Felix Klein Quotes

10 Sourced Quotes

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Felix Klein
Mathematics in general is fundamentally the science of self evident things.

Felix Klein
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 its own particular field of knowledge.

Felix Klein
Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.

Felix Klein
There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which includes the principal group as a sub-group, then the invariant theory of this group gives a definite kind of geometry, and every possible geometry can be obtained in this way.

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

Felix Klein
If the activity of a science can be supplied by a machine, that science cannot amount to much, so it is said; and hence it deserves a subordinate place. The answer to such arguments, however, is that the mathematician, even when he is himself operating with numbers and formulas, is by no means an inferior counterpart of the errorless machine...

Felix Klein
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 of analytical geometry.

Felix Klein
But it should always be required that a mathematical subject not be considered exhausted until it has become intuitively evident.

Felix Klein
It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

Felix Klein