Who is Kurt Gödel?June 25, 2021
Austrian-American logician, mathematician and philosopher of mathematics. He is best known for Gödel’s Incompleteness Theorem, which is named after him.
He proved that in any system complex enough to include integer arithmetic in its theorems, there will be propositions that cannot be proven true or false based on the axioms of the system. For this, he developed a method called Gödel numbering. He proved his famous theorem in 1931 during his doctoral study at the University of Vienna, thereby changing the direction of 20th century mathematics.
In the 1940s, at the Institute for Advanced Study at Princeton University, Kurt Gödel provided a solution to Einstein’s gravitational field equations that described a universe that revolves around its axis. The rotation of the universe would drag the light (and therefore the causal links between the objects) together. Therefore, it would draw a closed loop in space and time in the material body, without needing to exceed the speed of light. Gödel’s model revealed that going back in time is not prohibited by the theory of relativity. Kurt Gödel designed a model of the universe using Einstein’s field equations. The design was similar to Einstein’s, but Gödel’s approach gave a negative value to cosmological constants. Einstein also expressed his discomfort with the idea that his theory allows travel to the past in some cases. However, Gödel’s model is falsified by the gravitational redshift observed by astronomers.
Gödel, who is an introverted personality, started to eat nothing in his last years due to paranoia that he would be poisoned, as a result of which he was found dead in Princeton on January 14, 1978 from malnutrition and weighed only 29.5 kg.
Kurt Friedrich Gödel was born on April 28, 1906 in Brünn, Moravia, to his ethnic German family; Rudolf Gödel, a manager in a textile company, and Marianne Gödel, born in Handschuh, were born as a child. At the time of his birth, the German language was more common among the languages spoken in the city, and it was also the language of his parents.
Gödel became a Czechoslovak citizen at the age of 12, when the Austro-Hungarian Empire collapsed at the end of World War I. Gödel told his later biographer, John D. Dawson, that at this time he felt like an “Austrian exile in Czechoslovakia” (“ein österreichischer Verbannter in Tschechoslowakien”). He could never speak Czech and refused to learn at school. At the age of 23, he became an Austrian citizen by his own choice. When Nazi Germany invaded Austria, Gödel became a direct German citizen at the age of 32. II. At the end of World War II, Gödel was granted American citizenship at the age of 42.
In his youth, Gödel was known in his family as Der Herr Warum (“Mr. Why”) because of his relentless questions.
According to his older brother Rudolf, at the age of 6 or 7 Kurt fell ill with rheumatic fever; He recovered completely, but for the rest of his life he convinced himself that he had a permanent heart condition.
Gödel graduated from primary and secondary school, where education was in German, with honors in 1923. Although Kurt initially excelled in language, he later became more interested in mathematics and history. His interest in mathematics increased in 1920 when his older brother Rudolf (born 1902) went to Vienna to study medicine at the University of Vienna (UV). During his youth, Kurt read the Gabelsberger shorthand, Goethe’s Theory of Colors, criticisms of Isaac Newton, and the writings of Immanuel Kant.
At the age of 18, Kurt joined his older brother Rudolf and entered the University of Vienna. At that time, he already had college-level math knowledge. Although initially intending to study theoretical physics, Kurt also attended classes in mathematics and philosophy. He read Kant’s Metaphysische Anfangsgrunde der Naturwissenschaft and joined the Vienna Circle, which included Moritz Schlick, Hans Hahn, and Rudolf Carnap. Kurt later worked in number theory, but became interested in mathematical logic after attending a seminar given by Moritz Schlick on Bertrand Russell’s Introduction to Mathematical Philosophy.
His participation in a seminar given by David Hilbert on the completeness and consistency of mathematical systems in Bologna would have a significant impact on Gödel’s life.
In 1928 Hilbert and Wilhelm Ackermann published Grundzüge der theoretischen Logik (Principles of Theoretical Logic). This work was an introduction to first-level logic, the domain of the problem of completeness: Are the axioms of a formal system sufficient to derive statements that are true in all models of the system?. This was the topic Gödel chose for his doctoral study.
In 1929, at the age of 23, Gödel completed his doctoral thesis under the supervision of Hans Hahn. Gödel, in his doctoral thesis, today calls this result Gödel’s completeness theorem.