German mathematician, one of the most influential of the late nineteenth and early twentieth centuries, working chiefly at Gottingen. At the 1900 International Congress of Mathematicians in Paris he presented a list of twenty three unsolved problems that shaped mathematical research across the following century; Fermat's Last Theorem and the Riemann Hypothesis both appear on it. He championed formalism, the view that mathematics is fundamentally the manipulation of formal symbol systems by explicit rules, and proposed Hilbert's program to place all of mathematics on a finite, provably consistent axiomatic foundation, a project Godel's 1931 incompleteness theorems showed could not succeed in its original, most literal form.
Facts
BirthplaceKonigsberg, Kingdom of Prussia 2 Death PlaceGottingen, Nazi Germany 2 Nationality / Culture Defining ContributionThe 1900 list of 23 problems that shaped twentieth century mathematics; Hilbert spaces, foundational to functional analysis; the formalist program for the foundations of mathematics. 3 Notable WorkMathematische Probleme (1900, the 23 problems address); Grundlagen der Geometrie (1899) 3 Connections
Associated With
David Hilbert described the curve in 1891, refining Giuseppe Peano's 1890 space-filling curve.
Source Hilbert Curve (Wikipedia)
Source MacTutor History of Mathematics Archive
Courant was Hilbert's assistant at Gottingen and took his 1910 doctorate under Hilbert's supervision; the two later co-authored Methods of Mathematical Physics.
Source Richard Courant (1888-1972), Biography (MacTutor History of Mathematics, University of St Andrews)
Source MacTutor History of Mathematics Archive
Attributed Works
Source Formal System (Wikipedia)
Source Hilbert Cube (Wikipedia)
Source Hilbert Curve (Wikipedia)
Source Hilbert's Paradox of the Grand Hotel (Wikipedia)
Source Ring, Mathematics (Wikipedia)
In Branch
Source The Stanford Encyclopedia of Philosophy
Source The Stanford Encyclopedia of Philosophy
Source The Stanford Encyclopedia of Philosophy
Mentored
Source Hermann Weyl (Wikipedia)
Namesake Of
Proofs Credited
Source Entscheidungsproblem (Wikipedia)
Source Hilbert's irreducibility theorem, Wikipedia
Source Hilbert-Speiser theorem (Wikipedia)
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Sources
1. David Hilbert (Wikipedia)
Article text, pronouns he and hisQuote, Article text, pronouns he and his
He adopted and defended Georg Cantor's set theory and transfinite numbers.
2. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsAssociated With: Logic and Foundations, https://mathshistory.st-andrews.ac.uk/Biographies/Hilbert/
A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms and he analysed their significance.
Associated With: Ring (Abstract Algebra), https://mathshistory.st-andrews.ac.uk/HistTopics/Ring_theory/
the word number ring (Zahlring) or ring is due to Hilbert
View the Source 3. The Stanford Encyclopedia of Philosophy
Center for the Study of Language and Information, Stanford University
Richard Courant (1888-1972), Biography (MacTutor History of Mathematics, University of St Andrews)
MacTutor History of Mathematics, University of St AndrewsAssociated With: Richard CourantView the Source Hilbert Curve (Wikipedia)
Wikimedia Foundation- Associated With: Hilbert Curve
Attributed Works: Hilbert Curve, Lead
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.
View the Source Hermann Weyl (Wikipedia)
Mentored: Hermann Weyl, Infobox, doctoral advisor or academic advisorsQuote, Mentored: Hermann Weyl, Infobox, doctoral advisor or academic advisors
His doctorate was awarded at the University of Göttingen under the supervision of David Hilbert, whom he greatly admired.
Entscheidungsproblem (Wikipedia)
Proofs Credited: Entscheidungsproblem, Lead sentence, attributionQuote, Proofs Credited: Entscheidungsproblem, Lead sentence, attribution
posed by David Hilbert and Wilhelm Ackermann in 1928
Hilbert's Paradox of the Grand Hotel (Wikipedia)
Attributed Works: Hilbert's Paradox of the Grand Hotel, LeadQuote, Attributed Works: Hilbert's Paradox of the Grand Hotel, Lead
The idea was introduced by David Hilbert in a 1924-1925 lecture "Über das Unendliche", and was popularized through George Gamow's 1947 book One Two Three...
Ring, Mathematics (Wikipedia)
Wikimedia FoundationAttributed Works: Ring (Abstract Algebra), Lead sectionQuote, Attributed Works: Ring (Abstract Algebra), Lead section
key contributions by Richard Dedekind, David Hilbert, Abraham Fraenkel, and Emmy Noether
Formal System (Wikipedia)
Wikimedia FoundationAttributed Works: Formal System, Lead sectionQuote, Attributed Works: Formal System, Lead section
In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics.
Hilbert Cube (Wikipedia)
Attributed Works: Hilbert Cube, Lead sectionQuote, Attributed Works: Hilbert Cube, Lead section
the Hilbert cube, named after David Hilbert
Hilbert's irreducibility theorem, Wikipedia
Proofs Credited: Hilbert's Irreducibility Theorem, Lead sectionQuote, Proofs Credited: Hilbert's Irreducibility Theorem, Lead section
conceived by David Hilbert in 1892
Hilbert-Speiser theorem (Wikipedia)
Proofs Credited: Hilbert-Speiser Theorem, LeadQuote, Proofs Credited: Hilbert-Speiser Theorem, Lead
This result was introduced by Hilbert (1897, Satz 132, 1998, theorem 132) in his Zahlbericht and by Speiser (1916, corollary to proposition 8.1).
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