As a history of algebra in England and Scotland from the early seventeenth century to the mid-eighteenth century, this book considers not only technical algebra but also the personal, philosophical, religious, and institutional factors that affected the introduction, elaboration, and reception of the subject. The first chapter sets the scene for the study by discussing the new algebra that emerged in continental Europe in the sixteenth and early seventeenth centuries. This algebra – which I call “early modern algebra” – included new results (the solutions of the cubic and quartic equations), a new language (the symbolical), an expanded algebraic universe (with negative and, tentatively, imaginary numbers), a new emphasis on analysis as the special method of algebra, and a changing relationship between algebra and geometry. Chapters 2 through 10, the heart of the book, explore British algebra from the introduction of early modern algebra into England by William Oughtred and Thomas Harriot in 1631 through the post-Newtonian formulations of algebra by Colin MacLaurin and Nicholas Saunderson.

There is no book-length history of British algebra of the seventeenth and eighteenth centuries. Historians of British mathematics have concentrated on later algebra, since it was Great Britain of the late eighteenth and early nineteenth centuries that produced “symbolical algebra,” in which algebra began to take its modern, abstract form. While the present book centers on what was in itself as exciting and important an era in the development of algebra, it also provides essential background for the study of the emergence of nineteenth-century symbolical algebra.