When Einstein dies, he becomes even more withdrawn. He only eats food prepared by his wife because he believes they will poison him. When his wife is unable to cook due to illness, he refuses to eat completely. He dies of starvation.
He was born on April 28, 1906, in Czechoslovakia, a part of the Austro-Hungarian Empire, as the second son of a textile company manager father, and a mother related to his children.
Gödel, who started learning mathematics, religion, and languages at the age of 10, is known as "Mr. Why" in his family because of his endless curiosity and endless questions. He can't learn Czech for the rest of his life because he studied in German schools. After a successful high school education, he changed his mind at the University of Vienna, where he went to study theoretical physics at the age of 18, and moved to the mathematics department.
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege.
Gödel's mentor during this period was the mathematician and analyst Hans Hahn. Gödel would later become his most famous student. Hahn is a member of a think tank that discusses the positivist philosophical views of the physicist and philosopher Ernst Mach. In 1922, with the support of Hahn, Gödel began to attend the meetings of the society called the Vienna Circle, although it did not coincide with his dogmatic scientific ideas. The general views of the community are known today as logical positivism. Mainly influenced by Ludwig Wittgenstein's Tractatus Logico-Philosophicus, this community sees metaphysics and metaphysical problems as meaningless problems.
Starting to concentrate on mathematical logic since 1928, Gödel completed his doctorate in mathematics by presenting his doctoral thesis on completeness, as a continuation of David Hilbert's work, where he attended many seminars on the philosophy of mathematics. His doctoral thesis, which was finished in the summer of 1929, is today known as Gödel's Completeness Theorem.
Kurt Gödel is one of those people who can read the book Principia Mathematica, co-written by Alfred North Whitehead and Bertrand Russell. He says that there is no clear definition of the most basic axioms in the book, that is, he cannot see that every logical proposition is true or false if it is not, in theory.
In 1931, at the age of 25, he proved two theorems called the Incompleteness Theorem. Gödel turned the world of mathematics upside down with his famous article “On the Principia Mathematica and the Formally Undecidable Propositions of Related Strings – I”, in which he stated that a consistent axiomatic system for arithmetic must necessarily be missing. Axiomatic is the name given to the formal system that contains the rules of logical inference for generating new theorems.
The first of the two theorems states that in a logical axiomatic system showing the properties of integers and simple arithmetic operations, formally true propositions will always exist and be true by the rules of the system, but they cannot be proved within the system. The second theorem argues that such a system, which can prove itself to be consistent, is inconsistent. This view is a major blow to the David Hilbert program, which proved its consistency and sought to establish a strong axiomatic system. There is an anecdote about that day. While Gödel was explaining the incompleteness theorem, the mathematician John von Neumann, who was there, said, "It's all over."
Gödel reveals that in any branch of mathematics, including arithmetic, consistency, and completeness cannot be proved by the method allowed by that system. Gödel proves that there are problems that cannot be solved with any set of rules and procedures. His long-spoken views are widely accepted by world mathematicians. Stephen Hawking, in The Universe in a Nutshell (2001), describes Gödel's earthquake in mathematics in an article: “Gödel's theory has set fundamental limits to mathematics. This theory was a great shock to the scientific community because it undermined the widespread belief that mathematics is a coherent and complete system built on a single logical foundation.”
At first, most mathematicians sneered at such a strange and abstract result; but gradually here and there unsolvable problems begin to appear. For example, you have a stack of pieces of paper in different geometric shapes (square, rhombus); Can you completely tile the plane without creating holes and overlaps by taking a series of random shapes? This problem cannot be solved with mathematics. The truth is that an algorithm containing the shapes of the parts cannot tell you that a plane can or cannot be tiled without holes and overlaps with them.
Gödel's theorem slowly establishes itself and goes beyond the limits of mathematics. Gödel proves: “A precise definition of a language cannot be made in the same language; because in this way the correctness of a sentence cannot be defined.” Thus, it opens up to mathematics, philology, and philosophy.
Gödel, who also started to teach at the university he attended, suffers from depression due to travel and too much work. In 1938, he married Adele Nimbursky, 10 years older than him, whom his family objected to because of his previous marriage and divorce and being a nightclub dancer. One of the family's reasons for opposition is that Adele is Catholic, although they are strict Lutherans (Christian denominations).
Gödel just works, even putting cotton plugs in his ears to be completely isolated and not distracted. He is apolitical and more concerned with his own work than what is going on in the world. When Austria joined Nazi Germany, his associate professorship was abolished. He reapplies to the university, but the fact that his circle of friends in Vienna is Jewish is against Gödel. In addition, despite his poor health, he is considered suitable for military service. One night, he is attacked by a group of Nazi youths, and his glasses are broken. In the face of all this, he realizes that he has to leave Europe and immigrates to America with his wife in 1940, never returning to Europe. He begins work at the Princeton Institute for Advanced Study in San Francisco. He meets Einstein, who came to Princeton 7 years ago and establishes a close friendship.
After a while, Gödel's interest shifted from mathematics to philosophy and physics. He reads Kant and Husserl, as well as Leibniz, whom he will admire throughout his life. Gödel's thoughts are close to the heuristic tradition regarding the importance of intuition in attaining knowledge of mathematical objects; it differs from the intuitive tradition only in the existence of mathematical objects. Gödel is a Platonist, thinking that mathematical objects (numbers, sets, etc.) exist independently of the mind that thinks about them. In this respect, Gödel also differs from the logical positivists who make up the majority of the Vienna Circle.
Gödel has an introverted and interesting personality. He walks around in winter clothes in the summer, believes in ghosts, and sits in his house with the door open because he believes that he can be poisoned by refrigerator gas. Although it is unhealthy, it does not follow the recommendations of the doctors and even acts the opposite. He died in 1940 because he refused to go to the doctor due to stomach bleeding. When his close friend Einstein died in 1955, he became even more withdrawn. He prefers to talk on the phone, even with the people closest to him. He only eats food prepared by his wife because he believes that bad people will poison him. In 1977, when his wife is unable to cook due to illness, Gödel completely refuses to eat. He is taken to Princeton Hospital, where, when he refuses to eat, he dies of starvation two weeks later.