Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now that it had been "freed of the Jewish influence". I have seen this quote in several places but it seems to be related as more of an anecdote with no particular reference. Is there any such reference that can serve as evidence for the quote, and if possible with any commentary on the reaction of those present at the banquet to this statement (which was rather inflammatory, given the context)?
The following is how far we get from the direct English and German Wikipedia references. I had a look at the German Wikipedia reference wythagoras pointed out. In D. Nachmansohn, R. Schmidt: Die große Ära der Wissenschaft in Deutschland 1900–1933, 1988, Stuttgart : Wiss. Verl.-Ges., I could only find one reference regarding Hilbert, namely, the Hilbert biography by Constance Reid, which is the reference for the entry on the English Wikipedia as well. Reid's report is a little less detailed than the English Wikipedia:
Sitting next to the Nazis' newly appointed minister of education at a banquet, he was asked, "And how is mathematics in Göttingen now that it has been freed of the Jewish influence?" "Mathematics in Göttingen?" Hilbert repiled. "There is really none any more."
(Page 205 of C. Reid, Hilbert, 2nd printing, 1972 Springer.)
However, Nachmansohn and Schmid seem to have had another reference (or they were exaggerating), because they give a different dialogue which shows a much more offensive Hilbert. Page 55 says:
Bei einer Zusammenkunft in Göttingen im Jahre 1934 fragte ihn der Reichsminister für Wissenschaft Bernhard Rust, wie es seiner Fakultät gehe. Hilbert entgegnete, welche Fakultät er meine. Als Rust sagte, er meine natürlich die Mathematisch-physikalische Fakultät, antwortete Hilbert, daß sie nicht mehr existiere, denn er, Rust, habe sie zerstört, indem er die besten Wissenschaftler fortgejagt habe [...].
(The [...] just says for more details see the Hilbert biography by C. Reid 1970.)
It translates as follows.
In 1934, Hilbert and the Minister of Science, Education and National Culture Bernard Rust met in Göttingen, where Rust asked ihm, how his department was. Hilbert asked what department he meant. When Rust said he certainly meant the Mathematics and Physics Departement, Hilbert replied it wouldn't exist any more, because Rust himself destroyed it by expelling the best scientists.
The major difference is the following. According to Reid, it was Rust who asked not just how the mathematics department was, but how it was "now that it has been freed of the Jewish influence". So here it was Rust who pointed out that there were no Jewish scientists any more, whilst according to Nachmansohn-Schmid, Rust only asked how the mathematics- and physics department was, and Hilbert replied, that there was none any more, and that Rust himself had destroyed it, by expelling the best scientists.
We have two references now. Unfortunately, neither of them gives informations about how the surrounding people (or Rust) reacted, they tell slightly different stories, and both don't give useful further references.
Because of the difference between the dialogues, of which I don't know is more trustworthy, I begin to doubt at least that Hilbert's words were (a German analogue of) "Mathematics in Göttingen? There really is none anymore". I'd like to note that indeed Rust became the Minister of Science, Education and National Culture in 1934, but as a matter of fact, he kept his position; it's just the name of the Ministry that changed.
By the way, certainly, nothing about this story appears in the short biography written by Otto Blumenthal which appeared in the third volume of Hilbert's collected works in 1935. Nevertheless I'm advertising it for those interested in Hilbert's life and work!
In my grandfather book, lately translated from German: Recollections of a Jewish Mathematician in Germany, by Abraham A. Fraenkel, edited by Jiska Cohen-Mansfield, translated by Allison Brown.
Hilbert’s response to a question of Bernhard Rust, the Nazi Reich Minister for Science, Education, and Popular Culture, was typical. At a banquet in 1934 in Göttingen, Rust asked: “Is it really true, Mr. Professor, that your institute suffered so much from the departure of the Jews and their friends?” to which Hilbert replied, in his characteristic East Prussian dialect: “Suffered? No, it hasn’t suffered, Mr. Minister. It simply doesn’t exist anymore!”
It was published originally on 1967.