Overview

The progress of mathematics from its origins in simple counting to its ability to handle and manipulate variables, unknowns, and changing properties accelerated during the 1600s. Mathematics had from earliest times been a supremely practical science, either for enumerating items (counting) or for establishing the relationships among shapes (geometry). Most ancient mathematics took the form either of simple counting or of geometric measurement. The evolution of mathematics in the 1600s was nothing short of explosive, and the evolution of the equation—and the power of the equation as a tool for solving complex problems of many sorts—lay at the heart of the growth of mathematical capability. Equations are mathematical formulae whose purpose is, at least in principle, simple: equations consist of factors that must be balanced or made equal. By introducing systems for accommodating variables and...