It is known that Gödel was obsessed with Leibniz, and apparently he even believed that their was a worldwide conspiracy among academics to suppress Leibniz's works. Does anyone know where this came from?
The OP information probably comes from Wikipedia's article on Characteristica Universalis
"The logician Kurt Gödel, on the other hand, believed that the characteristica universalis was feasible, and that its development would revolutionize mathematical practice (Dawson 1997). He noticed, however, that a detailed treatment of the characteristica was conspicuously absent from Leibniz's publications. It appears that Gödel assembled all of Leibniz's texts mentioning the characteristica, and convinced himself that some sort of systematic and conspiratorial censoring had taken place, a belief that became obsessional. Gödel may have failed to appreciate the magnitude of the task facing the editors of Leibniz's manuscripts..."
Similar language is used in a blog review of Machinamenta. On the other hand, Dawson in Logical Dilemmas does not use the word "obsessed", only "preoccupied". Gödel did have a deep interest in Leibniz's work (as did Husserl, Gödel's another major influence), after all they were both fellow objective idealists and mathematical platonists. Here is Dawson, p.107:
"Equally remarkable is the near absence of library requests for readings in philosophy. In particular, though Menger has attested that Gödel had become deeply involved in the study of Leibniz some years before, he apparently owned only a single work by Leibniz (the Kleinere philosophische Schriften ), and none of Leibniz’s works show up among his request slips from 1935. The one item among them that is of interest is Edmund Husserl’s Vorlesungen zur Phänomenologie des Bewußtseins (Lectures on the Phenomenology of Consciousness)."
As for the anti-Leibniz conspiracy theories, Gödel was partial to such suspicions as early as 1939, according to Dawson, p.137:
"Early in the semester he composed a brief note (1939b) on his consistency proof for the GCH, which he communicated to Veblen for transmission to the National Academy of Sciences; by mid-April he had completed the manuscript for his monograph 1940, in which full details of his set-theoretic results were presented; and in his spare time, according to Menger’s testimony, he indulged his preoccupation with Leibniz, some of whose “important writings . . . [he believed] had not only failed to be published, but . . . [had been] destroyed in manuscript”."
According to Morgenstern, Gödel also studied Leibniz's works very intensely in 1944-45. He was particularly excited about calculus ratiocinator and characteristica universalis, which "would facilitate theoretical mathematics to the same extent as the decimal system of numbers has facilitated numerical computations", and which he believed Leibniz "had developed... to a large extent". He also "found" in Leibniz anticipations of game theory, the paradoxes of set theory ("cloaked in the language of concepts, but exactly the same"), Helmholtz’s resonance theory of hearing, and the conservation of energy law. Morgenstern calls these "fantasies".
Once Gödel took Morgenstern to the Princeton University Library and gathered books and articles that appeared during or shortly after Leibniz’s life containing exact references to his writings, together with the very collections or series to which the references had been made. In some cases neither in the cited pages nor elsewhere was any writing of Leibniz to be found, in other cases the series broke off just before the cited passages, or the volumes containing the cited passages were never published. One can see how someone as preoccupied with Leibniz as Gödel would conclude that he was "systematically sabotaged by his editors". But what really sealed the deal was Gödel's and Morgenstern's experience in 1949 with microfilming Leibniz's manuscripts kept in Hanover:
"Gödel had told Morgenstern that he was eager to curtail his work in physics in order to resume his studies of Leibniz. Leibniz’s manuscripts in Hanover had somehow escaped damage during the war, and Gödel and Morgenstern conceived the idea of requesting that they be microfilmed for deposition in the Princeton University library. Morgenstern began to look into the matter in May of 1949, but almost immediately his inquiries ran into difficulties that served once again to fuel Gödel’s conspiracy theories.
Problems first arose when Morgenstern attempted to locate a copy of the critical catalog of Leibniz’s manuscripts, prepared early in the century by the editors of the interacademy edition of Leibniz’s works... when Morgenstern wrote the academy about it, they could offer no clue as to its whereabouts. Subsequent inquiries to the Smithsonian Institution and the Library of Congress proved equally fruitless, and in the end the mystery of the catalog’s disappearance never was explained."
This was only the beginning, more problems arose with access to the manuscripts, the microfilming machinery, etc., and the endeavor went nowhere. Only in 1953 did Schrecker finally succeed, and the microfilms were deposited at the University of Pennsylvania library.