Following Gottlob Frege and Bertrand Russell, Hilbert sought to define mathematics logically using the method of formal systems, i.e., finitistic proofs from an agreed-upon set of axioms."A reliable source of Hilbert's axiomatic system, his comments on them and on the foundational "crisis" that was on-going at the time (translated into English), appears as Hilbert's" ‘The Foundations of Mathematics’ (1927).</ref> One of the main goals of Hilbert's program was a finitistic proof of the consistency of the axioms of arithmetic: that is his second problem.