Full Idea
The Formalists, led by Hilbert, maintain that arithmetic symbols are merely marks on paper, devoid of meaning, and that arithmetic consists of certain arbitrary rules, like the rules of chess, by which these marks can be manipulated.
Gist of Idea
Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess
Source
Bertrand Russell (My Philosophical Development [1959], Ch.10)
Book Reference
Russell,Bertrand: 'My Philosophical Development' [Routledge 1993], p.82
A Reaction
I just don't believe that maths is arbitrary, and this view pushes me into the arms of the empiricists, who say maths is far more likely to arise from experience than from arbitrary convention. The key to maths is patterns.