Hilbert agreed. As part of his doctoral examination in 1885 he defended the a priori nature of arithmetical judgments (those, that is, about the natural numbers). Forty-five years later, in the farewell address he gave to his native city of Königsberg, he explained that after the dross had been removed from Kant’s theory, “only that a priori will remain which also is the foundation of pure mathematical knowledge”—a foundation, he said, of intuitive insight.
