In ordinary geometry a surface is conceived as a locus of points; in Lie's geometry it appears as the totality of all the spheres having contact with… - Felix Klein

Next to the elementary transcental functions the elliptic functions are usually regarded as the most important. There is, however, another class for which at least equal importance must be claimed on account of their numerous applications in astronomy and mathematical physics; these are the hypergeometric functions, so called owing to their connecton with Gauss's hypergeometric series.

It has been the final aim of Lie from the beginning to make progress in the theory of differential equations ...

The proof that π is a transcental number will forerver mark an epoch in mathematical science. It gives the final answer to the problem of squaring the circle and settles this vexed question once for all. This problem requires to derive the number π by a finite number of elementary geometrical processes, i.e. with the use of the ruler and compasses alone.