Modern (19th century) geometry

I recently completed an M.SC. degree in maths with the U.K. Open University. This was done as a bit of fun on retirement and as a challenge and to “scratch an itch”.

One module of the course was a dissertation on a chosen topic in mathematics. I chose the history of modern geometry partly because I knew so little of projective or non-Euclidean geometry, but also because non-Euclidean geometry is essential to the theory of general relativity.

“Modern” geometry describes two branches of geometry that were both essentially developed during the first half of the 19’th century. Naturally there have been many developments since and some significant earlier work but the bulk of the relevant publications all appeared between 1820 and 1860.

The dissertation is entitled “The Significance of Projective and Non-Euclidean Geometry by 1910”. That meant that I could not refer to any work published after 1910, such as Einstein’s theory of general relativity (1915). Some of the references have publication dates later than 1910 but in essentially all cases these are later reprints of papers that were originally published before 1910. The two notable exceptions to this are the books by Pesic (2007) and Stillwell (1996) which are collections and recent translations of earlier papers.