Full Idea
Mathematics cannot proceed analytically, namely by analysis of concepts, but only synthetically.
Gist of Idea
Mathematics cannot proceed just by the analysis of concepts
Source
Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 284)
Book Reference
Kant,Immanuel: 'Prolegomena to Any Future Metaphysic', ed/tr. Lucas,Peter G. [Manchester UP 1971], p.39
A Reaction
I'm with Kant insofar as I take mathematics to be about the world, no matter how rarefied and 'abstract' it may become.
Related Idea
Idea 16916 A priori synthetic knowledge is only of appearances, not of things in themselves [Kant]