Page 158 - Textos de Matemática Vol. 40

146 Appendix
Hilbert appointed Paul Bernays (1888–1977) as his main collaborator in the area of foundations of mathematics, G¨ottingen also attracted researchers in the emerging field of mathematical logic. Among them there were the four main figures in the development of functional self-application: Moses Scho¨nfinkel, Haskell Curry, Alonzo Church, and Johann von Neumann.
Combinatory logic was first presented by Moses Scho¨nfinkel in the Ma- thematische Gesellschaft in G¨ottingen. He worked in G¨ottingen from 1914 to 1924, but we are not aware of information which would tell us the exact pur- pose of his stay.43 But we know that Scho¨nfinkel, together with Bernays, elaborated the official lecture notes of Hilbert’s course Probleme der math- ematischen Logik (Problems of mathematical logic) [Hil20].44 Although this course does not contain any reference to self-application, it is conceivable that Sch¨onfinkel had to consult the lecture notes of 1905 in course of the preparation of the notes of 1920.
Haskell Curry started to study the theory of combinators independently from Scho¨nfinkel while formalizing substitution.45 However, when he came across Scho¨nfinkel’s paper [Sch24] in 1928 he went to G¨ottingen to prepare his Ph.D. in Germany. Curry worked in Hilbert’s group under the supervision of Bernays, but, according to the university regulations, Hilbert was the official supervisor of his thesis.46 Even if it is hard to judge, how close the personal contact of Curry and Hilbert was,47 there is small trace in Curry’s book on combinatory logic. In a historical remark about the Y combinator he writes, [CF58, p. 185]: “[...] the idea that the Russell paradox (and some others) could be formulated in combinatory terms go[es] back to the early days of our subject (cf. [FPF], p. 373, which was essentially contained in Curry’s letter of December, 1929, to Hilbert, [...]).”48 Such a letter is not preserved in Hilbert’s Nachlaß, but it shows that Hilbert was the first addressee in this matter, a matter which,
43In general, we have only very bare information about Sch¨onfinkel. What seems to be known may be found in [Thi95b, Thi96] and at the beginning of §3 of [CH0x]. It is worth mentioning that the famous photograph of him which is reprinted in [Bar84, p. 2] is a cut-out of a photograph of the Mathematische Gesellschaft taken at Hilbert’s 60th birthday in 1922, cf. [Rei70, p. 238]. In 1924, in his publication [Sch24], Moskau (Moscow) is mentioned as his residence. From a short biography of Haskell Curry by Jonathan Seldin we learn that in 1928 “Alexander reported that Scho¨nfinkel was in a mental hospital and was unlikely to continue his work on combinators” [Sel80a, p. viii]. According to S. A. Yanovskaya [Yan48] “Scho¨nfinkel became mentally ill and died in Moscow in 1942” [Kli51, p. 47].
44The cover page of [Hil20] shows the initial “N.” instead of “M.” which is an obvious misprint.
45See the item of May 20th, 1922 in the collection of “Works of Haskell Curry” available at http://www.sadl.uleth.ca, [Sel0x, footnote 11].
46Cf. [Sel0x, Section 2.2].
47Kurt Schu¨tte (1909–1998), the last formal doctoral student of Hilbert in 1933, was, for instance, completely supervised by Bernays. Schu¨tte told the author once that he met Hilbert personally only twice in his life: at the preliminary discussion of his doctoral examination and at this examination itself.
48The reference [FPF] is [Cur36]. The letter seems to be the same, to which Curry refers later including the date [CF58, p. 273]: “In a letter to Hilbert dated December 19, 1929, [...].”