Combinatorics: Ancient & Modern

This book offers a comprehensive overview of the history of combinatorics, featuring contributions from experts. It highlights significant developments from ancient times to modern advancements, making the subject accessible to all readers.

Combinatorics: Ancient & Modern is a comprehensive exploration of the history and development of combinatorics, a branch of discrete mathematics focused on permutations, combinations, and the arrangement of sets. This book stands out as the first extensive survey of its kind, bringing together research that is often inaccessible to the general reader. It poses intriguing questions about the origins of well-known concepts, such as who first introduced Pascal's triangle or Hamiltonian graphs, revealing that these figures were not the original creators.

The structure of the book is designed to cater to a diverse audience. It begins with an introduction by Donald E. Knuth, setting the stage for a journey through two millennia of combinatorial thought. The first half of the book delves into early combinatorial work, tracing influences from ancient Indian and Chinese texts to late Renaissance discussions on the arithmetical triangle. The latter half shifts focus to the contributions of renowned mathematicians like Euler, highlighting developments in areas such as partitions, polyhedra, and graph theory throughout the 20th century.

With contributions from sixteen experts, Combinatorics: Ancient & Modern serves multiple purposes. It not only provides a stimulating historical context for combinatorialists but also encourages historians of mathematics to explore this overlooked field further. Additionally, it offers a captivating introduction for general readers, inviting them to engage with a subject that continues to inspire contemporary scholarship.