Thinking Conceptually Versus Thinking In Abstract Mathematical Symbols
Most human beings think almost entirely conceptually. The vast majority of human beings rarely if ever use abstract mathematical symbols to think, and then only in specialized contexts. A "cat" is a concept: a special kind of "animal," another concept, distinguishable from, for example, a "dog," yet another concept. Many things that scientists and engineers deal with are concepts: particle accelerators, rockets, airplanes, electrons, cancer, and so forth. In only a few special cases, such as simple geometrical forms like the perfect sphere, can we express the concept in purely symbolic mathematical terms that can be programmed on a computer.
-- John F. McGowan
Quoted on Wed Jun 22nd, 2011