We must admit with humility that, while number is purely a product of our mind, space has a reality outside of our mind, so that we cannot prescribe … - Carl Friedrich Gauss

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

But in our opinion truths of this kind should be drawn from notions rather than from notations.

Gauss's aim was always to give his investigations the form of perfect works of art. He would not rest sooner and never gave a piece of work to the public until he had given it the perfection of form he desired for it. A good building should not show its scaffolding when completed, he used to say. In his demonstrations he used almost entirely the synthetic method, which he had come to prize through his studies of Archimedes and Newton. It is distinguished from the analytic method by its brevity and comprehensiveness. But the road leading to the discovery remains veiled; and indeed it often seems that Gauss frequently and intentionally turned aside from the road that led to mere instruction.