In 1932, David Hilbert and Stefan Cohn-Vossen authored an unusual book entitled “Anschauliche Geometrie” (literally: descriptive, or intuitive geometry), which was later translated by P. Nemenyi in 1952 as “Geometry and the Imagination”.Nemenyi is presumably also responsible for the title of the English translation. I’m a bit frustrated not to be able to decide if P. Nemenyi is Paul Nemenyi or his son Peter. MathSciNet implies that it is the former; however, it is a fact that he died in 1952 and the book is not mentioned in his obituary (incidentally, Paul Nemenyi is thought to be the biological father of Chess champion Bobby Fischer, but that’s not mentioned in his obituary either). Coxeter, reviewing the English translation, wrote that
This excellent translation by Dr. Nemenyi may help to restore interest in geometry, a subject that seems lately to have lost favor in America.
Of the original book, Coxeter said that it
has been a classic for twenty years . . . Although it deals with elementary topics, it reaches the fringe of our knowledge in many directions.
and that it contained
an extraordinarily high concentration of interesting ideas and information.
Photo of a display at the University of Gottingen of lecture drafts by W. Rosemann from Hilbert’s course in 1920/21 on the subject of “Anschauliche Geometrie”. The book of Hilbert and Cohn-Vossen was adapted from these drafts.
In the very(?) late 80′s, Peter Doyle, John Conway, Jane Gilman and Bill Thurston taught an introductory course on geometry at Princeton, using “Geometry and the Imagination” as the title of the course. An expanded version of this course was taught at the Geometry Center in 1991; notes from the course are still available. The “philosophical statement” at the start of these notes includes the following inspiring thought:
Imagination, an essential part of mathematics, means not only the facility which is imaginative, but also the facility which calls to mind and manipulates mental images. One aim of the course is to develop the imagination.
My intention in writing this blog is to try to follow in the steps of H-CV-D-C-G-T in a new medium, and to explore geometry through examples, through ideas, and through images (mental or otherwise). Geometry is a method and a philosophy, but it is in addition a psychological attitude, and this blog aims to celebrate geometry in all its aspects, both as a science and as one of the humanities.