David Hilbert 8302 223121235 2008-07-02T17:45:25Z SpellingBot 6773085 avaliable → available {{Infobox_Scientist | name = David Hilbert | image = Hilbert1912.jpg | image_width = 300px | caption = David Hilbert (1912) | birth_date = {{birth date|1862|1|23|mf=y}} | birth_place = [[Königsberg]] or [[Wehlau]] (today [[Znamensk, Kaliningrad Oblast]]), [[Province of Prussia]] | death_date = {{death date and age|1943|2|14|1862|1|23|mf=y}} | death_place = [[Göttingen]], [[Germany]] | residence = [[Image:Flag of Germany.svg|20px|]] [[Germany]] | nationality = [[Image:Flag of Germany.svg|20px|]] [[Germany|German]] | field = [[Mathematician]] and [[Philosopher]] | work_institutions = [[University of Königsberg]]</br>[[Göttingen University]] | alma_mater = [[University of Königsberg]] | doctoral_advisor = [[Ferdinand von Lindemann]] | doctoral_students = [[Wilhelm Ackermann]]</br>[[Otto Blumenthal]]</br>[[Richard Courant]]</br>[[Max Dehn]]</br>[[Erich Hecke]]</br>[[Hellmuth Kneser]]</br>[[Robert König]]</br>[[Emanuel Lasker]]</br>[[Erhard Schmidt]]</br>[[Hugo Steinhaus]]</br>[[Teiji Takagi]]</br>[[Hermann Weyl]]</br>[[Ernst Zermelo]] | known_for = [[Hilbert's basis theorem]]</br>[[Hilbert's axioms]]</br>[[Hilbert's problems]]</br>[[Hilbert's program]]</br>[[Einstein–Hilbert action]]</br>[[Hilbert space]] | prizes = <!-- (Insert notable prizes and medals) --> | religion = <!-- (Insert religious belief system/affiliation) --> }} '''David Hilbert''' ([[January 23]], [[1862]] &ndash; [[February 14]], [[1943]]) was a [[Germany|German]] [[mathematician]], recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He invented or developed a broad range of fundamental ideas, in [[invariant theory]], the [[Hilbert's axioms|axiomatization of geometry]], and with the notion of [[Hilbert space]],<ref>{{cite web | url = http://www.britannica.com/eb/article-9040439/David-Hilbert | title = David Hilbert | publisher = Encyclopædia Britannica | date = [[2007]] | accessdate = 2007-09-08 }}</ref> one of the foundations of [[functional analysis]]. Hilbert adopted and warmly defended [[Georg Cantor]]'s set theory and [[transfinite]] numbers. A famous example of his leadership in [[mathematics]] is his 1900 presentation of a [[Hilbert's problems|collection of problems]] that set the course for much of the mathematical research of the 20th century. Hilbert and his students supplied significant portions of the mathematical infrastructure required for [[quantum mechanics]] and [[general relativity]]. He is also known as one of the founders of [[proof theory]], [[mathematical logic]] and the distinction between mathematics and [[metamathematics]]. ==Life== Hilbert, the first of two children and only son of Otto and Maria Therese (Erdtmann) Hilbert, was born in either [[Königsberg]] (according to Hilberts own statement) or in Wehlau (today [[Znamensk, Kaliningrad Oblast]])) near Königsberg where his father was occupied at the time of his birth in the [[Province of Prussia]].<ref>Reid 1996, pp. 1–2; also on p. 8, Reid notes that there is some ambiguity of exactly where Hilbert was born. Hilbert himself stated that he was born in Königsberg.</ref> In the fall of 1872 he entered the <!--''Collegium fridericianum''--> Friedrichskolleg [[Gymnasium (school)|Gymnasium]] (the same school that [[Immanuel Kant]] had attended 140 years before), but after an unhappy duration he transferred (fall 1879) to and graduated from (spring 1880) the more science-oriented Wilhelm Gymnasium.<ref>Reid 1996, pp. 4–7.</ref> Upon graduation he enrolled (autumn 1880) at the [[University of Königsberg]], the "Albertina". In the spring of 1882 [[Hermann Minkowski]] (two years younger than Hilbert and also a native of Königsberg but so talented he had graduated early from his gymnasium and gone to Berlin for three semesters),<ref>Reid 1996, p. 11.</ref> returned to Königsberg and entered the university. "Hilbert knew his luck when he saw it. In spite of his father's disapproval, he soon became friends with the shy, gifted Minkowski."<ref>Reid 1996, p. 12.</ref> In 1884 [[Adolf Hurwitz]] arrived from Göttingen as an [[Extraordinarius]], i.e., an associate professor<!--at the Albertina in 1884-->. An intense and fruitful scientific exchange between the three began and especially Minkowski and Hilbert 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 form]]s, in particular the spherical harmonic functions"). Hilbert remained at the University of Königsberg as a professor from 1886 to 1895. In 1892, Hilbert married Käthe Jerosch (1864–1945), "the daughter of a Konigsberg merchant, an outspoken young lady with an independence of mind that matched his own".<ref>Reid 1996, p. 36.</ref> While at Königsberg they had their one child Franz Hilbert (1893–1969). In 1895, as a result of intervention on his behalf by [[Felix Klein]] he obtained the position of Chairman of Mathematics at the [[University of Göttingen]], at that time the best research center for mathematics in the world and where he remained for the rest of his life. His son Franz would suffer his entire life from an (undiagnosed) mental illness, his inferior intellect a terrible disappointment to his father and this tragedy a matter of distress to the mathematicians and students at Göttingen.<ref>Reid 1996, p. 139.</ref> Sadly, Minkowski — Hilbert's "best and truest friend"<ref>Reid 1996, p. 121.</ref> — would die prematurely of a ruptured appendix in 1909. [[Image:Mathematik Göttingen.jpg|thumb|left|300px|Math department in Göttingen where Hilbert worked from 1895 until his retirement in 1930]] ===The Göttingen school=== Among the students of Hilbert, there were [[Hermann Weyl]], the champion of chess [[Emanuel Lasker]], [[Ernst Zermelo]], and [[Carl Gustav Hempel]]. [[John von Neumann]] was his assistant. At the University of Göttingen, 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]]. 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), [[Wilhelm Ackermann]] (1925).<ref>{{cite web|url=http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=7298| title = The Mathematics Genealogy Project - David Hilbert | accessdate=2007-07-07}}</ref> Between 1902 and 1939 Hilbert was editor of the ''[[Mathematische Annalen]]'', the leading mathematical journal of the time. ===Later years=== Hilbert lived to see the [[Nazism|Nazis]] purge many of the prominent faculty members at [[Georg August University of Göttingen|University of Göttingen]], in 1933.<ref>{{citeweb|url=http://www.mphpa.org/index.php?option=com_content&task=view&id=167|title="Shame" at Göttingen}} (Hilbert's colleagues exiled)</ref> Among those forced out were [[Hermann Weyl]], who had taken Hilbert's chair when he retired in 1930, [[Emmy Noether]] and [[Edmund Landau]]. One of those who had to leave Germany was [[Paul Bernays]], Hilbert's collaborator in [[mathematical logic]], and co-author with him of the important book ''Die Grundlagen der Mathematik'' (which eventually appeared in two volumes, in 1934 and 1939). This was a sequel to the Hilbert – [[Wilhelm Ackermann|Ackermann]] book ''[[Principles of Theoretical Logic]]'' from 1928. About a year later, he attended a banquet, and was seated next to the new Minister of Education, [[Bernhard Rust]]. Rust asked, "How is mathematics in Göttingen now that it has been freed of the Jewish influence?" Hilbert replied, "Mathematics in Göttingen? There is really none any more."<ref>Reid 1996, p. 205.</ref> [[Image:HilbertGrab.jpg|thumb|Hilbert's tomb:<br>''Wir müssen wissen<br>Wir werden wissen'']] By the time Hilbert died in 1943, the Nazis had nearly completely restructured the university, many of the former faculty being either 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 fellow mathematician and also a son of the City of Königsberg.<ref>Reid 1996, p. 213.</ref> On his tombstone, at Göttingen, one can read his epitaph, the famous lines he had spoken at the end of his retirement address to the Society of German Scientists and Physicians in the fall of 1930<ref> Reid p. 192</ref>: :''Wir müssen wissen.'' :''Wir werden wissen.'' As translated into English the inscriptions read: : We must know. : We will know. (Ironically, the day before Hilbert pronounced this phrase at the 1930 annual meeting of the Society of German Scientists and Physicians [[Kurt Gödel]]—in a roundtable discussion during the Conference on Epistemology held jointly with the Society meetings—tentatively announced the first expression of his (now-famous) [[incompleteness theorem]].<ref>"The Conference on Epistemology of the Exact Sciences ran for three days, from 5 to 7 September" (Dawson 1997:68). "It ... was held in conjunction with and just before the ninety-first annual meeting of the Society of German Scientists and Physicians ... and the sixth Assembly of German Physicists and Mathematicians.... Gödel's contributed talk took place on Saturday, 6 September [1930], from 3 until 3:20 in the afternoon, and on Sunday the meeting concluded with a round table discussion of the first day's addresses. During the latter event, without warning and almost offhandedly, Gödel quietly announced that "one can even give examples of propositions (and in fact of those of the type of [[Christian Goldbach|Goldbach]] or [[Pierre de Fermat|Fermat]]) that, while contentually true, are unprovable in the formal system of classical mathematics [153]" (Dawson:69) "... As it happened, Hilbert himself was present at Königsberg, though apparently not at the Conference on Epistemology. The day after the roundtable discussion he delivered the opening address before the Society of German Scientists and Physicians -- his famous lecture 'Naturerkennen und Logik" (Logic and the uncovering of nature), at the end of which he declared: 'For the mathematician there is no Ignorabimus, and, in my opinion, not at all for natural science either. ... The true reason why [no one] has succeeded in finding an unsolvable problem is, in my opinion, that there is ''no'' unsolvable problem. In contrast to the foolish Ignorabimus, our credo avers: We must know, We shall know [159]'"(Dawson:71). Gödel's paper was received on November 17, 1930 (cf Reid p. 197, van Heijenoort 1976:592) and published on 25 March 1931 (Dawson 1997:74). But Gödel had given a talk about it beforehand... "An abstract had been presented on October 1930 to the Vienna Academy of Sciences by [[Hans Hahn]]" (van Heijenoort:592); this abstract and the full paper both appear in van Heijenoort:583ff.</ref>, the news of which would make Hilbert "somewhat angry".)<ref>Reid p. 198</ref> ==The finiteness theorem== 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. The attempts to generalize his method to functions with more than two variables failed because of the enormous difficulty of the calculations involved. 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 [[algebraic form|quantic]]s 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]]<ref>Reid 1996, pp. 36–37.</ref> and relied on use of the [[Law of Excluded Middle]] in an infinite extension. Hilbert sent his results to the ''[[Mathematische Annalen]]''. Gordan, the house expert on the theory of invariants for the ''Mathematische Annalen'', was not able to appreciate the revolutionary nature of Hilbert's theorem and rejected the article, criticizing the exposition because it was insufficiently comprehensive. His comment was: :''Das ist nicht Mathematik. Das ist Theologie.'' ::(''This is not Mathematics. This is Theology.'')<ref>Reid 1996, p. 34.</ref> Klein, on the other hand, recognized the importance of the work, and guaranteed that it would be published without any alterations. Encouraged by Klein and by the comments of Gordan, Hilbert in a second article extended his method, providing estimations on the maximum degree of the minimum set of generators, and he sent it once more to the ''Annalen''. After having read the manuscript, Klein wrote to him, saying: :''Without doubt this is the most important work on general algebra that the ''Annalen'' has ever published.''<ref>Rowe, p. 195</ref> Later, after the usefulness of Hilbert's method was universally recognized, Gordan himself would say: :''I have convinced myself that even theology has its merits.''<ref>Reid 1996, p. 37.</ref> For all his successes, the nature of his proof stirred up more trouble than Hilbert could imagine at the time. Although Kronecker had conceded, Hilbert would later respond to others' similar crictisms that "many different constructions are subsumed under one fundamental idea" — in other words (to quote Reid): "Through a proof of existence, Hilbert had been able to obtain a construction"; "the proof" (i.e. the symbols on the page) ''was'' "the object".<ref> Reid 1996, p. 37.</ref> Not all were convinced. While [[Kronecker]] would die soon after, his [[constructivist]] banner would be carried forward in full cry by the young [[Luitzen Egbertus Jan Brouwer|Brouwer]] and his developing [[intuitionist]] "school", much to Hilbert's torment in his later years.<ref>cf. Reid 1996, pp. 148–149.</ref> Indeed Hilbert would lose his "gifted pupil" [[Weyl]] to intuitionism — "Hilbert was disturbed by his former student's fascination with the ideas of Brouwer, which aroused in Hilbert the memory of Kronecker".<ref>Reid 1996, p. 148.</ref> Brouwer the intuitionist in particular raged against the use of the Law of Excluded Middle over infinite sets (as Hilbert had used it). Hilbert would respond: ::" 'Taking the Principle of the Excluded Middle from the mathematician ... is the same as ... prohibiting the boxer the use of his fists.' :"The possible loss did not seem to bother Weyl."<ref>Reid 1996, p. 150.</ref> ==Axiomatization of geometry== {{Main|Hilbert's axioms}} The text ''[[Grundlagen der Geometrie]]'' (tr.: ''Foundations of Geometry'') published by Hilbert in 1899 proposes a formal set, the [[Hilbert's axioms]], substituting the traditional [[Euclid's elements|axioms of Euclid]]. They avoid weaknesses identified in those of [[Euclid]], whose works at the time were still used textbook-fashion. Independently and contemporaneously, a 19-year-old American student named [[Robert Lee Moore]] published an equivalent set of axioms. Some of the axioms coincide, while some of the axioms in Moore's system are theorems in Hilbert's and vice-versa. Hilbert's approach signaled the shift to the modern [[axiomatic method]]. 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 (geometry)|point]], [[line]], [[plane (geometry)|plane]], and others, could be substituted, as Hilbert says, by tables, chairs, glasses of beer and other such objects. It is their defined relationships that are discussed. Hilbert first enumerates the undefined concepts: point, line, plane, lying on (a relation between points and planes), betweenness, congruence of pairs of points, and [[criteria of congruence of angles|congruence]] of [[angle]]s. The axioms unify both the [[plane geometry]] and [[solid geometry]] of Euclid in a single system. ==The 23 Problems== {{main|Hilbert's problems}} He put forth a most influential list of 23 unsolved problems at the [[International Congress of Mathematicians]] in [[Paris]] in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician. After re-working the foundations of classical geometry, Hilbert could have extrapolated to the rest of mathematics. His approach differed, however, from the later 'foundationalist' Russell-Whitehead or 'encyclopedist' [[Nicolas Bourbaki]], and from his contemporary [[Giuseppe Peano]]. The mathematical community as a whole could enlist in problems, which he had identified as crucial aspects of the areas of mathematics he took to be key. The problem set was launched as a talk "The Problems of Mathematics" presented during the course of the Second International Congress of Mathematicians held in Paris. Here is the introduction of the speech that Hilbert gave: :''Who among us would not be happy to lift the veil behind which is hidden the future; to gaze at the coming developments of our science and at the secrets of its development in the centuries to come? What will be the ends toward which the spirit of future generations of mathematicians will tend? What methods, what new facts will the new century reveal in the vast and rich field of mathematical thought?'' He presented fewer than half the problems at the Congress, which were published in the acts of the Congress. In a subsequent publication, he extended the panorama, and arrived at the formulation of the now-canonical 23 Problems of Hilbert. The full text is important, since the exegesis of the questions still can be a matter of inevitable debate, whenever it is asked how many have been solved. Some of these were solved within a short time. Others have been discussed throughout the 20th century, with a few now taken to be unsuitably open-ended to come to closure. Some even continue to this day to remain a challenge for mathematicians. ==Formalism== In an account that had become standard by the mid-century, Hilbert's problem set was also a kind of manifesto, that opened the way for the development of the [[formalism|formalist]] school, one of three major schools of mathematics of the 20th century. According to the formalist, mathematics is a game devoid of meaning in which one plays with symbols devoid of meaning according to formal rules which are agreed upon in advance. It is therefore an autonomous activity of thought. There is, however, room to doubt whether Hilbert's own views were simplistically formalist in this sense. ===Hilbert's program=== 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: #all of mathematics follows from a correctly-chosen finite system of [[axiom]]s; and #that some such axiom system is provably consistent through some means such as the [[epsilon calculus]]. He seems to have had both technical and philosophical reasons for formulating this proposal. It affirmed his dislike of what had become known as the ''[[ignorabimus]]'', still an active issue in his time in German thought, and traced back in that formulation to [[Emil du Bois-Reymond]]. This program is still recognizable in the most popular [[philosophy of mathematics]], where it is usually called ''formalism''. For example, the [[Bourbaki]] group adopted a watered-down and selective version of it as adequate to the requirements of their twin projects of (a) writing encyclopedic foundational works, and (b) supporting the [[axiomatic method]] as a research tool. This approach has been successful and influential in relation with Hilbert's work in algebra and functional analysis, but has failed to engage in the same way with his interests in physics and logic. ===Gödel's work=== Hilbert and the talented mathematicians who worked with him in his enterprise were committed to the project. His attempt to support axiomatized mathematics with definitive principles, which could banish theoretical uncertainties, was however to end in failure. [[Kurt Gödel|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 [[Gödel's incompleteness theorem|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]]. Nevertheless, the subsequent achievements of [[proof theory]] at the very least ''clarified'' consistency as it relates to theories of central concern to mathematicians. Hilbert's work had started logic on this course of clarification; the need to understand Gödel's work then led to the development of [[recursion theory]] and then [[mathematical logic]] as an autonomous discipline in the 1930s. The basis for later [[theoretical computer science]], in [[Alonzo Church]] and [[Alan Turing]] also grew directly out of this 'debate'. ==Functional analysis== Around 1909, Hilbert dedicated himself to the study of differential and [[integral equation]]s; 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 space is the most important single idea in the area of [[functional analysis]] that grew up around it during the 20th century. ==Physics== Until 1912, Hilbert was almost exclusively a "pure" mathematician. When planning a visit from Bonn, where he was immersed in studying physics, his fellow mathematician and friend [[Hermann Minkowski]] joked he had to spend 10 days in quarantine before being able to visit Hilbert. In fact, Minkowski seems responsible for most of Hilbert's physics investigations prior to 1912, including their joint seminar in the subject in 1905. 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.<ref>Reid 1996, p. 129.</ref> He started studying [[Kinetic theory|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|Einstein]] and others were followed closely. Hilbert invited Einstein to Göttingen to deliver a week of lectures in June-July 1915 on general relativity and his developing theory of gravity.<ref> Sauer 1999, Folsing 1998.</ref> The exchange of ideas led to the final form of the field equations of [[General Relativity]], namely the [[Einstein field equations]] and the [[Einstein-Hilbert action]]. In spite of the fact that Einstein and Hilbert never engaged in a public priority dispute, there has been some [[Relativity priority dispute|dispute about the discovery of the field equations]]. 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 [[Schrödinger equation|wave equation]] and his namesake [[Hilbert space]] plays an important part in quantum theory. In 1926 von Neuman 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.<ref> It is of interest to note that in 1926, the year after the matrix mechanics formulation of quantum theory by [[Max Born]] and [[Werner Heisenberg]], the mathematician [[John von Neumann]] became an assistant to David Hilbert at Göttingen. When von Neumann left in 1932, von Neumann’s book on the mathematical foundations of quantum mechanics, based on Hilbert’s mathematics, was published under the title ''Mathematische Grundlagen der Quantenmechanik''. See: Norman Macrae, ''John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More'' (Reprinted by the American Mathematical Society, 1999) and Reid 1996.</ref> Throughout this immersion in physics, Hilbert worked on putting rigor into the mathematics of physics. While highly dependent on higher math, the physicist tended to be "sloppy" with it. To a "pure" mathematician like Hilbert, this was both "ugly" and difficult to understand. As he began to understand the physics and how the physicists were using mathematics, he developed a coherent mathematical theory for what he found, most importantly in the area of [[integral equations]]. When his colleague [[Richard Courant]] wrote the now classic [[Methods of Mathematical Physics]] including some of Hilbert's ideas, he added Hilbert's name as author even though Hilbert had not directly contributed to the writing. 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. ==Number theory == Hilbert unified the field of [[algebraic number theory]] with his 1897 treatise ''Zahlbericht'' (literally "report on numbers"). He disposed of [[Waring's problem]] in the wide sense. He then had little more to publish on the subject; but the emergence of [[Hilbert modular form]]s in the dissertation of a student means his name is further attached to a major area. He made a series of conjectures on [[class field theory]]. The concepts were highly influential, and his own contribution is seen in the names of the [[Hilbert class field]] and the [[Hilbert symbol]] of [[local class field theory]]. Results on them were mostly proved by 1930, after breakthrough work by [[Teiji Takagi]] that established him as Japan's first mathematician of international stature. 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. ==Miscellaneous talks, essays, and contributions== * His [[Hilbert's paradox of the Grand Hotel|paradox of the Grand Hotel]], a meditation on strange properties of the infinite, is often used in popular accounts of infinite [[cardinal number]]s. * His [[Erdős number]] is (at most) 4.<ref>{{cite web|url=http://www.oakland.edu/enp/erdpaths.html|title=Some Famous People with Finite Erdős Numbers}}</ref> * [[Foreign member of the Royal Society]] * He was awarded the second [[Bolyai prize]] in 1910. ==See also== <div class= style="-moz-column-count:3; column-count:3;"> *[[Cayley–Klein–Hilbert metric]] <ref>[http://mathworld.wolfram.com/Cayley-Klein-HilbertMetric.html Wolfram MathWorld – Cayley-Klein-Herbert metric]</ref> *[[Einstein–Hilbert action]] *[[Hilbert class field]] <ref>[http://mathworld.wolfram.com/HilbertClassField.html Wolfram MathWorld – Hilbert class field]</ref> *[[Hilbert C*-module]] *[[Hilbert cube]] *[[Hilbert curve]] *[[Hilbert function]] *[[Hilbert inequality]] <ref>[http://mathworld.wolfram.com/HilbertsInequality.html Wolfram MathWorld – Hilbert inequality]</ref> *[[Hilbert matrix]] *[[Hilbert number]] <ref>[http://mathworld.wolfram.com/HilbertNumber.html Wolfam MathWorld - Hilbert number]</ref> *[[Hilbert polynomial]] *[[Hilbert series]] <ref>[http://mathworld.wolfram.com/HilbertSeries.html Wolfram MathWorld – Hilbert Series]</ref> *[[Hilbert space]] *[[Hilbert spectrum]] *[[Hilbert symbol]] *[[Hilbert transform]] *[[Hilbert's Arithmetic of Ends]] *[[Hilbert's axioms]] *[[Hilbert's basis theorem]] *[[Hilbert’s constants]] <ref>[http://mathworld.wolfram.com/HilbertsConstants.html Wolfram MathWorld – Hilbert’s constants]</ref> *[[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]] *[[Hilbert–Pólya conjecture]] *[[Hilbert–Schmidt operator]] *[[Hilbert–Smith conjecture]] *[[Hilbert–Speiser theorem]] *[[Principles of Theoretical Logic]] *[[Relativity priority dispute]] </div> ==Notes== {{reflist|2}} ==References== ===Primary literature in English translation=== *Ewald, William B., ed., 1996. ''From Kant to Hilbert: A Source Book in the Foundations of Mathematics'', 2 vols. Oxford Uni. Press. **1918. "Axiomatic thought," 1115–14. **1922. "The new grounding of mathematics: First report," 1115–33. **1923. "The logical foundations of mathematics," 1134–47. **1930. "Logic and the knowledge of nature," 1157–65. **1931. "The grounding of elementary number theory," 1148–56. **1904. "On the foundations of logic and arithmetic," 129–38. **1925. "On the infinite," 367–92. **1927. "The foundations of mathematics," with comment by [[Weyl]] and Appendix by [[Bernays]], 464–89. *[[Jean van Heijenoort]], 1967. ''From Frege to Godel: A Source Book in Mathematical Logic, 1879–1931''. Harvard Univ. Press. * {{cite book | title = Geometry and Imagination | author = David Hilbert |coauthors=[[Stephan Cohn-Vossen|Cohn-Vossen, S.]]| year = 1999 | publisher = American Mathematical Society | id = ISBN 0-8218-1998-4}} - an accessible set of lectures originally for the citizens of Göttingen. *{{cite book | title = David Hilbert's Lectures on the foundations of Mathematics and Physics, 1891–1933 | author = David Hilbert |editor= Michael Hallett and Ulrich Majer| year = 2004 | publisher = Springer-Verlag Berlin Heidelberg| id = ISBN 3-540-64373-7}} ===Secondary literature=== *B, Umberto, 2003. ''Il flauto di Hilbert. Storia della matematica''. [[UTET]], ISBN 88-7750-852-3 * Corry, L., Renn, J., and Stachel, J., 1997, "Belated Decision in the Hilbert-Einstein Priority Dispute," ''Science 278'': nn-nn. *Dawson, John W. Jr 1997. ''Logical Dilemmas: The Life and Work of Kurt Gödel''. Wellesley MA: A. K. Peters. ISBN 1-56881-256-6. *Folsing, Albrecht, 1998. ''Albert Einstein''. Penguin. *[[Ivor Grattan-Guinness|Grattan-Guiness, Ivor]], 2000. ''The Search for Mathematical Roots 1870-1940''. Princeton Univ. Press. *Gray, Jeremy, 2000. ''The Hilbert Challenge''. ISBN 0-19-850651-1 *{{cite book | title = From Brouwer to Hilbert, The Debate on the Foundations of Mathematics in the 1920's| first = Paolo |last= Mancosu| year = 1998 | publisher = Oxford Univ. Press| id = ISBN 0-19-509631-2}} *Mehra, Jagdish, 1974. ''Einstein, Hilbert, and the Theory of Gravitation''. Reidel. *[[Piergiorgio Odifreddi]], 2003. ''Divertimento Geometrico - Da Euclide ad Hilbert''. Bollati Boringhieri, ISBN 88-339-5714-4. A clear exposition of the "errors" of Euclid and of the solutions presented in the ''Grundlagen der Geometrie'', with reference to [[non-Euclidean geometry]]. *Reid, Constance, 1996. ''Hilbert'', [[Springer Science and Business Media|Springer]], ISBN 0-387-94674-8. ''The'' biography in English. *{{cite journal | last = Rowe | first = David E. | year = 1989 | title = Klein, Hilbert, and the Gottingen Mathematical Tradition | journal = Osiris | volume = 5 | pages = 186–213 | doi = 10.1086/368687 }} *Sauer, Tilman, 1999, "[http://arxiv.org/abs/physics/9811050 The relativity of discovery: Hilbert's first note on the foundations of physics,]" ''Arch. Hist. Exact Sci.'' 53: 529-75. * Sieg, Wilfried, and Ravaglia, Mark, 2005, "Grundlagen der Mathematik" in [[Ivor Grattan-Guinness|Grattan-Guinness, I.]], ed., ''Landmark Writings in Western Mathematics''. Elsevier: 981-99. (in English) *[[Kip Thorne|Thorne, Kip]], 1995. ''[[Black Holes and Time Warps|Black Holes and Time Warps: Einstein's Outrageous Legacy]]'', W. W. Norton & Company; Reprint edition. ISBN 0-393-31276-3. ==External links== {{wikiquote}} {{commons}} {{portalpar|Logic}} *{{MacTutor Biography|id=Hilbert}} *{{MathGenealogy|id=7298}} *[http://www.ags.uni-sb.de/~cp/p/hilbertbernays/goal.htm Hilbert Bernays Project] *[http://aleph0.clarku.edu/~djoyce/hilbert/problems.html Hilbert's 23 Problems Address] *[http://plato.stanford.edu/entries/hilbert-program/ Hilbert's Program] *{{gutenberg author| id=David+Hilbert | name=David Hilbert}} *[http://math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.mp3 Hilberts radio speech recorded in Königsberg 1930 (in German)], with English [http://math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.pdf translation] *[http://www.gresham.ac.uk/event.asp?PageId=45&EventId=628 'From Hilbert's Problems to the Future'], lecture by Professor Robin Wilson, [[Gresham College]], 27 February 2008 (available in text, audio and video formats). <!-- Metadata: see [[Wikipedia:Persondata]] --> {{Logic}} {{Persondata |NAME= Hilbert., David |ALTERNATIVE NAMES= |SHORT DESCRIPTION= [[Mathematician]] |DATE OF BIRTH= {{birth date|1862|1|23|mf=y}} |PLACE OF BIRTH= [[Königsberg]], [[East Prussia]] |DATE OF DEATH= {{death date|1943|2|14|mf=y}} |PLACE OF DEATH= [[Göttingen]], [[Germany]] }} {{DEFAULTSORT:Hilbert, David}} [[Category:German mathematicians]] [[Category:19th century mathematicians]] [[Category:20th century mathematicians]] [[Category:University of Königsberg alumni]] [[Category:University of Königsberg faculty]] [[Category:University of Göttingen faculty]] [[Category:Relativists]] [[Category:Geometers]] [[Category:Mathematical analysts]] [[Category:Number theorists]] [[Category:Foreign Members of the Royal Society]] [[Category:German Lutherans]] [[Category:People from Königsberg]] [[Category:People from the Province of Prussia]] [[Category:1862 births]] [[Category:1943 deaths]] [[ar:ديفيد هيلبرت]] [[bn:ডেভিড হিলবার্ট]] [[bs:David Hilbert]] [[bg:Давид Хилберт]] [[ca:David Hilbert]] [[cs:David Hilbert]] [[da:David Hilbert]] [[de:David Hilbert]] [[et:David Hilbert]] [[el:Ντάβιντ Χίλμπερτ]] [[es:David Hilbert]] [[eo:David Hilbert]] [[eu:David Hilbert]] [[fa:داوید هیلبرت]] [[fo:David Hilbert]] [[fr:David Hilbert]] [[ko:다비드 힐베르트]] [[hi:डेविड हिल्बर्ट]] [[id:David Hilbert]] [[is:David Hilbert]] [[it:David Hilbert]] [[he:דויד הילברט]] [[ka:დავიდ ჰილბერტი]] [[lv:Dāvids Hilberts]] [[lt:David Hilbert]] [[hu:David Hilbert]] [[nl:David Hilbert]] [[ja:ダフィット・ヒルベルト]] [[no:David Hilbert]] [[pms:David Hilbert]] [[pl:David Hilbert]] [[pt:David Hilbert]] [[ro:David Hilbert]] [[ru:Гильберт, Давид]] [[sa:डेविड हिल्बर्ट]] [[sco:David Hilbert]] [[simple:David Hilbert]] [[sk:David Hilbert]] [[sl:David Hilbert]] [[sr:Давид Хилберт]] [[sh:David Hilbert]] [[fi:David Hilbert]] [[sv:David Hilbert]] [[tl:David Hilbert]] [[th:ดาฟิด ฮิลแบร์ท]] [[vi:David Hilbert]] [[tr:David Hilbert]] [[uk:Гільберт Давид]] [[zh:大卫·希尔伯特]]