“Fifty years ago Kurt Gödel… proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics.”

Source: Infinite in All Directions (1988), Ch. 3 : Manchester and Athens
Context: Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. … I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.

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Freeman Dyson 90
theoretical physicist and mathematician 1923

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Gödel demonstrated that every logical scheme, including mathematics, is dependent upon axioms that it cannot prove and that cannot be reduced to the scheme itself. In an elegant mathematical proof, introduced to the world by the great mathematician and computer scientist John von Neumann in September 1930, Gödel demonstrated that mathematics was intrinsically incomplete. Gödel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle. It was one of the famously paranoid Gödel's more reasonable fears. As the economist Steven Landsberg, an academic atheist, put it, "Mathematics is the only faith-based science that can prove it."

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