Full Idea
Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost.
Gist of Idea
The equivalent algebra model of geometry loses some essential spatial meaning
Source
Tyler Burge (Frege on Apriority (with ps) [2000], 4)
Book Reference
Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.384
A Reaction
I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic.