### Lewis Carroll in Numberland, by Robin Wilson

, or for a student of the mathemagical art.

To most people, Lewis Carroll is nothing but an author of childrens' books and a photographer of ill repute. Nothing could be further from the truth. He was also Charles Lutwidge Dodgson, an eminent mathematician at Oxford, with most of his work being in geometry and matrix algebra. He spent much of his time teaching undergraduates, but also children in various schools around Oxford and private pupils, and published at least as much serious work as he did fiction and nonsense. It is said that after Queen Victoria read "Alice's Adventures in Wonderland", she was so charmed that she demanded that she be sent a copy of his next book. And duly, she received "An Elementary Treatise on Determinants, With Their Application to Simultaneous Linear Equations and Algebraic Equations" and was not amused.

Much of his mathematical work, being pedagogical, is now out of date and sometimes even wrong. For example, much of his energy was spent on teaching Euclid to undergraduates, material that is these days covered at A-level in a completely different way, and he was so opposed to the study of non-Euclidean geometries as to waste time writing against them. But that doesn't detract from the fact that he was a great teacher of mathematics, to students at all levels from young children to the most learnèd.

Of his works that are still relevant, his two-part "Symbolic Logic" appears (from its description in this short biography) to be worth looking at, for his method of figuring out syllogisms through diagrams, and how he expanded his diagrams to deal with showing the interactions of any number of sets, where Venn diagrams break down at six sets. In 1884 he published what is now an obscure work on psephology, "The Principles of Parliamentary Representation" in which he considers what it means for an election to be fair, and methods to achieve this in reality. I'm very pleased to say that he comes to the same conclusion that I did: large multi-member constituencies with some form of proportional representation within each constituency. And related to this, and driven by his interest in tennis, he analysed whether the traditional knockout style of tournament was a good way of ranking players by ability (it isn't: consider what happens if the best and second-best players meet in the first round) and published under his Carroll pen-name a pamphlet with the delightful title of "Lawn Tennis Tournaments: The True Method of Assigning Prizes with a Proof of the Fallacy of the Present Method" whose recommendations have not, unfortunately, been taken up. It is an interesting "what-if" to imagine whether they would have been if he had published it under the name of Dodgson and the effect this would have on knock-out tournaments in all manner of sports.

I would have liked to see a bit more space given in this biography to all three of those subjects, even bearing in mind that a biography is a book about the man, not about the details of his work. After all, if the author could fit in so much material about puns and mathematical games, he could surely fit in a bit more about those works of Dodgson's that are the most relevant today. I wonder if, perhaps, Wilson was concerned that that would make the book "too technical". If that's the reason, then Shame, Shame!

For those with an interest in mathematics (at any level, from schoolchild to professional), this book is very much worth reading and worth buying. For general readers I hesitate to recommend purchasing it except to Carroll's most ardent fans.