A deeper intuition

Something of the luxurious freedom and naive license of the heroic past [of mathematics] may have been curtailed by the close analysis of thoughtlessly inherited intuitions of space and number…In bringing these assumptions to the surface, where they could be seen by anybody, the abstractionists and the topologists did not uproot intuition, to let it wither like a noxious weed on the rubbish heap of the past, but nourished and strengthened it—”in general.” If curves and surfaces became somewhat more complicated than the geometers and analysts of the nineteenth century had imagined them, the new definitions did not preclude what was consistent in the old; they merely attempted to clarify it and make it explicit…In short, a deeper intuition broadened and deepened a shallower. It justified itself as mathematics which its practitioners and others found even more interesting than some of the classical geometry and analysis of the past.

—Eric Temple Bell, The Development of Mathematics