A mathematician, a real one, one for whom mathematical objects are abstract and exist only in his mind or in some remote Platonic universe, never "sees" a curve. A curve is infinitely narrow and invisible. Yet, we all have "seen" straight lines, circles, parabolas, etc. when many years ago (for some of us) we were taught elementary geometry at school. E. Mach wanted to suppress from physics everything that could not be perceived: physics and metaphysics must not exist together. Many a scientist was deeply influenced by his philosophy. In his book Claude Tricot tells us that a curve has a...