David Hilbert’s Picture and Vision of the Mathematics

Abstract

It has been widely believed that David Hilbert, a precursor of formalism, consid-ered mathematics an ordinary “game of signs”. In this paper, I try to show that Hilbert worked out and applied in his research a cohesive, holistic and organic, as well as universal picture of mathematics (as a supranational discipline) and a vision of its development. This scientific area was supposed to constitute a complex construction, and was perceived by him in an optimistic and humanistic way (it enabled solution to any research problem and fulfilled diverse human needs). External experience (e.g. in the case of geometric pictures) and abstraction of its internal structures (a priori state, mathematical analysis of infinity) are particularly important for this exact science. Mathematics creates a bridge between theory and practice, between thinking and ob-servation.