In the late summer of 1893, following the Congress of Mathematicians
held in Chicago, Felix Klein gave two weeks of lectures on the current
state of mathematics. Rather than offering a universal perspective,
Klein presented his personal view of the most important topics of the
time. It is remarkable how most of the topics continue to be important
today. Originally published in 1893 and re-published by the AMS in 1911,
this work is once again in print with this new edition. Klein begins by
highlighting the works of Clebsch and of Lie. In particular, he
discusses Clebsch's work on Abelian functions and compares his approach
to the theory with Riemann's more geometrical point of view. Klein
devotes two lectures to Sophus Lie, focussing on his contributions to
geometry, including sphere geometry and contact geometry. Klein's
ability to connect different mathematical disciplines clearly comes
through in his lectures on mathematical developments. For instance, he
discusses recent progress in non-Euclidean geometry by emphasizing the
connections to projective geometry and the role of transformation
groups.
