Non-Euclidean Quotes (3 quotes)

*Every teacher certainly should know something of non-euclidean geometry*. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, 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 non-euclidean geometry would not make a better impression.

On the other hand, I should like to advise emphatically against bringing non-euclidean 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.

The most suggestive and notable achievement of the last century is the discovery of Non-Euclidean geometry.

We find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsiessuch as Apollonius work on conic sections, or the non-Euclidean geometries, whose practical value became apparent only later.