Charles Dodgson is best known for his "Alice" books, "Alice's Adventures in Wonderland" and "Through the Looking-Glass", written under his pen-name of Lewis Carroll.
If he hadn't written them, he'd be mainly remembered as a pioneering photographer, one of the first to consider photography as an art rather than as simply a means of recording images. But if Dodgson had not written the Alice books or been a photographer, he might be remembered as a mathematician, the career he held as a lecturer at Christ Church in Oxford University.
But what mathematics did he do? How good a mathematician was he? How influential was his work?
In this illustrated paper, I'll describe his work in geometry, algebra, logic and the mathematics of voting, in the context of his other activities and, on the lighter side, I present some of the puzzles and paradoxes that he delighted in showing to his child-friends and contemporaries.