David Hilbert was bornon January 23, 1862 in Königsberg or Wehlau, Province of Prussia (today Znamensk, Kaliningrad Oblast, Russia), German, is Mathematician. 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.

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"Good, he did not have enough imagination to become a mathematician".

— Hilbert's response upon hearing that one of his students had dropped out to study poetry.

1872

In late 1872, Hilbert entered the Friedrichskolleg Gymnasium (*Collegium fridericianum*, the same school that Immanuel Kant had attended 140 years before); but, after an unhappy period, he transferred to (late 1879) and graduated from (early 1880) the more science-oriented Wilhelm Gymnasium. Upon graduation, in autumn 1880, Hilbert enrolled at the University of Königsberg, the "Albertina". In early 1882, Hermann Minkowski (two years younger than Hilbert and also a native of Königsberg but had gone to Berlin for three semesters), returned to Königsberg and entered the university. Hilbert developed a lifelong friendship with the shy, gifted Minkowski.

1882

Hilbert's approach signaled the shift to the modern axiomatic method. In this, Hilbert was anticipated by Moritz Pasch's work from 1882. Axioms are not taken as self-evident truths. Geometry may treat *things*, about which we have powerful intuitions, but it is not necessary to assign any explicit meaning to the undefined concepts. The elements, such as point, line, plane, and others, could be substituted, as Hilbert is reported to have said to Schoenflies and Kötter, by tables, chairs, glasses of beer and other such objects. It is their defined relationships that are discussed.

1884

In 1884, Adolf Hurwitz arrived from Göttingen as an Extraordinarius (i.e., an associate professor). An intense and fruitful scientific exchange among the three began, and Minkowski and Hilbert especially would exercise a reciprocal influence over each other at various times in their scientific careers. Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled *Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen* ("On the invariant properties of special binary forms, in particular the spherical harmonic functions").

1886

Hilbert remained at the University of Königsberg as a *Privatdozent* (senior lecturer) from 1886 to 1895. In 1895, as a result of intervention on his behalf by Felix Klein, he obtained the position of Professor of Mathematics at the University of Göttingen. During the Klein and Hilbert years, Göttingen became the preeminent institution in the mathematical world. He remained there for the rest of his life.

1888

Hilbert's first work on invariant functions led him to the demonstration in 1888 of his famous *finiteness theorem*. Twenty years earlier, Paul Gordan had demonstrated the theorem of the finiteness of generators for binary forms using a complex computational approach. Attempts to generalize his method to functions with more than two variables failed because of the enormous difficulty of the calculations involved. In order to solve what had become known in some circles as *Gordan's Problem*, Hilbert realized that it was necessary to take a completely different path. As a result, he demonstrated *Hilbert's basis theorem*, showing the existence of a finite set of generators, for the invariants of quantics in any number of variables, but in an abstract form. That is, while demonstrating the existence of such a set, it was not a constructive proof — it did not display "an object" — but rather, it was an existence proof and relied on use of the law of excluded middle in an infinite extension.

1892

In 1892, Hilbert married Käthe Jerosch (1864–1945), "the daughter of a Königsberg merchant, an outspoken young lady with an independence of mind that matched his own". While at Königsberg they had their one child, Franz Hilbert (1893–1969).

1897

Hilbert unified the field of algebraic number theory with his 1897 treatise *Zahlbericht* (literally "report on numbers"). He also resolved a significant number-theory Problem formulated by Waring in 1770. As with the finiteness theorem, he used an existence proof that shows there must be solutions for the Problem rather than providing a mechanism to produce the answers. He then had little more to publish on the subject; but the emergence of Hilbert modular forms in the dissertation of a student means his name is further attached to a major area.

1898

Among his 69 Ph.D. students in Göttingen were many who later became famous mathematicians, including (with date of thesis): Otto Blumenthal (1898), Felix Bernstein (1901), Hermann Weyl (1908), Richard Courant (1910), Erich Hecke (1910), Hugo Steinhaus (1911), and Wilhelm Ackermann (1925). Between 1902 and 1939 Hilbert was Editor of the *Mathematische Annalen*, the leading mathematical journal of the time.

1899

The text *Grundlagen der Geometrie* (tr.: *Foundations of Geometry*) published by Hilbert in 1899 proposes a formal set, called Hilbert's axioms, substituting for the traditional axioms of Euclid. They avoid weaknesses identified in those of Euclid, whose works at the time were still used textbook-fashion. It is difficult to specify the axioms used by Hilbert without referring to the publication history of the *Grundlagen* since Hilbert changed and modified them several times. The original monograph was quickly followed by a French translation, in which Hilbert added V.2, the Completeness Axiom. An English translation, authorized by Hilbert, was made by E.J. Townsend and copyrighted in 1902. This translation incorporated the changes made in the French translation and so is considered to be a translation of the 2nd edition. Hilbert continued to make changes in the text and several editions appeared in German. The 7th edition was the last to appear in Hilbert's lifetime. New editions followed the 7th, but the main text was essentially not revised.

1900

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 as the most successful and deeply considered compilation of open problems ever to be produced by an individual Mathematician.

1907

By 1907 Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years with a confounding Problem of putting the theory into final form. By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject. Einstein received an enthusiastic reception at Göttingen. Over the summer Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915 Einstein published several papers culminating in "The Field Equations of Gravitation" (see Einstein field equations). Nearly simultaneously David Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (see Einstein–Hilbert action). Hilbert fully credited Einstein as the originator of the theory, and no public priority dispute concerning the field equations ever arose between the two men during their lives. See more at priority.

1909

Around 1909, Hilbert dedicated himself to the study of differential and integral equations; his work had direct consequences for important parts of modern functional analysis. In order to carry out these studies, Hilbert introduced the concept of an infinite dimensional Euclidean space, later called Hilbert space. His work in this part of analysis provided the basis for important contributions to the mathematics of physics in the next two decades, though from an unanticipated direction. Later on, Stefan Banach amplified the concept, defining Banach spaces. Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators, that grew up around it during the 20th century.

1912

In 1912, three years after his friend's death, Hilbert turned his focus to the subject almost exclusively. He arranged to have a "physics tutor" for himself. He started studying kinetic gas theory and moved on to elementary radiation theory and the molecular theory of matter. Even after the war started in 1914, he continued seminars and classes where the works of Albert Einstein and others were followed closely.

1920

In 1920 he proposed explicitly a research project (in *metamathematics*, as it was then termed) that became known as Hilbert's program. He wanted mathematics to be formulated on a solid and complete logical foundation. He believed that in principle this could be done, by showing that:

1925

Around 1925, Hilbert developed pernicious anemia, a then-untreatable vitamin deficiency whose primary symptom is exhaustion; his assistant Eugene Wigner described him as subject to "enormous fatigue" and how he "seemed quite old", and that even after eventually being diagnosed and treated, he "was hardly a scientist after 1925, and certainly not a Hilbert."

1926

Additionally, Hilbert's work anticipated and assisted several advances in the mathematical formulation of quantum mechanics. His work was a key aspect of Hermann Weyl and John von Neumann's work on the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation and his namesake Hilbert space plays an important part in quantum theory. In 1926 von Neumann showed that if atomic states were understood as vectors in Hilbert space, then they would correspond with both Schrödinger's wave function theory and Heisenberg's matrices.

1930

He made a series of conjectures on class field theory. The concepts were highly influential, and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved by 1930, after work by Teiji Takagi.

1931

Gödel demonstrated that any non-contradictory formal system, which was comprehensive enough to include at least arithmetic, cannot demonstrate its completeness by way of its own axioms. In 1931 his incompleteness theorem showed that Hilbert's grand plan was impossible as stated. The second point cannot in any reasonable way be combined with the first point, as long as the axiom system is genuinely finitary.

1933

Hilbert lived to see the Nazis purge many of the prominent faculty members at University of Göttingen in 1933. Those forced out included Hermann Weyl (who had taken Hilbert's chair when he retired in 1930), Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic, and co-authored with him the important book *Grundlagen der Mathematik* (which eventually appeared in two volumes, in 1934 and 1939). This was a sequel to the Hilbert-Ackermann book *Principles of Mathematical Logic* from 1928. Hermann Weyl's successor was Helmut Hasse.

1943

By the time Hilbert died in 1943, the Nazis had nearly completely restaffed the university, as many of the former faculty had either been Jewish or married to Jews. Hilbert's funeral was attended by fewer than a dozen people, only two of whom were fellow academics, among them Arnold Sommerfeld, a theoretical Physicist and also a native of Königsberg. News of his death only became known to the wider world six months after he had died.

1946

Hilbert, the first of two children of Otto and Maria Therese (Erdtmann) Hilbert, was born in the Province of Prussia, Kingdom of Prussia, either in Königsberg (according to Hilbert's own statement) or in Wehlau (known since 1946 as Znamensk) near Königsberg where his father worked at the time of his birth.

2013

Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture, for reasons that are anecdotal.

2014

His collected works (*Gesammelte Abhandlungen*) have been published several times. The original versions of his papers contained "many technical errors of varying degree"; when the collection was first published, the errors were corrected and it was found that this could be done without major changes in the statements of the theorems, with one exception—a claimed proof of the continuum hypothesis. The errors were nonetheless so numerous and significant that it took Olga Taussky-Todd three years to make the corrections.

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