Editing David Hilbert (section)

==Life==

===Early life and education===
Hilbert, the first of two children and only son of Otto, a county judge, and Maria Therese Hilbert ([[née]] Erdtmann), the daughter of a merchant, 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, Kaliningrad Oblast|Znamensk]]) near Königsberg where his father worked at the time of his birth. His paternal grandfather was David Hilbert, a judge and ''[[Geheimrat]]''. His mother Maria had an interest in philosophy, astronomy and [[prime number]]s, while his father Otto taught him [[Prussian virtues]]. After his father became a city judge, the family moved to Königsberg. David's sister, Elise, was born when he was six. He began his schooling aged eight, two years later than the usual starting age.<ref>{{Harvnb|Reid|1996|pp=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA1 1–3]}}; also on [https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA8 p.&nbsp;8], Reid notes that there is some ambiguity as to exactly where Hilbert was born. Hilbert himself stated that he was born in Königsberg.</ref>

In late 1872, Hilbert entered the [[Friedrichskolleg]] [[Gymnasium (school)|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 [[Wilhelmsgymnasium (Königsberg)|Wilhelm Gymnasium]].{{Sfn|Reid|1996|p=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA4 4–7]}} 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),{{Sfn|Reid|1996|p=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA11 11]}} returned to Königsberg and entered the university. Hilbert developed a lifelong friendship with the shy, gifted Minkowski.{{Sfn|Reid|1996|p=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA12 12]}}<ref>{{citation|first=Hermann|last=Weyl|title=Levels of Infinity/Selected writings on Mathematics and Philosophy|chapter=David Hilbert and his Mathematical Work|page=94|year=2012|publisher=Dover|editor= Peter Pesic|isbn=978-0-486-48903-2}}</ref>

===Career===
{{Multiple image| image1 = David Hilbert 1886.jpg| image2 = David Hilbert, 1907.jpg| caption2 = Hilbert in 1907| caption1 = Hilbert in 1886| direction = horizontal| align = left| total_width = 390}}
In 1884, [[Adolf Hurwitz]] arrived from Göttingen as an [[Professor|Extraordinarius]] (i.e., an associate professor)<!--at the Albertina in 1884-->. 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]],<ref name="Lindemann"/> titled ''Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen'' ("On the invariant properties of special [[binary quantic|binary forms]], in particular the [[Spherical harmonics|spherical harmonic functions"]]).

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.<ref>{{citation|first=Jeff|last=Suzuki|title=Mathematics in Historical Context|year=2009|publisher=Mathematical Association of America|isbn=978-0-88385-570-6|page=342|url=https://books.google.com/books?id=lew5IC5piCwC&q=gottingen+mathematics&pg=PA342}}</ref> He remained there for the rest of his life.

[[File:Mathematik Göttingen.jpg|thumb|right|The Mathematical Institute in Göttingen. Its new building, constructed with funds from the [[Rockefeller Foundation]], was opened by Hilbert and Courant in 1930.]]

===Göttingen school===
Among Hilbert's students were [[Hermann Weyl]], [[chess]] champion [[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 (mathematician)|Felix Bernstein]] (1901), [[Hermann Weyl]] (1908), [[Richard Courant]] (1910), [[Erich Hecke]] (1910), [[Hugo Steinhaus]] (1911), and [[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 | access-date=7 July 2007}}</ref> Between 1902 and 1939 Hilbert was editor of the ''[[Mathematische Annalen]]'', the leading mathematical journal of the time. He was elected an International Member of the United States [[National Academy of Sciences]] in 1907.<ref>{{Cite web |title=David Hilbert |url=http://www.nasonline.org/member-directory/deceased-members/20001326.html |access-date=30 June 2023 |website=www.nasonline.org}}</ref>

===Personal life===
[[File:ConstantinCaratheodory KatheHilbert MFO633.jpg|thumb|Käthe Hilbert with [[Constantin Carathéodory]], before 1932]]
{{Multiple image| image1 = David Hilbert and Käthe Jerosch.png| image2 = FranzHilbert MFO.jpg| caption2 = Franz Hilbert| caption1 = Hilbert and his wife Käthe Jerosch (1892)| direction = horizontal| align = left| total_width = 370}}
In 1892, Hilbert married Käthe Jerosch (1864–1945), who was the daughter of a Königsberg merchant, "an outspoken young lady with an independence of mind that matched [Hilbert's]."{{Sfn|Reid|1996|p=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA36 36]}} While at Königsberg, they had their one child, Franz Hilbert (1893–1969).
Franz suffered throughout his life from mental illness, and after he was admitted into a psychiatric clinic, Hilbert said, "From now on, I must consider myself as not having a son." His attitude toward Franz brought Käthe considerable sorrow.{{Sfn|Reid|1996|p=[https://books.google.com/books?id=mR4SdJGD7tEC&pg=PA139 139]}}

Hilbert considered the mathematician [[Hermann Minkowski]] to be his "best and truest friend".{{Sfn|Reid|1996|p=121}}

Hilbert was baptized and raised a [[Calvinist]] in the [[Prussian Union of churches|Prussian Evangelical Church]].<ref group=lower-alpha>The Hilberts had, by this time, left the Calvinist Protestant church in which they had been baptized and married. – Reid 1996, p.91</ref> He later left the Church and became an [[agnostic]].<ref name=hilbertagnostic group=lower-alpha>
David Hilbert seemed to be agnostic and had nothing to do with theology proper or even religion. Constance Reid tells a story on the subject:<blockquote>The Hilberts had by this time [around 1902] left the Reformed Protestant Church in which they had been baptized and married. It was told in Göttingen that when [David Hilbert's son] Franz had started to school he could not answer the question, "What religion are you?" (1970, p.&nbsp;91)</blockquote> In the 1927 Hamburg address, Hilbert asserted: "mathematics is pre-suppositionless science (die Mathematik ist eine voraussetzungslose Wissenschaft)" and "to found it I do not need a good God ([z]u ihrer Begründung brauche ich weder den lieben Gott)" (1928, S. 85; van Heijenoort, 1967, p.&nbsp;479). However, from Mathematische Probleme (1900) to Naturerkennen und Logik (1930) he placed his quasi-religious faith in the human spirit and in the power of pure thought with its beloved child– mathematics. He was deeply convinced that every mathematical problem could be solved by pure reason: in both mathematics and any part of natural science (through mathematics) there was "no ignorabimus" (Hilbert, 1900, S. 262; 1930, S. 963; Ewald, 1996, pp. 1102, 1165). That is why finding an inner absolute grounding for mathematics turned into Hilbert's life-work. He never gave up this position, and it is symbolic that his words "wir müssen wissen, wir werden wissen" ("we must know, we shall know") from his 1930 Königsberg address were engraved on his tombstone. Here, we meet a ghost of departed theology (to modify George Berkeley's words), for to absolutize human cognition means to identify it tacitly with a divine one. —{{cite journal
 | last = Shaposhnikov  | first = Vladislav
 | year = 2016
 | title = Theological Underpinnings of the Modern Philosophy of Mathematics. Part II: The Quest for Autonomous Foundations
 | journal = Studies in Logic, Grammar and Rhetoric
 | volume = 44  | issue = 1  | pages = 147–168
 | doi = 10.1515/slgr-2016-0009  | doi-access = free
}}
</ref> He also argued that mathematical truth was independent of the existence of God or other ''[[A priori and a posteriori|a priori]]'' assumptions.<ref group=lower-alpha>"Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs." David Hilbert, ''Die Grundlagen der Mathematik'', [http://people.cs.uchicago.edu/~odonnell/OData/Courses/22C:096/Lecture_notes/Hilbert_program.html Hilbert's program, 22C:096, University of Iowa].</ref><ref group=lower-alpha>{{cite book|title=Science, Worldviews and Education|year=2009|publisher=Springer|isbn=978-90-481-2779-5|page=129|author=Michael R. Matthews|quote=As is well known, Hilbert rejected Leopold Kronecker's God for the solution of the problem of the foundations of mathematics.}}</ref> When [[Galileo Galilei]] was criticized for failing to stand up for his convictions on the [[Heliocentric theory]], Hilbert objected: "But [Galileo] was not an idiot. Only an idiot could believe that scientific truth needs martyrdom; that may be necessary in religion, but scientific results prove themselves in due time."<ref group=lower-alpha>{{cite book |author1=Constance Reid |author2=Hermann Weyl |title=Hilbert |url=https://archive.org/details/hilbert0000reid_e2z0 |url-access=registration |date=1970 |publisher=Springer-Verlag |isbn=978-0-387-04999-1 |page=[https://archive.org/details/hilbert0000reid_e2z0/page/92 92] |quote=Perhaps the guests would be discussing Galileo's trial and someone would blame Galileo for failing to stand up for his convictions. "But he was not an idiot," Hilbert would object. "Only an idiot could believe that scientific truth needs martyrdom; that may be necessary in religion, but scientific results prove themselves in due time."}}</ref>

===Later years===
Like [[Albert Einstein]], Hilbert had closest contacts with the [[Berlin Circle|Berlin Group]], whose leading founders had studied under Hilbert in Göttingen ([[Kurt Grelling]], [[Hans Reichenbach]], and [[Walter Dubislav]]).<ref>{{cite book|first1=Nikolay|last1=Milkov|first2=Volker|last2=Peckhaus|chapter=The Berlin Group and the Vienna Circle: Affinities and Divergences |url=https://philpapers.org/archive/MILTBG-2.pdf |archive-url=https://web.archive.org/web/20140820161819/http://philpapers.org/archive/MILTBG-2.pdf |archive-date=2014-08-20 |url-status=live|page=20|date=2013-01-01 |doi=10.1007/978-94-007-5485-0_1|title=The Berlin Group and the Philosophy of Logical Empiricism|access-date=2021-05-19 |series=Boston Studies un the Philosophy and History of Science|volume=273|isbn=978-94-007-5485-0|oclc=7325392474}}</ref>

Around 1925, Hilbert developed [[pernicious anemia]], a then-untreatable vitamin deficiency of which the 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".<ref>{{cite book |date=1992-10-01 |first2=Andrew |last2=Szanton |first1=Eugene P. |last1=Wigner |title=The Recollections of Eugene P. Wigner |publisher=Plenum |isbn=0-306-44326-0 }}</ref>

Hilbert was elected to the [[American Philosophical Society]] in 1932.<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=David+Hilbert&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2023-06-30 |website=search.amphilsoc.org}}</ref>

Hilbert lived to see the [[Law for the Restoration of the Professional Civil Service|Nazis purge]] many of the prominent faculty members at [[Georg August University of Göttingen|University of Göttingen]] in 1933.<ref>{{cite web |first=Steve |last=Tappan |url=http://www.atomicheritage.org/index.php/component/content/167.html?task=view |title="Shame" at Göttingen| access-date=2013-06-05 | archive-date=2013-11-05 | archive-url=https://web.archive.org/web/20131105154634/http://www.atomicheritage.org/index.php/component/content/167.html?task=view| url-status=dead}} (Hilbert's colleagues exiled)</ref> 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]]''<ref>{{cite journal
	| url = https://www.nature.com/articles/136126a0
	| title = abstract for Grundlagen der Mathematik
	| last = Milne-Thomson
	| first = L
	| date = 1935
	| journal = Nature
	| volume = 136
	| issue = 3430
	| pages = 126–127
	| doi = 10.1038/136126a0
	| s2cid = 4122792
	| access-date = 2023-12-15
	| quote = This is probably the most important book on mathematical foundations that has appeared since Whitehead and Russell's "Principia Mathematica".
}}

</ref> (which eventually appeared in two volumes, in 1934 and 1939). This was a sequel to the Hilbert–[[Wilhelm Ackermann|Ackermann]] book ''[[Principles of Mathematical Logic]]'' (1928). Hermann Weyl's successor was [[Helmut Hasse]].{{fact|date=May 2025}}

About a year later, Hilbert attended a banquet and was seated next to the new Minister of Education, [[Bernhard Rust]]. Rust asked whether "the Mathematical Institute really suffered so much because of the departure of the [[Jews]]". Hilbert replied: "Suffered? It doesn't exist any longer, does it?"<ref>{{cite book |first=Eckart |last=Menzler-Trott |title=Gentzens Problem. Mathematische Logik im nationalsozialistischen Deutschland. |publisher=Birkhäuser |date=2001 |isbn=3-764-36574-9 |location=Auflage |page=142 }}</ref><ref>{{cite book |first=Hajo G. |last=Meyer |title=Tragisches Schicksal. Das deutsche Judentum und die Wirkung historischer Kräfte: Eine Übung in angewandter Geschichtsphilosophie |publisher=Frank & Timme |date=2008 |isbn=3-865-96174-6 |page=202 }}</ref>

===Death===
[[File:Göttingen Stadtfriedhof Grab David Hilbert.jpg|thumb|Hilbert's grave:<br />''Wir müssen wissen<br />Wir werden wissen'']]
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.{{Sfn|Reid|1996|p=213}} News of his death only became known to the wider world several months after he died.{{Sfn|Reid|1996|p=214}}

The epitaph on his tombstone in Göttingen consists of the famous lines he spoke at the conclusion of his retirement address to the Society of German Scientists and Physicians on 8 September 1930. The words were given in response to the Latin maxim: "''[[Ignoramus et ignorabimus]]''" or "We do not know and we shall not know":{{Sfn|Reid|1996|p=192}}

{{verse translation|lang=ger|
Wir müssen wissen.
Wir werden wissen.
|
We must know.
We shall know.
}}

The day before Hilbert pronounced these phrases at the 1930 annual meeting of the Society of German Scientists and Physicians, [[Kurt Gödel]]—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.<ref group=lower-alpha>
"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 knowledge 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.&nbsp;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 in October 1930 to the Vienna Academy of Sciences by [[Hans Hahn (mathematician)|Hans Hahn]]" (van Heijenoort:592); this abstract and the full paper both appear in van Heijenoort:583ff.</ref> [[Gödel's incompleteness theorems]] show that even [[elementary proof|elementary]] axiomatic systems such as [[Peano arithmetic]] are either self-contradicting or contain logical propositions that are impossible to prove or disprove within that system.