Kurt Gödel, the mathematician

The Austrian man Kurt Gödel was one of the foremost mathematicians of the 20th century. Already in his 20s, he introduced revolutionary mathematical theorems. However, later in life, he developed serious mental disorders. Suffering from paralyzing paranoia, he refused to eat anything other than food his wife cooked and tasted herself. He died of starvation when his wife fell ill and was taken to hospital. There was then no one he trusted when it came to cooking his food.

Kurt Gödel was born in Brünn (Brno) in 1906 in what is today the Czech Republic. As a boy he was extremely gifted, but also very worried. The family called him ”Herr Warum” (Mr Why) because of his quirkiness and curiosity. In the early school age, he suffered from a rheumatic fever, which he thought at an adult age had caused him chronic heart failure.

Gödel attended Deutsche Staats-Realgymnasium 1916 – 1924 in Brünn. At school and university, he showed that he was an exceptionally talented and diligent student. In high school he had the highest marks in all subjects. During the high school years, he learned to stenograph (Gabelsberger shorthand), read Goethe’s colour theory, studied criticism of Newton and read Kant’s writings. At university, Gödel read mathematics and philosophy. He became a doctorate in mathematics at the age of 23.

Gödel made a great impression on lectures given by Professor Moritz Schlick, who was shot to death by one of his former students when he walked up to the podium to give a lecture. This event should have triggered Gödel a nervous breakdown.

During his time at the University of Vienna, he fell in love with Adele Numbursky, a six-year older ballet dancer. His parents opposed the proposed marriage, which greatly upset the son. He had previously been very close to his mother. The couple first married ten years later and then came to live their entire lives together.

In the same mathematical area that was dealt with in the doctoral dissertation, in 1931 Gödel published his revolutionary ideas about incomplete theories and theories of numbers that are true, but for which it is not possible to prove that they are true. His theory of incomplete theorems shocked the contemporary mathematical world, which had to rethink the mathematical concept of ”truth”. Gödel’s ”incompleteness theorem” is two fundamental theorems in modern logic. They deal with the determinability and provability of statements in formal systems and were presented by Kurt Gödel in 1931. The theorem states that the problems of the German mathematician David Hilbert, about the axiomatization of arithmetic, require an infinite number of axioms. This means that Hilbert’s program, which seeks to find a complete and consistent, that is, not contradictory, axiom system for all mathematics, according to Gödel, is unworkable.

Later, Gödel developed the theory of ”recursive functions”, which became one of the foundations for computer programming. He further developed the ”incompleteness theorem”, which made it clear that the first order of the predicate logic is ”complete”. All true statements within this logic can be proved within the system. Gödel also clarified the connection between classical logic, intuitionistic logic and model logic. But during his work on developing the theories, he suffered from serious mental illness. For a long time in the 1930s, he was admitted to various psychiatric clinics.

Kurt Gödel belonged to the group of intellectual scholars in Vienna during the interwar period, which came to be known as the Vienna Circle. Other well-known academics in the circle, or who had contact with it, were Herbert Feigl, Hans Reichenbach, Carl Gustav Hempel, Alfred Tarski, Karl Popper and Willard Van Orman Quine.

But when Germany annexed Austria in 1938, Gödel and his wife fled to Princeton University, New Jersey (about 80 miles southwest of New York City). There he was then active until his death in 1978. A general understanding is that he was one of the most prominent mathematicians after Aristotle. The three most prominent were considered to be Gottlob Frege, Bertrand Russell and Kurt Gödel.

In Princeton, Gödel got to know Albert Einstein. They used to take long walks and they always talked in German. They became good friends, both as researchers and privately. Other people who heard them talk told that, despite being fluent in German and having a long academic education, they could not understand anything about what they were talking about.

Einstein was present when Gödel applied for American citizenship in 1947 and would appear before Judge Philip Forman and show, among other things, that he knew of some basic principles in the American republic. Gödel then began to talk incoherently about the American constitution, which he believed had some deficiencies, which according to him, could mean the risk of the State being turned into a dictatorship. This puzzled the judge and Gödel’s present friends tried to silence him so as not to risk him being denied citizenship. But the application for citizenship was upheld. Gödel was born an Austrian citizen, at the time of the annexation became a German citizen at the age of 32 and at the age of 42 he became an American citizen.

A person who was at Princeton at that time has later told that Einstein and Gödel really only wanted to talk to each other and not to anyone else. However, the two professors were diametrically opposed personalities. Einstein was optimistic and often in a good mood. He laughed often. But on the other hand, Gödel was pessimistic, serious and withdrawn. Although Gödel was a distinct intellectual and widely regarded as the foremost mathematical logician after Aristotle, he could sometimes be childishly fond of simple entertainment. Gödel’s favourite movie was Disney’s ”Snow White and the Seven Dwarfs”. Later in life, he became increasingly interested in philosophy and physics, less in logic and mathematics. He studied Gottfried Leibniz in particular. To some extent, he took on Kant and Husserl.

Over time, Gödel developed very serious paranoid disease symptoms. He believed in ghosts, he was afraid of being poisoned and he was quite convinced that mathematicians who visited him at the appropriate time would try to poison him. His food sometimes consisted only of butter, baby food and laxatives.

Einstein died in 1955 and Gödel then isolated himself and did everything possible to avoid all contacts. If someone wanted to talk to him anyway, they had to try to make an appointment with him. This also applied to professors who were his colleagues at Princeton and had their study rooms in the same building and also in the same corridor. It often happened that he did not come to agreed meetings at all, nor did he explain why he did not attend.

Gödel was awarded the prestigious ”National Medel of Science” award in 1975 but refused to attend the awards ceremony at the White House. This despite the fact that the president himself offered a car with a driver at Gödel’s disposal for the journey to Washington.

Gödel was so scared to get sick that he sometimes wore a face mask while staying outdoors. He refused for a long time to eat any food other than cooked by his wife and he demanded that she tested the food he was served.

At times Gödel could be confused and could then speak of evil forces ”that were immediately below the good forces”. He was absolutely convinced that there were people who wanted to poison him or kill him otherwise. The wife was taken to hospital in 1977 and could then no longer cook for her husband. As a result, Gödel completely stopped eating, lost weight quickly and was soon taken to hospital. Two weeks later he died as a result of self-imposed starvation. The death certificate states that he died by malnutrition and inability to eat, which was something that depended on his personal circumstances. He was 71 years old at the time and weighed only about 30 kg. The wife died three years later.

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