Full Idea
We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory.
Gist of Idea
Mathematics divides in two: meaningful finitary statements, and empty idealised statements
Source
David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.174