Is there evidence that Gödel said "phoned with God"?

Question

Wolfgang Rautenberg wrote in "A Concise Introduction to Mathematical Logic" that Kurt Gödel, to show that finite sequences from ℕ can be coded and manipulated by purely arithmetical formulae, "phoned with God", and attributes this claim to Andrzej Mostowski. I have been unable to find any other source that makes this exact claim. Did Gödel really say something like this to Mostowski?

Answer 1

I have not been able to locate the passage in Rautenberg's book in which the episode is reported (EDIT: is in Chapter 6.4 "The Representability Theorem" on page 243), however a similar anecdote (but without the reference to the problem it refers to) is given in O życiu i działalności Andrzeja Mostowskiego [On the Life and Work of Andrzej Mostowski] by Stanisław Krajewski and Marian Srebrny, Wiadomosci matematyczne, Annales Societatis Mathematicae Polonae XXII.1 (1979), pp. 53–64. An English traslation (with some updates) of this paper is On the Life and Work of Andrzej Mostowski (1913–1975) in Seventy Years of Foundational Studies: A Tribute to Andrzej Mostowski A. Ehrenfeucht, V.W. Marek and M. Srebrny (2007):

However, the classes on applied mathematics turned out to be “horribly boring”[*] mainly due to the paucity of the mathematical means that were being used. And so, Mostowski abandoned this field – as it later turned out – forever. What aroused his interest were the classes of George Pólya and the seminar of Paul Bernays. Additionally, Mostowski was lucky to have the opportunity of listening to the lectures of the greatest masters: Kurt Gödel’s (in Vienna) on the consistency of the axiom of choice, Herman Weyl’s on symmetry and Wolfgang Pauli’s on physics (both in Zürich). He always spoke of Gödel with utmost respect as of a genius. He once said that Gödel knows the solutions of the most difficult problems – as if he had a direct phone line to God. In reference to Weyl, Mostowski’s attitude towards him can be best exemplified by the fact that for years Weyl’s portrait hung on the wall of the Professor’s office, on the ninth floor (room 908) of the Palace of Culture and Science in Warsaw, as the sole decoration.

Krajewski reports the same story in Kurt Gódel i jego dzieło, Wiadomości Matematyczne XXIII, 2 (1981):

Postać Godła owiewa legenda obrazująca jego genialność. Dobrym jej przykładem jest powiedzenie A. Mostowskiego, który chodził na seminarium Godła w Wiedniu: „Gódel miał taką znajomość problemów, którymi się zajmował — a były to przecież najtrudniejsze kwestie w podstawach matematyki! — jakby miał bezpośredni telefon do Pana Boga”.

i.e.

The figure of the Gödel is shrouded in legend illustrating its genius. A good example of it is the saying of A. Mostowski, who attended Gödel's seminar in Vienna: "Gödel had such familiarity with the problems he dealt with - and these were, after all, the most difficult questions in the foundations of mathematics! - as if he had a direct phone call to the Lord God".

Clearly, the problem lies in identifying the source of the story reported by Krajewski, but fortunately these are indicated in the first cited article:

The information included in this article has been taken from the following sources. Firstly, from the existing publications on the life and scientific output of Andrzej Mostowski. They are listed at the end of this text. The article by S. Hartman, which presents the profile of Mostowski, is of particular interest. We have also used the outline of the biography of A. Mostowski prepared by A. Śródka for the Archive of the Polish Academy of Sciences. The second source of data which we have used is the personal files and other documents of Andrzej Mostowski that have been found in the files of the University of Warsaw and the Institute of Mathematics of the Polish Academy of Sciences. The third – the oral information provided by various people and our own memories.

The paper of Hartman is S. Hartman, Andrzej Mostowski, Matematyka 2 (1976), pp. 67–70, but I'm unable to find it online; while the reference to Śródka is probably to Andrzej Stefan Śródka who wrote the Uczeni Polscy XIX-XX stulecia (a biographical dictionary of Polish scholars of the 19th and 20th centuries).

From the above, it seems that it was not actually Gödel who claimed to be in telephone contact with God, but that it was instead Mostowki's consideration that Gödel's genius suggested that he was in direct contact with God.

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For what it is worth, my impression is that instead the story comes from orally reported anecdotes. Curiously, Henk Barendregt in Keys to two intimacies: Mathesis and Mysticism (2015) reports the same tale but referring to Solovay instead of Gödel:

For both experiencing mathematics and mysticism one only can create the right conditions, the rest is ---one could say---divine grace. In this way one describes it in many traditions of mysticism. But this parlance is also in vogue among mathematicians. Thus spoke Polish logician Andrzej Mostowski with admiration about his American colleague Robert Solovay: "He must have a direct phone line to God." So far the personal keys to mentioned subjects.

Therefore, assuming that Barendregt reports the episode correctly, this reinforces the idea that it is rather a figure of speech of Mostowski who, speaking of a mathematician of genius, such as Godel and Solovay, in order to emphasise the naturalness with which they solved the most difficult problems, imagined that they 'were on the phone with God'.

_{[*]: “horribly boring” is a quote form J. N. Crossley (ed.), Algebra and Logic, Lecture Notes in Mathematics 450, Springer, 1975, p. 45.}