Being a human activity, calculation has a history, even if its operations yield “facts” apparently true in any context. One plus one might always be two, but the methods to arrive at such results, not to mention what they might mean, are another matter. Recent histories involving calculation on this blog include Staffan Müller-Wille and Giuditta Parolini, “Punnett Squares and Hybrid Crosses: How Mendelians Learned Their Trade by the Book”; D. Senthil Babu, “Handbooks of the Mind into Ready Reckoners in Print: The Story of the ‘Encuvati’ in the Nineteenth Century”; and Karine Chemla, “Reading and (Re-)Classifying Canonical Instructions of the Past: Commentaries on ‘The Nine Chapters on Mathematical Procedures’…”
The earliest extant Chinese mathematical writings include two types of components of particular interest for our discussion on manuals and handbooks. On the one hand, there are mathematical problems that often evoke tasks carried out by officials working in the imperial bureaucracy. On the other hand, there are mathematical “procedures,” or “algorithms” in today’s parlance, to solve such problems. This description fits most of the mathematical books composed in China until the seventh century.