Full Idea
Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects.
Gist of Idea
Nearly all of mathematics has to quantify over abstract objects
Source
Willard Quine (Word and Object [1960], §55)
Book Reference
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.269
A Reaction
Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually).