This is an English translation of the famous speech on geometry and symmetry that Felix Klein prepared — but never actually gave! — upon his appointment to a professorship at Erlangen in 1872.

- Felix Klein, A comparative review of recent researches in geometry, trans. M. W. Haskell,
Bull. New York Math. Soc.2, (1892-1893), 215-249.as a LaTeXed paper in PDF format,

or as a scan of the original article in PDF or DjVu format.

For the original German version, try these:

More recently a translated version has been placed on the arXiv:

- Johan Ernst Mebius, Felix Klein's Erlanger Programm.

- Felix Klein,
Vergleichende Betrachtungen über neuere geometrische Forschungen, Verlag von Andreas Deichert, Erlangen, 1872. Available online at the University of Michigan Historical Mathematics Collection.

- Felix Klein, A comparative review of recent researches in geometry, arXiv:0807.3161.

You can read more about the Erlangen program in Klein's own words here:

Luckily Dover keeps its books in print!

- Felix Klein,
Elementary Mathematics from an Advanced Standpoint: Geometry, part 3: Systematic discussion of geometry and its foundations, Dover, New York, 1939.

For more on the Erlangen program, try these:

For more about Klein, try:

- Garrett Birkhoff and M. K. Bennett, Felix Klein and his "Erlanger Programm", in
History and Philosophy of Modern Mathematics, eds. W. Aspray and P. Kitcher, Minnesota Stud. Philos. Sci. XI, University of Minnesota Press, Minneapolis, 1988, pp. 145-176.

- Hans A. Kastrup, The contributions of Emmy Noether, Felix Klein and Sophus Lie to the modern concept of symmetries in physical systems, in
Symmetries in Physics (1600-1980), ed. M. G. Doncel, World Scientific, Singapore, 1987, pp. 113-163.

- I. M. Yaglom,
Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century, trans. S. Sossinsky, Birkhauser, Boston, 1988.

- MacTutor History of Mathematics Archive, Felix Klein.

I thank Thomas Love for pointing out the existence of Haskell's English translation of Klein's famous speech. I thank Chris Hillman for scanning it in and creating jpg files of each page. These are available below.

I thank Robin Houston for preparing a PDF file of the whole paper using Adam Langley's JBIG2 encoder. If you have an old PDF viewer that doesn't understand JBIG2 files, this PDF file won't work for you.

I thank Lukas-Fabian Moser for preparing a DjVu file of the whole paper.

And, I thank Nitin C. Rughoonauth for carrying out the wonderful step of LaTeXing the paper! There may be some typos — I've seen one so far. If you spot typos, please send me email and I'll fix them. The LaTeX source code is available here. Ronald Brown has created a version with some typos removed, available here in LaTeX and PDF format, but I have not yet had time to review this. It seems to compile correctly using PDFLaTeX but not LaTeX.

© 2011 John Baez

baez@math.removethis.ucr.andthis.edu