GÖDEL AND THE INCOMPLETE PROOF

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The narrative focuses on the “brilliant, eccentric, unsettlingly precise” Gödel, a figure whom the author, in an introduction, compares to Albert Einstein and Charles Darwin and describes as not only a mathematician, but also a “philosopher of mystery” who found new puzzles in settled certainties. “In any system that’s powerful enough to talk about arithmetic,” Navarro writes, “there will always be true statements that the system can never prove.” As a way to pursue these questions further, the author imagines Gödel journeying to a series of afterworld locations to have conversations with a wide variety of famous artists and thinkers from the past. Gödel talks with fellow philosophers, of course, but he also chats with such figures as painter Jackson Pollock (“‘Logic and paint,’ Pollock mused, ‘both dance around the unknown’”) and even Jesus, whom he asks about the incompleteness at the heart of mathematics: “If I left no room for doubt, then there would be no true faith,” Jesus tells him. “Faith must be chosen.” In each encounter, Gödel doggedly inquires about the nature of belief and certainty and looks into the possibility of quantifying morality and doubt. It’s a familiar but inspired storytelling device, and Navarro uses it skillfully, delicately navigating the dramatics of presenting each conversation and his indefatigable main character’s overarching philosophical quest. Socrates, for instance, asks the protagonist whether one can ever fully grasp truth, and readers are told that Gödel “had always admired [mathematician Blaise] Pascal’s mind, not only for his rigorous approach to mathematical truth but for his willingness to engage with the ineffable.” Philosophical discussion dominates the narrative; as a result, some historical figures end up sounding more alike than they likely would have in real life. This slight shortcoming is a result of the book’s pedagogical nature, but it never entirely blunts the fun.

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