Paul Bernays facts for kids
Quick facts for kids
Paul Bernays
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| Born | 17 October 1888 |
| Died | 18 September 1977 (aged 88) |
| Nationality | Swiss |
| Alma mater | University of Berlin |
| Known for | Mathematical logic Axiomatic set theory Philosophy of mathematics |
| Scientific career | |
| Fields | Mathematics |
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| Doctoral advisor | Edmund Landau |
| Doctoral students | Corrado Böhm Julius Richard Büchi Haskell Curry Erwin Engeler Gerhard Gentzen Saunders Mac Lane |
| Other notable students | Hao Wang |
Paul Isaac Bernays (born October 17, 1888 – died September 18, 1977) was a Swiss mathematician. He made very important contributions to mathematical logic, set theory, and the philosophy of mathematics. He worked closely with the famous mathematician David Hilbert.
Contents
Who Was Paul Bernays?
Paul Bernays was born in London, United Kingdom. His family was well-known for being scholars and business people. His great-grandfather was a chief rabbi in Hamburg, Germany.
His Early Life and Education
Paul grew up in Berlin, Germany. He went to a school called Köllnische Gymnasium from 1895 to 1907. After school, he studied at the University of Berlin. There, he learned mathematics, philosophy, and physics. Some of his teachers were famous thinkers like Max Planck.
Later, he also studied at the University of Göttingen. He continued to learn mathematics, physics, and philosophy.
Becoming a Doctor of Mathematics
In 1912, Paul Bernays earned his Ph.D. in mathematics. This was from the University of Berlin. His main teacher for this was Edmund Landau. His thesis was about numbers and forms.
In the same year, he also got a special qualification called "habilitation." This allowed him to teach at universities. He got this from the University of Zurich. He taught there from 1912 to 1917.
Working with David Hilbert
Starting in 1917, Paul Bernays began working with David Hilbert. Hilbert was a very important mathematician. Bernays helped Hilbert with his studies on the basic rules of arithmetic. Bernays also gave lectures on other math topics.
In 1918, he received another habilitation. This was for his work on the rules of logic.
Challenges and Moving to Switzerland
In 1922, Bernays became a professor at Göttingen. One of his best students there was Gerhard Gentzen. Sadly, in 1933, he lost his job. This happened because of laws against people of Jewish background in Nazi Germany.
After working privately for Hilbert for a few months, Bernays moved to Switzerland. He had Swiss nationality from his father. He sometimes worked at the ETH Zurich university. He also visited universities in the United States.
Paul Bernays's Mathematical Work
Paul Bernays made big contributions to how we understand mathematics.
Foundations of Mathematics
Bernays worked with David Hilbert on a two-volume book. It was called Grundlagen der Mathematik, which means Foundations of Mathematics. These books were published in 1934 and 1939. They talked about the basic ideas of math.
One important idea from their work is called the Hilbert–Bernays paradox. It shows that a strong, consistent theory cannot refer to itself in a certain way.
Developing Set Theory
Bernays also worked on set theory. Set theory is a branch of mathematics that studies collections of objects. Between 1937 and 1954, he published seven papers about this.
He built on ideas from another mathematician, John von Neumann. Bernays changed von Neumann's theory. He made it so that "classes" and "sets" were the main building blocks. His theory, with some changes by Kurt Gödel, is now called von Neumann–Bernays–Gödel set theory. It is a very important way to understand sets in mathematics.
