Mathematician:David Hilbert

Mathematician

One of the most influential mathematicians in the late $19$th and early $20$th century.

Most famous for the Hilbert $23$, a list he delivered in $1900$ of $23$ problems which were at the time still unsolved.

Nationality

German

History

• Born: 23 Jan 1862, Königsberg, Prussia (now Kaliningrad, Russia)
• Died: 14 Feb 1943, Göttingen, Germany

Theorems and Definitions

• Hilbert's Axioms
• Hilbert Class Field
• Hilbert C*-Module
• Hilbert Cube
• Hilbert Curve
• Hilbert's Invariant Integral
• Hilbert Matrix
• Hilbert Metric
• Hilbert Modular Form
• Hilbert Number (Analysis)
• Hilbert Number (Number Theory)
• Hilbert Polynomial (or Hilbert Function)
• Hilbert's Problems (also known as The Hilbert $23$)
• Hilbert's Program
• Hilbert Ring (also known as a Jacobson Ring)

• Hilbert Sequence Space
• Hilbert Space
• Hilbert Spectrum
• Hilbert Symbol

• Hilbert-Poincaré Series (with Henri Poincaré)
• Hilbert-Schmidt Norm (with Erhard Schmidt)
• Hilbert-Schmidt Operator (with Erhard Schmidt)

• Hilbert Inequality
• Hilbert Transform
• Hilbert's Arithmetic of Ends
• Hilbert's Basis Theorem
• Hilbert's Basis Theorem for Finitely Generated Algebras
• Hilbert's Constants
• Hilbert's Irreducibility Theorem
• Hilbert's Nullstellensatz
• Hilbert's Paradox of the Grand Hotel
• Hilbert's Theorem (Differential Geometry)
• Hilbert's Theorem 90
• Hilbert's Syzygy Theorem
• Hilbert-Style Deduction System

• Einstein-Hilbert Action (with Albert Einstein)
• Einstein-Hilbert Equations (with Albert Einstein)
• Hilbert-Pólya Conjecture (with George Pólya)
• Hilbert-Smith Conjecture (with Paul Althaus Smith)
• Hilbert-Speiser Theorem (with Andreas Speiser)
• Hilbert-Waring Theorem (conjectured by Edward Waring in $1770$, proved by Hilbert)
• Riemann-Hilbert Problem (with Bernhard Riemann)

Results named for David Hilbert can be found here.

Definitions of concepts named for David Hilbert can be found here.

Axioms named for David Hilbert can be found here.

Publications

• 1893: Über die Transcendenz der Zahlen e und pi (Math. Ann. Vol. 43: pp. 216 – 219)
• 1894: Ein Beitrag zur Theorie des Legendreschen Polynoms (in which the Hilbert Matrix was introduced)
• 1897: Zahlbericht ("Report on Number Theory")
• 1899: Grundlagen der Geometrie (in which Hilbert's axioms were introduced)
• 1902: Mathematical Problems (Bull. Amer. Math. Soc. Vol. 8, no. 10: pp. 437 – 479) (in which the definition of Hilbert 23 is presented)

(translated by Mary Winston Newson from "Mathematische Probleme")

• 1919 - 1920: Natur und mathematisches Erkennen: Vorlesungen, gehalten
• 1931: Die Grundlegung der elementaren Zahlenlehre (Math. Ann. Vol. 104: pp. 485 – 494) (in which the definition of Hilbert's Program is presented)
• 1934: Grundlagen der Mathematik, Volume 1 (with Paul Bernays)
• 1939: Grundlagen der Mathematik, Volume 2 (with Paul Bernays)

Work in progress.

Notable Quotes

The infinite! No other question has ever moved so profoundly the spirit of man. (1921)

-- Quoted in 1937: Eric Temple Bell: Men of Mathematics: They Say: What Say They? : Let Them Say

Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertrieben können.

(No one can chase us out of the paradise that Cantor has created for us.)

-- Quoted:

in preface to 1999: András Hajnal and Peter Hamburger: Set Theory

in introduction to 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics

Wir müssen wissen, wir werden wissen.

(We must know, we shall know.)

Sources

• John J. O'Connor and Edmund F. Robertson: "David Hilbert": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): They Say: What Say They? : Let Them Say
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hilbert, David (1862-1943)
• 1991: David Wells: Curious and Interesting Geometry ... (previous) ... (next): A Chronological List Of Mathematicians
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Introduction
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hilbert, David (1862-1943)
• 1999: András Hajnal and Peter Hamburger: Set Theory ... (next): Preface
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hilbert, David (1862-1943)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Hilbert, David (1862-1943)