Editing David Hilbert (section)

===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.