Mathematics

Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

“It’s magic,” the chief cook concluded, in awe.
“No, not magic,” the ship’s doctor replied. “It’s much more. It’s mathematics.”