In 2002, Crowe gave a talk[1] summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000.

Chapter four is on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait as an advocate of Quaternions and James Clerk Maxwell as a critic of Quaternions); the fifth chapter describes the development of the modern system of vector analysis by Josiah Willard Gibbs and Oliver Heaviside.

In chapter six, "Struggle for existence", Michael J. Crowe delves into the zeitgeist that pruned down quaternion theory into vector analysis on three-dimensional space.

He makes clear the ambition of this effort by considering five major texts as well as a couple dozen articles authored by participants in "The Great Vector Debate".

Stanley Goldberg[3] wrote "The polemics on both sides make very rich reading, especially when they are spiced with the sarcastic wit of a Heaviside, and the fervent, almost religious railing of a Tait."

In 2003 Sandro Caparrini challenged Crowe’s conclusions by noting that "geometrical representations of forces and velocities by means of directed line segments...was already fairly well known by the middle of the eighteenth century" in his essay "Early Theories of Vectors".