(source) 
Felix Klein
(25 Apr 1849  22 Jun 1925)

Science Quotes by Felix Klein (3 quotes)
Every teacher certainly should know something of noneuclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catchwords, is talked about in wide circles, so that any teacher may be asked about it at any moment. ... Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about noneuclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing noneuclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
On the other hand, I should like to advise emphatically against bringing noneuclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
— Felix Klein
The axioms of geometry areaccording to my way of thinkingnot arbitrary, but sensible. statements, which are, in general, induced by space perception and are determined as to their precise content by expediency.
— Felix Klein
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
Quotes by others about Felix Klein (2)
These estimates may well be enhanced by one from F. Klein (18491925), the leading German mathematician of the last quarter of the nineteenth century. Mathematics in general is fundamentally the science of selfevident things. ... If mathematics is indeed the science of selfevident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sensethat of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.
Consciously and systematically Klein sought to enthrall me with the problems of mathematical physics, and to win me over to his conception of these problems as developed it in lecture courses in previous years. I have always regarded Klein as my real teacher only in things mathematical, but also in mathematical physics and in my conception of mechanics.
See also:
 25 Apr  short biography, births, deaths and events on date of Klein's birth.