David Hilbert

David Hilbert

German Mathematician David Hilbert was among the most influential mathematician of the 20^th century. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundation of mathematics. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

He was born on January 23, 1862 in Wehlau, near Konigsberg, then the principal city of East Prussia. His father Otto Hilbert was a judge while his mother Maria Theresa was a lover of mathematics and Hilbert is said to have inherited the love of mathematics from the early childhood is from her. When Otto Hilbert became a senior judge the family moved into Koinsberg itself, where David was enrolled at the Royal Friedrichkolleg at the age of eight years. The school was not suitable for the child prodigy Hilbert so after completing one year in the school he attended the more progressive and science oriented Wilhelm Gymnasium.

He completed his graduation in 1880 from Wilhelm Gymnasium and later he enrolled at University of Koinsberg to complete his doctorate. He did doctorate under Lindemann. Lindemann was not among the first rank of mathematicians, but he had a wide range of interests, one of which was the theory of invariants. This was the subject on which Hilbert wrote his dissertation entitled Über invariante Eigenschaften specieller binärer Formen, insbesondere der Kugelfunctionen ("On the invariant properties of special binary forms, in particular the spherical harmonic functions"). One of Hilbert's friends there was Minkowski, who was also a doctoral student at Königsberg, and they were to strongly influence each others mathematical progress.

In 1884 Hurwitz was appointed to the University of Konigsberg and quickly became friends with Hilbert, a friendship which was another important factor in Hilbert's mathematical development.  In 1886, he was appointed as an assistant professor in the University of Konigsberg. He remained there as a professor from 1886 to 1895. The University of Gottingen had a flourishing tradition in mathematics, primarily as the result of the contributions of Carl Friedrich Gauss, Dirichlet, and Bernhard Riemann in the 19th century. In 1888 he demonstrated his first work on invariant function known as finiteness theorem. In 1892, Hilbert married Käthe Jerosch , the daughter of a Konigsberg merchant. They had a son named Franz who died young at the age of 21 and never lived a normal life.

 In 1893, Hilbert began a work on algebraic number theory. In 1895, as a result of intervention on his behalf by Felix Klein he obtained the position of Chairman of Mathematics at the University of Göttingen, at that time the best research center for mathematics in the world and where he remained for the rest of his life. Hilbert’s intense interest in mathematical physics also contributed to the university’s reputation in physics. Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms and he analyzed their significance. He published Grundlagen der Geometrie in 1899 putting geometry in a formal axiomatic setting. 

Hilbert put forth a most influential list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician. Hilbert's famous 23 Paris problems challenged mathematicians to solve fundamental questions that included the the continuum hypothesis, the well ordering of the real, Goldbach's conjecture, the transcendence of powers of algebraic numbers, the Riemann hypothesis, the extension of Dirichlet's principle and many more. Many of the problems were solved during this century, and each time one of the problems was solved it was a major event for mathematics.

Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations. In 1905 the Hungarian Academy of Sciences gave a special citation for Hilbert. Hilbert’s work in integral equation in 1909 led to the research in functional analysis. His work also established the basis for his work on infinite dimensional space, later called Hilbert space, a concept that is useful in mathematical analysis and quantum mechanics. Making use of his results on integral equations, Hilbert contributed to the development of mathematical physics by his important memoirs on kinetic gas theory and the theory of radiations. In 1909 he proved the conjecture in number theory that for any n, all positive integers are sums of a certain fixed number of nth powers.

In 1930 Hilbert retired and the city of Königsberg made him an honorary citizen of the city; although he continued to lecture occasionally. In 1932 Gottingen celebrated his seventieth birthday with a torchlight processions. After 1934 he never again set foot in the Mathematical Institute.

Hilbert died on February 13, 1943, ten years after the Nazis came to power.it was the middle of the war and barely a dozen people attended his funeral. News of his death only became known to the wider world six months after he had died. The epitaph on his tombstone in Göttingen is the famous lines he had spoken at the conclusion of his retirement address to the Society of German Scientists and Physicians in the fall of 1930.

Wir müssen wissen.

Wir werden wissen.

In English:

We must know.

We will know.