Felix Klein

The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity and split into diverse branches.

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus as well as analytical geometry.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

Projective geometry has opened up for us with the greatest facility new territories in our science and has rightly been called the royal road to our particular field of knowledge.