David hilbert, who was born on January 23, 1862, in Königsberg, Prussia (now Kaliningrad, Russia) – was a German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the foundations of formal mathematics. His 1909 work on integral equations led to 20th century research on functional analysis.
Hilbert He began his career at the University of Königsberg, where, in 1884, he completed his Doctorate; he remained at Königsberg as Privatdozent (professor or assistant professor) between 1886 and 1892, as Extraordinarius (associate professor) between 1892 and 1893, and as Ordinarius in 1893-95. In 1892 he married Käthe Jerosch, and they had a son, Franz. In 1895, he accepted a chair of mathematics at the University of Göttingen, where he remained for the rest of his life.
The University of Göttingen had a flourishing reputation in mathematics, mainly as a result of the contributions of Carl Friedrich Gauss, Peter Gustav Lejeune Dirichlet, and Bernhard Riemann. During the first three decades of the 20th century, this mathematical tradition reached even greater eminence, largely due to Hilbert. The Göttingen Institute of Mathematics attracted students and visitors from all over the world.
The intense interest of Hilbert in mathematical physics he also contributed to the reputation of the university in physics. His colleague and friend, the mathematician Hermann Minkowski, assisted in the new application of mathematics to physics, until his untimely death in 1909. Three winners of the Nobel Prize in Physics: Max von Laue in 1914, James Franck in 1925 and Werner Heisenberg in 1932 – they spent significant parts of their careers at the University of Göttingen, during the lifetime of Hilbert.
In a very original way,
Hilbert he extensively modified the mathematics of invariants, entities that do not alter during geometric changes such as rotation, dilation, and reflection. He proved the invariant theorem: all invariants can be expressed in terms of a finite number. In its
Zahlbericht (“Commentary on Numbers”), a report on the theory of algebraic numbers, published in 1897, consolidated the knowledge on this subject, marking the way for the developments that followed. In 1899 he published the
Grundlagen der Geometrie (The Foundations of Geometry, 1902), which contained his definitive set of axioms for Euclidean geometry and an in-depth analysis of their importance. This popular book, which appeared in 10 editions, marked a turning point in the axiomatic treatment of geometry.
A substantial part of the fame of Hilbert it rests on a list of 23 research problems that he enunciated in 1900 at the International Congress of Mathematics in Paris. In his speech, “The problems of mathematics“He examined almost all the mathematics of his day and strove to expose the problems that he believed would be important to mathematicians in the 20th century. Many of the problems have since been solved, and each solution was a remarkable event Of those that remain, however, one, in part, requires a solution to the Riemann hypothesis, which is generally considered the most important unsolved problem in mathematics.
In 1905 (and again since 1918)
Hilbert he tried to establish a firm foundation for mathematics, showing consistency, that is, that finite steps of reasoning in logic could not lead to a contradiction. But in 1931, the Austrian-American mathematician Kurt Gödel proved that this goal was unattainable: therefore, it cannot be known with certainty whether mathematical axioms do not lead to contradictions. After
Hilbert However, the development of logic was different, since it established the formal foundations of mathematics.
The work of Hilbert in integral equations around 1909 led directly to the 20th century investigation of functional analysis. His work also established the basis for his analysis of infinite dimensional space, later called Hilbert space, a concept that is useful in mathematical analysis and quantum mechanics. Using his results in integral equations, Hilbert contributed to the development of mathematical physics through his important memoirs on the theory of kinetic gas and the theory of radiation.
The city of Königsberg in 1930, the year of his retirement from the University of Göttingen, appointed Hilbert honorary citizen. For this occasion he prepared a dissertation entitled “Naturerkennen und Logik“(” Understanding Nature and Logic “). The last six words of Hilbert’s address summarize his enthusiasm for mathematics and the devotion he put into his life to raise it to a new level:”Wir müssen wissen, wir werden wissen“(” We should know, we will know “). In 1939 he received together with the French mathematician Émile Picard the first Mittag-Leffler prize from the Swedish Academy.
The last decade of the life of Hilbert it was overshadowed by the tragedy that the Nazi regime brought to him and many of his students and colleagues. He died in Göttingen, Germany, on February 14, 1943.