Full Idea
It did not become clear to mathematicians before modern times that they study nothing but hypotheses without as pure mathematicians caring at all how the actual facts may be.
Gist of Idea
We now know that mathematics only studies hypotheses, not facts
Source
Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
Book Reference
Peirce,Charles Sanders: 'Reasoning and the Logic of Things', ed/tr. Ketner,K.L. [Harvard 1992], p.114
A Reaction
'Modern' here is 1898. As a logical principle this would seem to qualify as 'if-thenism' (see alphabetical themes). It's modern descendant might be modal structuralism (see Geoffrey Hellman). It take maths to be hypotheses abstracted from experience.