Tracing the roots of mathematics, this fascinating survey covers the ancient beginnings and subsequent branches of growth in this rich, diverse, and rapidly expanding scientific field, with discussions that progress from the theoretical mathematics in ancient Mesopotamia and Egypt to the emergence of higher analysis mathematics in the late seventeenth century. Well-documented, it presents both established and promising emerging theses, with careful consideration throughout to the remappings, redivisions, and renarrations presented by each new body of historians. Reflects on the nature and roots of mathematics, and a look at some of our more important historiographical issues. Considers mathematics before civilization, with examinations of the Neolithic Revolution and writing and metrology in ancient Sumer, and tracks the science from proto- to theoretical mathematics. Provides a broad survey of mathematics progression in the Islamic world, Latin West, and Maya America from the Middle Ages to 1500, and contain discussions on such topics as the age of absolutism, the culture of science, inventions of differential and fluxional calculus, as well as algebra, number theory, and probability.