Euclid and his modern rivals

Lewis Carroll is known all over the world for his Alice books. But he also produced mathematical works under his real name of Charles Dodgson. For this work he uses his pseudonym, and indeed it is a peculiar hybrid of mathematical discussion and nonsense writing. It's written as a play - I very much doubt that it's ever been performed - and criticises the attempts that were being made at the time to dethrone Euclid's Elements from its acceptance as the textbook for the teaching of geometry. Dedicated fans of Lewis Carroll might might be interested in reading it, as well as those interested in his psychological state, but I can't recommend it for general readership.

The book might also serve as an illustration of the resistance to innovation in acacdemic circles. It's difficult to judge whether Carroll's criticisms were justified, since we now live in a different era, but I would suspect that they were the sort of minor faults one can find with any book. It seems that Carroll thought that the way to make a subject more interesting was to add jokes, rather than to structure it in a more understandable way.

One of the most surprising things about the book is that versions of the parallel axiom are discussed at great length, but Carroll seems totally unaware of the invention of non-Euclidean geometries 50 years before. Indeed, the book might be of interest to historians of mathematics, showing the sort of ideas which were circulating concerning the treatment of mathematics via axioms.