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Full Idea
Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist.
Gist of Idea
No scientific explanation would collapse if mathematical objects were shown not to exist
Source
Charles Chihara (A Structural Account of Mathematics [2004], 09.1)
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.236
A Reaction
It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either.