37 Facts About Hilbert

David Hilbert was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries.

Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics .

Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers.

Hilbert is known as one of the founders of proof theory and mathematical logic.

Hilbert, the first of two children and only son of Otto and Maria Therese Hilbert, was born in the Province of Prussia, Kingdom of Prussia, either in Konigsberg or in Wehlau near Konigsberg where his father worked at the time of his birth.

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In late 1872, Hilbert entered the Friedrichskolleg Gymnasium ; but, after an unhappy period, he transferred to and graduated from the more science-oriented Wilhelm Gymnasium.

Hilbert developed a lifelong friendship with the shy, gifted Minkowski.

Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Uber invariante Eigenschaften spezieller binarer Formen, insbesondere der Kugelfunktionen .

Hilbert remained at the University of Konigsberg as a Privatdozent from 1886 to 1895.

At the University of Gottingen, Hilbert was surrounded by a social circle of some of the most important mathematicians of the 20th century, such as Emmy Noether and Alonzo Church.

Between 1902 and 1939 Hilbert was editor of the Mathematische Annalen, the leading mathematical journal of the time.

In 1892, Hilbert married Kathe Jerosch, who was the daughter of a Konigsberg merchant, an outspoken young lady with an independence of mind that matched [Hilbert's].

Hilbert considered the mathematician Hermann Minkowski to be his "best and truest friend".

Hilbert was baptized and raised a Calvinist in the Prussian Evangelical Church.

Hilbert lived to see the Nazis purge many of the prominent faculty members at University of Gottingen in 1933.

About a year later, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust.

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 a native of Konigsberg.

Day before Hilbert pronounced these phrases at the 1930 annual meeting of the Society of German Scientists and Physicians, Kurt Godel—in a round table discussion during the Conference on Epistemology held jointly with the Society meetings—tentatively announced the first expression of his incompleteness theorem.

Later, after the usefulness of Hilbert's method was universally recognized, Gordan himself would say:.

Hilbert continued to make changes in the text and several editions appeared in German.

Hilbert's approach signaled the shift to the modern axiomatic method.

The elements, such as point, line, plane, and others, could be substituted, as Hilbert is reported to have said to Schoenflies and Kotter, by tables, chairs, glasses of beer and other such objects.

Hilbert first enumerates the undefined concepts: point, line, plane, lying on, betweenness, congruence of pairs of points, and congruence of angles.

Hilbert put forth a most influential list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900.

Hilbert'sapproach differed from the later 'foundationalist' Russell–Whitehead or 'encyclopedist' Nicolas Bourbaki, and from his contemporary Giuseppe Peano.

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In 1920, Hilbert proposed a research project in metamathematics that became known as Hilbert's program.

Hilbert published his views on the foundations of mathematics in the 2-volume work, Grundlagen der Mathematik.

Hilbert's work had started logic on this course of clarification; the need to understand Godel's work then led to the development of recursion theory and then mathematical logic as an autonomous discipline in the 1930s.

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.

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.

In 1912, three years after his friend's death, Hilbert turned his focus to the subject almost exclusively.

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.

Additionally, Hilbert's work anticipated and assisted several advances in the mathematical formulation of quantum mechanics.

Hilbert'swork 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 Schrodinger's wave equation, and his namesake Hilbert space plays an important part in quantum theory.

Hilbert said "Physics is too hard for physicists", implying that the necessary mathematics was generally beyond them; the Courant-Hilbert book made it easier for them.

Hilbert unified the field of algebraic number theory with his 1897 treatise Zahlbericht .

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