Full Idea
Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics.
Gist of Idea
Reducing real numbers to rationals suggested arithmetic as the foundation of maths
Source
Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1)
Book Reference
Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.5
A Reaction
The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist.
Related Idea
Idea 10572 A cut between rational numbers creates and defines an irrational number [Dedekind]