Lewis Carroll's books have delighted children and adults for generations, but behind their exuberant fantasy and delightful nonsense was the mind of a brilliant mathematician. Now his forgotten achievements in the world of numbers are brought to light by acclaimed author and mathematician Robin Wilson. Here he explores the curious imagination of a man whose pioneering work at Oxford University included investigations into voting patterns and tennis seeding, who dreamt up numerical conundrums in bed at night and who filled his writings with problems, paradoxes, puzzles and teasing games of logic. Taking us into a world of mock turtles and maps, gryphons and gravity, Lewis Carroll in Numberland reveals the singular mind of a genius.

Charles Lutwidge 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. Yet, whilst lauded for his work in children's fiction and his pioneering work in the world of Victorian photography, his everyday job was a lecturer in Mathematics at Christ Church, Oxford University. The Mathematical World of Charles L. Dodgson (Lewis Carroll) explores the academic background behind this complex individual, outlining his mathematical life, describing his writings in geometry, algebra, logic, the theory of voting, and recreational mathematics, before going on to discuss his mathematical legacy. This is the first academic work that collects the research on Dodgson's wide-ranging mathematical achievements into a single practical volume. Much material appears here for the first time, such as Dodgson's personal letters and drawings, as well as the results of recent investigations into the life and work of Dodgson. Complementing this are many illustrations, both historical and explanatory, as well as a full mathematical bibliography of Dodgson's mathematical publications.

“A fine mathematical biography.”—John Allen Paulos, New York Times Book Review Just when we thought we knew everything about Lewis Carroll, here comes this “insightful . . . scholarly . . . serious” (John Butcher, American Scientist) biography that will appeal to Alice fans everywhere. Fascinated by the inner life of Charles Lutwidge Dodgson, Robin Wilson, a Carroll scholar and a noted mathematics professor, has produced this revelatory book—filled with more than one hundred striking and often playful illustrations—that examines the many inspirations and sources for Carroll’s fantastical writings, mathematical and otherwise. As Wilson demonstrates, Carroll made significant contributions to subjects as varied as voting patterns and the design of tennis tournaments, in the process creating large numbers of imaginative recreational puzzles based on mathematical ideas. Some images in this ebook have been redacted.

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Following his acclaimed life of Dickens, Robert Douglas-Fairhurst illuminates the tangled history of two lives and two books. Drawing on numerous unpublished sources, he examines in detail the peculiar friendship between the Oxford mathematician Charles Dodgson (Lewis Carroll) and Alice Liddell, the child for whom he invented the Alice stories, and analyzes how this relationship stirred Carroll’s imagination and influenced the creation of Wonderland. It also explains why Alice in Wonderland (1865) and its sequel, Through the Looking-Glass (1871), took on an unstoppable cultural momentum in the Victorian era and why, a century and a half later, they continue to enthrall and delight readers of all ages. The Story of Alice reveals Carroll as both an innovator and a stodgy traditionalist, entrenched in habits and routines. He had a keen double interest in keeping things moving and keeping them just as they are. (In Looking-Glass Land, Alice must run faster and faster just to stay in one place.) Tracing the development of the Alice books from their inception in 1862 to Liddell’s death in 1934, Douglas-Fairhurst also provides a keyhole through which to observe a larger, shifting cultural landscape: the birth of photography, changing definitions of childhood, murky questions about sex and sexuality, and the relationship between Carroll’s books and other works of Victorian literature. In the stormy transition from the Victorian to the modern era, Douglas-Fairhurst shows, Wonderland became a sheltered world apart, where the line between the actual and the possible was continually blurred.

With almost 5 million copies sold 60 years after its original publication, generations of readers have now journeyed with Milo to the Lands Beyond in this beloved classic. Enriched by Jules Feiffer’s splendid illustrations, the wit, wisdom, and wordplay of Norton Juster’s offbeat fantasy are as beguiling as ever. “Comes up bright and new every time I read it . . . it will continue to charm and delight for a very long time yet. And teach us some wisdom, too.” --Phillip Pullman For Milo, everything’s a bore. When a tollbooth mysteriously appears in his room, he drives through only because he’s got nothing better to do. But on the other side, things seem different. Milo visits the Island of Conclusions (you get there by jumping), learns about time from a ticking watchdog named Tock, and even embarks on a quest to rescue Rhyme and Reason. Somewhere along the way, Milo realizes something astonishing. Life is far from dull. In fact, it’s exciting beyond his wildest dreams!

Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.