David Hilbert was the perfect example of a celebrated, established and meticulous mathematician. His 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. Serving the role of a teacher and mentor, his works inspired young minds and encouraged brimming talent to take interest in this domain. David Hilbert discovered the invariant theory and studied a major spectrum of mathematics including axiomatization of geometry, formulation of Hilbert spaces and the foundations of functional analysis. Scroll down to know more about his career and life.
Childhood And Early Life
On January 23, 1862, David Hilbert was born in Konigsberg, Prussia. Though his family survived with limited means, Otto Hilbert, Hilbert’s father, was a respectable city judge and his mother, Maria, was a philosophy and astronomy enthusiast. It is said that Hilbert’s mother was very fascinated with prime numbers and shapes. This is probably one of the reasons why Hilbert exhibited excellence in mathematics at a very early age. Hilbert also showed interest in language, but set aside this interest to concentrate on the subjects he loved the most; mathematics and science.
Hilbert studied at the University of Konigsberg in 1844, and learned under Heinrich Weber, who was the only full time professor of mathematics at the university. In order to attend additional lectures on differential equations, he studied at another university, for a semester, in Heidelberg. Later, under the supervision of Ferdinand Lindemann, Hilbert completed his oral exam and also submitted a thesis on certain algebraic forms of invariant properties in 1845. The following year, he was awarded a Doctorate in Philosophy from the University of Konigsberg. Hurwitz, a friend who influenced Hilbert’s mathematical progress, suggested him to visit and learn from famous mathematicians in Europe. Taking his advice, Hilbert met Felix Klein in Leipzig, Henri Poincare in Paris and Leopold Kronecker in Berlin only to find their ideas uninspiring.
Hilbert was accorded the position of a lecturer at the University of Gottingen but he refused owing to the low salary. He had to depend upon the fees of his pupils which varied according to the number who attended his lectures and Hilbert found it difficult to carry on as a lecturer. He even complained to the university that there were about 11 trainers in Konigsberg which meant a teacher-student ratio of 1:1. When he felt that nothing was turning good for him, he went for another study trip to overcome his boredom. Because his last experience was not exemplary, this time he planned his trip beforehand to meet the world’s greatest 21 mathematicians. It was during this journey that he got an opportunity to meet Paul Gordon, Klein, Kronecker, Weierstrass and Schwartz. Hilbert was fully satiated with the experience, and got back to Königsberg to work on discovering a solution to a mathematical problem on the rules of finite basis, posed by Paul Gordon. After months of hard work, Hilbert believed that he had devised a foolproof solution to the problem. Believing that his solution was a mathematical breakthrough, Hilbert was overjoyed with his discovery.
Alas, the solution did not impress the eminent mathematicians, and Gordan was too adamant to agree on the proof presented for the problem on finite basis. When Felix Klein, another prominent mathematician, went through these results, he was satisfied with the solution. This led him to bring Hilbert to Gottingen for further education. This helped Hilbert come up with constructive proof in 1892 to the same problem; this time, the proof satisfied Gordan.
Following this successful breakthrough, David Hilbert achieved grand successes and great changes in his personal life as well. After Hurwitz became a full time professor in Zurich, at the Swiss Federal Institute of Technology, Hilbert got a chance as an assistant professor at Konigsberg. After a few weeks, Hilbert was appointed by the German Mathematical Society to conduct a comprehensive study of the number theory. He attained this honor because of his achievement of finding the closest proof of the transcendence of ‘pi’ and ‘e’. He divided the work with another mathematician friend, Minkowski, who was to work on the geometric aspects of the number theory while he himself took up the algebraic number theory. Minkowski, however, failed to complete his part of the work. According to a reader of Hilbert’s published works, Hilbert was ‘a veritable jewel of mathematical literature.’ Even before the book got published, he received a telegram from Felix Klein in which he was offered the position of a full time professor at Gottingen. This was the university that shaped the lives of great mathematicians such as Carl Friedrich Gauss, a renowned number theorist. The faculty and pupils at Gottingen University were genius mathematical minds of the time, and Klein felt that the arrival of Hilbert would complete this intellectual fraternity. Hilbert focused more on the theory of invariants and his proofs for the ‘Gordan Problem’ made him the celebrity mathematician of his academic batch.
David Hilbert married his second cousin, KŠthe Jerosch on October 12, 1892 and the following year, Franz, their son, was born. After Hilbert received the offer from Klein, he decided to live the rest of his life with his family in the city of Gottingen.
David Hilbert contributed a great deal to the fields of modern algebra and geometry. Weyl, a prolific mathematician, appreciated Hilbert’s mathematical works related to the theory of invariants and also commended the dedication Hilbert showed towards the subject. One of his major contributions was the ‘Satz 90’, a theorem based on the relative cyclic fields that happened to be one of the most prominent milestones in his long career.
Retirement And Death
David Hilbert served as the editor for one of the leading mathematical journals between the years 1902-1939. In 1930, at the age of 68, he was compulsory asked to retire from the university. This was because of the stringent laws enforced by the chancellor of Germany, Adolf Hitler, who restricted the Jews from teaching. Hence, the Nazi rule brought an end to Hilbert’s mathematical career. On February 14, 1943, Hilbert died of frustration and health ailments. His funeral was attended by lesser than ten people, most of who were fellow academicians. News of his death only became known to the wider world, six months later.