# David Hilbert

David Hilbert was a renowned German Mathematician works helped pave the path for modern mathematical research in the 20th century. He was the first to distinguish between mathematics and metamathematics. Regarded as one of the finest mathematicians of the twentieth century, David Hilbert left an indelible mark with his vast knowledge in different divisions of mathematics and was also the first to discover the invariant theory. His strong foothold in mathematics proved significant in areas ranging from number systems to geometry and extended mathematics to mathematical physics. His work on integral equations laid the foundation for research in functional analysis. After completing his Ph.D., he began his teaching career at the University of Königsberg, where he also collaborated with fellow mathematicians Hermann Minkowski and Adolf Hurwitz. Later, he joined the University of Göttingen, the global mathematical hub of the century, as Professor of Mathematics. Initially, he worked on number theory and abstract algebra, but before long he turned his attention to integral equations and completely transformed the field. Many important mathematical terms and theorems have been named after him, including Hilbert space, Hilbert curves, Hilbert classification, and Hilbert inequality. At the Paris International Congress of Mathematicians in 1900, he presented 23 important questions that intrigued mathematicians over the century. A great leader and spokesperson for the discipline, he was absolutely hopeful that future mathematicians would find the solution to the 23 problems. Even though he retired before the rise of Nazism, he lived to see prominent Jewish faculty members being ousted from the University of Göttingen in 1933.

**Childhood & Early Life**

- David Hilbert was born on 23 January 1862 to Otto Hilbert and Maria Therese Hilbert. He was born either in Königsberg or Wehlau, Province of Prussia (today Znamensk, Kaliningrad Oblast, Russia).
- His father Otto was a reputable city judge and his mother Maria was interested in philosophy and astronomy. Right from his childhood, he excelled in mathematics and showed interest in language.
- In 1872, he joined Friedrichskolleg Gymnasium. Later in 1879, he moved to, and eventually graduated from the Wilhelm Gymnasium.
- After graduation, he decided to stay close to home. In autumn 1880, he enrolled at the University of Königsberg to study mathematics. Two years later, he befriended a younger talented Polish-German mathematician Hermann Minkowski at the university.

**Career**

- In 1884, David Hilbert and Minkowski were joined by another German mathematician, Adolf Hurwitz who had arrived from Göttingen as an Associate Professor. The trio began a powerful and productive collaboration that greatly influenced their mathematical careers.
- Hilbert received his doctorate degree in 1885. His dissertation titled ‘On the invariant properties of special binary forms, in particular the spherical harmonic functions’ was completed under the guidance of Ferdinand von Lindemann. After finishing his Ph.D. he spent the winter at the University of Leipzig and then Paris.
- He continued at the University of Königsberg as a Senior Lecturer of Mathematics from 1886 - 1895.Thereafter in 1895, he became Professor of Mathematics at the University of Göttingen.
- The University of Göttingen was the 20th century global hub of renowned mathematicians. It was here that he enjoyed the company of notable mathematicians like Emmy Noether and Alonzo Church. Some of his prominent students were Hermann Weyl and Ernst Zermelo.
- He supervised the doctoral studies of 69 Ph.D. students at Göttingen, many of whom like Otto Blumenthal, Felix Bernstein, Richard Courant, Erich Hecke, Hugo Steinhaus, and Wilhelm Ackermann later became celebrated mathematicians themselves.
- In 1900, he listed 23 unsolved mathematical problems at the International Congress of Mathematicians in Paris. The concise list set the stage for the mathematical works of the 20th Century.
- In 1902, he became the co-editor of the world’s leading mathematical journal, ‘Mathematische Annalen’. He continued in the position till 1939. He retired from the University of Göttingen in 1930, aged 68.
- In the build-up to the World War II, the Nazis removed many of the well-known Jewish faculty members from University of Göttingen including Hermann Weyl, Emmy Noether and Edmund Landau.
- He co-authored an important book ‘Grundlagen der Mathematik’ which was published in two volumes in 1934 and 1939. The book was intended as a follow-up to Hilbert-Ackermann book ‘Principles of Mathematical Logic’ (1928).
- Along with Minkowski, he had a keen interest in mathematical physics. During his lifetime, three Nobel laureates for Physics—Max von Laue, James Franck, and Werner Heisenberg—spent considerable part of their careers at the University of Göttingen.

**Major Works**

- In 1899, he published a book ‘The Foundations of Geometry’ in which he illustrated a set of axioms that removed the errors from Euclidean geometry. He also aimed to axiomatize mathematics.
- In 1900, he delivered a lecture titled ‘Mathematical Problems’ before the Paris International Congress of Mathematicians. He listed 23 mathematical problems whose solutions were to be found by the 20th century mathematicians. These problems are now referred to as Hilbert’s problems and many of them remain unsolved even to this day.
- David Hilbert excelled in various fields of mathematics such as axiomatic theory, algebraic number theory, invariant theory, class field theory and functional analysis. He invented ‘Hilbert space’, one of the most important concepts of functional analysis and modern mathematical physics.
- He discovered mathematical fields such as modern logic and met mathematics. ‘Satz 90’, a theorem built on relative cyclic fields was another important contribution of his work.

**Awards & Achievements**

- In 1905, Hilbert received a special citation at the first award ceremony of the Wolfgang Bolyai prize of the Hungarian Academy of Sciences.

**Personal Life & Legacy**

- David Hilbert was baptized and brought up according to the Reformed Protestant Church. Later on however, he became a nonbeliever. He argued that mathematical truth was independent of the existence of God.
- In 1892, he married Käthe Jerosch. While at Königsberg, the couple had a son named Franz Hilbert (1893–1969). All through his life, Franz suffered from an undiagnosed psychological illness which caused terrible disappointment to his mathematician father.
- By the time he died on 14 February 1943, the Nazis had already re-staffed almost the whole university, replacing all the Jews. His funeral was attended by very few people and the news of his death came to light months after he died.

**Trivia**

- He considered famous fellow mathematician, Hermann Minkowski to be his “best and truest friend”.

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