Kurt Gödel - Mathematicians, Family and Family

Kurt Friedrich Gödel was born on April 28, 1906, in Brno, the second largest city in the Czech Republic. At the time of his birth, it was a textile-producing city in the Austro-Hungarian province of Moravia and was known as Brünn.

His father, Rudolf Gödel, was initially a textile worker. Later, he became the manager and eventually the part owner of the Friedrich Redlich textile factory. His mother, Marianne Gödel (née Handschuh) was educated at a French institute; she had broad cultural interests.

Kurt was the younger of his parents’ two children. His elder brother, also named Rudolf, later became a radiologist in Vienna. Although his father was Catholic, he was baptized in his mother’s religion, a Lutheran and derived his middle name from his godfather Friedrich Redlich.

He had a very happy childhood. He was vey devoted to his mother and felt helpless when she was not around. He was also very inquisitive and kept on asking questions. Because of that, his family called him Herr Warum or Mr. Why.

However, from his childhood, he suffered from different ailments. At the age of five, he had a mild anxiety neurosis, but recovered completely from it. At six, he suffered from rheumatic fever. Although he recovered from this too, he became convinced that his heart had been damaged permanently.

In 1912, Kurt started his education at Evangelische Privat-Volks-und Bürgerschule, a Lutheran primary school in Brünn. In spite of his bad health he was a brilliant student and graduated from there in 1916.

Thereafter, he entered Staats-Realgymnasium, a German speaking high school in Brünn. Here too he excelled academically and became fascinated first with foreign languages and then with history.

In 1918, with the breakup of Austro-Hungarian Empire, Gödel automatically became a Czechoslovak citizen. Young though he was, he could not accept that and considered himself an Austrian.

Sometime in 1920, he developed an interest in mathematics and by the next year, in philosophy. By 1922, he had read Kant and soon started working on university level mathematics. By the time he graduated in 1924, he had mastered a good deal of it.

However, when Kurt Gödel joined the University of Vienna in 1924, he took up theoretical physics as his major. Sometime before this, he had read Goethe’s theory of colors and became interest in the subject. At the same time, he attended classes on mathematics and philosophy as well.

Soon he came in contact with great mathematicians and in 1926, influenced by number theorist Philipp Furtwängler, he decided to change his subject and take up mathematics. Besides that, he was highly influenced by Karl Menger’s course in dimension theory and attended Heinrich Gomperz’s course in the history of philosophy.

Also in 1926, he entered the Vienna Circle, a group of positivist philosophers formed around Moritz Schlick, and until 1928, attended their meetings regularly. After graduation, he started working for his doctoral degree under Hans Hahn. His dissertation was on the problem of completeness.

In the summer of 1929, Gödel submitted his dissertation, titled ‘Über die Vollständigkeit des Logikkalküls’ (On the Completeness of the Calculus of Logic). Subsequently in February 1930, he received his doctorate in mathematics from the University of Vienna. Sometime now, he also became an Austrian citizen.

Later in the same year, he published his dissertation in a slightly abridged form. The work established that all of the first-order logical truths can be proved in standard first-order proof systems. Thereafter, working further on the subject, he published his second paper on the same topic in January 1931.

Titled, ‘Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I’ (On Formally Undecidable Propositions of Principia Mathematica and Related Systems I), the paper had a number of theorems that would have great implications for consistency proofs in mathematics. It also contained many techniques, which would help to prove these theorems.

Later, Kurt Gödel submitted the paper for his habilitation and spent the academic years of 1931 and 1932 working as an assistant to his doctoral guide Hans Hahn. Finally his habilitation was accepted on 1 December 1932 and in March 1933, Kurt Gödel became a Privatdozent at the University of Vienna.

As a Privatdozent, Kurt Gödel gave his first course on the foundations of arithmetic. He was an extremely shy person and gave his lectures facing the blackboard. During the seven years he spent at the university, he taught only two more courses.

Also in 1933, he was appointed a visiting professor at the Institute for Advanced Study, Princeton, U.S.A. Accordingly, from February to May 1934, he gave a series of lectures titled ‘On undecidable propositions of formal mathematical systems’ at the IAS.

These lectures were noted down by young Stephen Cole Kleene, an American mathematician and later published in book form. Sometime now, Gödel also met Albert Einstein and established a life-long friendship.

In the mid-1930s, his mental health deteriorated and he suffered a nervous breakdown. Thereafter, he spent several months in a sanatorium receiving treatment for depression.

His bout of depression reappeared when in June 1936, German philosopher Moritz Schlick was murdered by a deranged student. Gödel again had to undergo treatment. Thus he could not return to his academic life until 1937.

On March 12, 1938, Germany annexed Austria. They abolished the position of Privatdozent and so Gödel had to apply afresh. All along, he had been close to several Jewish scholars and this went against him. He was not only turned down for an academic post but also found physically fit for conscription into the Nazi army.

When in 1939 the Second World War broke out, Kurt Gödel decided to leave for the U.S.A. Thanks to his friends in the U.S.A., he received a non-quota immigrant visa and also a Soviet transit visa by January 1940.

He then took the Trans Siberian Railway to reach Yokohama and from there sailed through the Pacific Ocean to reach San Francisco on March 4, 1940. Finally, he took a train to Princeton, where he was appointed an ordinary member of the Institute of Advanced Study.

Since he did not have any formal duty at the IAS, he spent his time working on his mathematical research. In the same year, he published ‘Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory’.

He spent the summer of 1942 working on the independence of the axiom of choice from finite type theory and possibly discovered a proof. Although he never published the work, scholars were able to deduce that after examining his notebooks relating to that period.

From 1942 onwards, he turned his attention away from mathematics and began to work first on philosophy of mathematics and then on philosophy in general. From 1943 to 1946, he concentrated mainly on Gottfried Leibniz but also studied Immanuel Kant and Edmund Husserl.

Meanwhile in 1944, he published his first philosophical paper, titled ‘On Russell's Mathematical Logic.’ During this period, he also had a quiet social life and spent a lot of time with Albert Einstein discussing everything from politics to philosophy and physics. Later he also became friendly with Morgenstern.

In 1946, Gödel was made a permanent member of the IAS. In 1947, he published his second paper on philosophy, titled ‘What is Cantor's Continuum Hypothesis?’ Sometime now, he also studied the U.S. Constitution and discovered an inconsistency, which could allow the United States to become a dictatorship.

Therefore, when on December 5, 1947, he was asked to appear for his U.S. citizenship examination, Einstein and Morgenstern accompanied him. They were afraid, that Gödel might say something that would jeopardize his chances.

However, everything went on smoothly and Gödel became a US citizen. He then continued working on philosophy and in 1949 published his paper on the subject, ‘A Remark on the Relationship between Relativity Theory and Idealistic Philosophy.’

In 1953, Gödel became a full professor at the Institute. By that time, his involvement in philosophy had deepened. From then on until 1959, he worked on a submission to the Schilpp volume on Rudolf Carnap. Titled ‘Is Mathematics a Syntax of Language?’ It for some reason was never published.

Gödel remained with the Institute until his retirement in 1976. Thereafter he remained attached to it as an emeritus professor. In his later years, although he worked consistently, he did not publish any paper. However, he circulated many of them in manuscript form.

’Some considerations leading to the probable conclusion that the true power of the continuum is ℵ2’ and ‘Ontologischer Beweis’, both circulated in 1970, are some such works. Together they give expression to his core ideas, resulting from his long involvement with mathematics and philosophy.

Gödel is best remembered for his two incompleteness theorems, published in 1931. While working on mathematical logic, he discovered that there were some inherent limitations in every formal axiomatic system containing basic arithmetic. Later these theorems were found to be as much important for mathematical logic as for the philosophy of mathematics.

In 1951, Gödel was awarded the first Albert Einstein Award jointly with Julian Schwinger.

In 1968, he was elected a Foreign Member of the Royal Society.

In 1974, he was awarded the National Medal of Science.

In 1927, Kurt Gödel met Adele Nimbursky (née Porkert) at a night club, where she was employed as a dancer. She was six years older to him and a divorcee. Although his family did not approve of the match, he married her on September 20, 1938, just before they left for the U.S.A.

Late in life he began to suffer from Persecutory delusions and feared of being poisoned. He did not take any food unless his wife prepared it.

Unfortunately, late in 1977, Adele was hospitalized for six months. During that period Gödel refused to eat. As the situation became alarming, he was admitted to Princeton Hospital, where he died on January 14, 1978. His death certificate stated that he died of "malnutrition and inanition caused by personality disturbance".

Concepts like Gödel metric, Gödel numbering, and Gödel's ontological proof bear his legacy.

The Kurt Gödel Society, an international organization founded in 1987 for the promotion of research in logic, philosophy, and the history of mathematics, was named in his honor.