Who is David Hilbert?June 25, 2021
David Hilbert Ki Famous German mathematician and logician.
The German mathematician David Hilbert, who reduced geometry to a set of axioms and contributed significantly to the formation of the formal foundations of mathematics, pioneered the development of functional analysis in the 20th century with his work on integral equations.
Between 1895 and 1929 he was a professor at the University of Göttingen. At the beginning of the twentieth century, he is considered the leader of the German school of mathematics. In 1897 he established the concept of field and the theory of algebraic field of numbers. During his early work in the 1890s, he succeeded in revealing the fundamental laws of the theory of invariants, laying the foundations for algebraic geometry and the theory of polynomial ideals that play an important role in modern algebra. In 1899 he published “The Fundamentals of Geometry”, a synthesis of his research on the foundations of geometry. This gave rise to many fruitful works in various parts of mathematics aimed at axiomization.
Avoiding reference to concrete images, Hilbert introduced the “three-object system”, which he called points, lines, and planes, into mathematics. These objects, which are not clearly shown what they are, reveal some relations that are explained by 21 axioms gathered in 5 groups. These are the axiom of belonging, order, equality or equivalence, parallelism and continuity. After that, he set up geometries in which one or the other of the axioms was not validated. He treated fundamental terms as logical entities with no properties other than those axiomically charged to them. His discussions with Brouwer to defend and demonstrate the self-evidence of classical mathematics led to extensive studies in mathematics.
Hilbert, who retired from the University of Göttingen in 1930, was elected an honorary compatriot of Königsberg the same year. The last sentence of Hilbert’s speech titled Naturerkennen und Logik (Understanding Nature and Logic) given for this choice is as follows:
Wir mussen wissen, wir werden wissen. (We should know, we will know.)