 Hilbert’s lecture and monograph inspired a sharp reaction from his contemporary Gottlob Frege, who found both Hilbert’s understanding of axioms, and his approach to consistency and independence demonstrations, virtually incomprehensible and at any rate seriously flawed. Frege’s reaction is first laid out in his correspondence with Hilbert from December 1899 to September 1900, and subsequently in two series of essays (both entitled “On the Foundations of Geometry”) published in 1903 and 1906. Hilbert was never moved by Frege’s criticisms, and did not respond to them after 1900. Frege, for his part, was never convinced of the reliability of Hilbert’s methods, and held until the end that the latter’s consistency and independence proofs were fatally  flawed.[1] 