Mathematics and Education Studies

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.

I hope we still have some bright twelve-year-olds who are interested in science. We must be careful not to discourage our twelve-year-olds by making them waste the best years of their lives on preparing for examinations.

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