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Mathematical Treasure: Dodgson's Defense of Euclid

Frank J. Swetz (Pennsylvania State University)

The latter part of the nineteenth century found British mathematicians embroiled in a heated controversy concerning the content and form of geometry teaching. For hundreds of years Euclidean geometry as set forth by Euclid had been held by the English as the highest standard of school learning. Now, new non-Euclidean geometries had been discovered and projective geometry had increased in importance to emerge as a superset of the Euclidean theory. Further, French innovations in teaching and textbook writing encouraged many mathematicians to compose their own versions of Euclid’s geometry. The traditionalists accused these innovators of “destroying Euclid.” Charles Dodgson (1832-1898) was such a traditionalist and was particularly critical of his colleagues James Wilson and John Playfair. In Euclid and His Modern Rivals (1879), Dodgson stated his case for defending the classical Euclid. For more detailed information on this Victorian mathematical controversy, see Mathematical Visions: The Pursuit of Geometry in Victorian England (1988) by Joan Richards.

In his book, Euclid and his Modern Rivals, Dodgson included a dialogue between Euclid and Minos, a mythological wise man and judge. He concluded this dialogue on the page shown above. Dodgson also wrote Alice's Adventures in Wonderland (1865) and Through the Looking Glass (1872) using the pen name Lewis Carroll.


Richards, Joan, Mathematical Visions: The Pursuit of Geometry in Victorian England, New York: Academic Press, 1988.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.


Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Dodgson's Defense of Euclid," Convergence (October 2013)