In the steam-powered mechanical age of the eighteenth and nineteenth centuries, the work of late Georgian and early Victorian mathematicians depended on far more than the properties of number. British mathematicians came to rely on industrialised paper and pen manufacture, railways and mail, and the print industries of the book, disciplinary journal, magazine, and newspaper. Though not always physically present with one another, the characters central to this book - from George Green to William Rowan Hamilton - relied heavily on communication technologies as they developed their theories in consort with colleagues. The letters they exchanged, together with the equations, diagrams, tables, or pictures that filled their manuscripts and publications, were all tangible traces of abstract ideas that extended mathematicians into their social and material environment.