Full Idea
In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern.
Gist of Idea
Mathematical constants and quantifiers only exist as locations within structures or patterns
Source
Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1)
Book Reference
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.201
A Reaction
This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns.