In his revolutionary paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I,” Gödel introduced his Incompleteness Theorem, which "showed that even powerful logical systems could not hope to encompass the full scope of mathematical truth." Gödel showed that, for any axiomatic system powerful enough to describe the natural numbers 1: If the system is consistent, then it cannot be complete, and 2: the consistency of the axioms cannot be proven within the system. Just a year earlier, Gödel had published “Die Vollständigkeit der Axiome des logischen Funktionenkalküls,” a concise version of his 1929 doctoral thesis, in which he gave the first proof of his Completeness theorem, showing that the axiomatic system of logic is complete.

Known in English as "On formally Undecidable Propositions in Principia Mathematica and Related Systems I," and "The Completeness of the Axioms of the Functional Calculus of Logic" the papers had an enormous impact on the fields of mathematics, computer science, and philosophy. Von Neumann said of them: “Kurt Gödels' achievement in modern logic is singular and monumental. Indeed it is more than a monument, it is a landmark which will remain visible far in space and time. The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement." (Halmos)

At this stage in his life, Feynman had no need to work out Gödel's proof for himself, so was likely preparing to explain to proof to his students; one of the several annotations in the book made by Feynman includes the underlined of the sentence "Gödel showed (i) how to construct an arithmetical formula G that represents the meta-mathematical statement: 'The formula G is not demonstrable'"  noting in the margin "This is the hard part. All the rest of the steps are easy and evident."

Kurt Gödel, along with Feynman's co-Nobelist Julian Schwinger, was the first of only 13 recipients of the Albert Einstein Award. Feynman was the third recipient.