older than Gödel. Later, in the 1950's, when Einstein had more or less given up on his unified field theory, he told a colleague that the only reason he still went to the Institute every day was so that he could walk home with Gödel.
Title page, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory, delivered by Kurt Gödel, Princeton University Press, 1940 (Linda Hall Library)
In 1938, Gödel had given some lectures at the IAS on the Axiom of Choice, which deals with the possibility of building a new set from elements of existing sets, even infinite ones; the lectures were taken down by an attendee and subsequently published (third image). In 1942, Gödel decided to continue his work on the Axiom of Choice, and he and Adele spent the summer at the Blue Hill House in Blue Hill, Maine, on Penobscot Bay. I perked up when I first read this, many years ago, because my mother and her family came from Blue Hill, and I spent several summers there as a child, and even a night at what is now the Blue Hill Inn. Gödel liked to think while walking, and he used to leave his room at sunset and walk down the dark lanes to various points on the bay, coming back after midnight. What the townsfolk thought of this man in a trench coat and a fedora, with a thick German accent, walking their streets at night in the middle of a war with Germany, I have no idea, but as they do in Maine, they left him to his own affairs. My grandmother, Lena Saunders, was postmistress in the Blue Hill post office in 1942, and I like to think that she handled a few letters to Gödel from Einstein, and vice versa.
Blue Hill Inn, Blue Hill, Maine, home to Kurt and Adele Gödel in the summer of 1942, recent photograph, owners of the Inn (bluehillinn.com)
It is said that Gödel and Adele went to dinner at the Blue Hill House every night, but never ate. This was because Gödel had a morbid, pathological fear of being poisoned, stemming from his days in Vienna, when one of his teachers was murdered by a student fanatic. He would only eat food prepared by Adele. Much later, when Adele was hospitalized for a stroke in late 1977 and unavailable as a cook, Gödel quit eating, and died of starvation early in 1978, a sad ending to a brilliant career.
Tombstone of Kurt and Adele Gödel, Princeton Cemetery (Wikimedia commons)
There have been many books written about Gödel and Incompleteness, Gödel and the Axiom of Choice, Gödel and Einstein – we have several dozen in our collections, a surprising number, given that only a few people can understand Gödel’s work. I have always been partial to a book that is now 47 years old. Gödel was one of the three titular subjects of Douglas Hofstadter's mind-blowing work, Gödel, Escher, Bach: An Eternal Golden Braid (1979), which wove a strange tale around the similarities between J.S. Bach's Musical Offering (1747); the self-referential lithographs and woodcuts of Maurits Escher, especially Drawing Hands (1948); and Gödel’s Incompleteness Theorems. The book can still be highly recommended to all of you who are, like myself, mathematically disadvantaged, but nevertheless curious about the "strange loops" that are often manifest in the world.
William B. Ashworth, Jr., Consultant for the History of Science, Linda Hall Library and Associate Professor emeritus, Department of History, University of Missouri-Kansas City. Comments or corrections are welcome; please direct to ashworthw@umkc.edu.
