Despite the allusion in the title to the well-known tale by Hans Christian Andersen, the almost four hundred well-written and finely illustrated pages of Catherine Jami's wonderful new book were obviously not composed to suggest that the Kangxi Emperor (b. 1654, r. 1662–1722) was foolish enough to believe in imaginary garments. To the contrary, Jami shows him to be a shrewd and canny monarch who carefully assessed the form and function of the mathematical wardrobe he acquired during his long reign. By placing the Manchu ruler at center stage, Jami opens an original and rich perspective on the history of the first phase of Western learning in China (approx. 1600–1750), a much-debated subject. The book shows how Kangxi's intense involvement with the mathematical sciences fit into his strategy for legitimizing Manchu authority over the Han Chinese intellectual elite. Jami follows the emperor from his ascent to power in 1669, when at the tender age of fifteen he overthrew his regents, to the publication of the Yuzhi lüli yuanyuan (Imperially composed treatise on the origins of pitchpipes and the calendar), the large compendium of mathematics, astronomy, and musical theory that Kangxi commissioned and that appeared posthumously in 1723.

The body of the book starts with an overview of the relevant background events of the late Ming and the reign of Kangxi's predecessor. After this valuable synthesis of scholarship, Jami introduces the emperor in his first act as ruler, restoring the use of Western astronomical methods at the Astronomical Bureau and appointing the Flemish Jesuit Ferdinand Verbiest (1623–88) as Administrator of the Calendar and Director of the Chinese Section of the bureau. These game-changing events took place after European astronomers bested their Chinese rivals in predicting the expected length of a gnomon shadow at midday, and they inspired Kangxi's lifelong interest in mathematical methods. He started to take intensive lessons, choosing his teachers from among the Jesuits residing in Beijing. Jami reveals in vivid detail how these lessons took shape, with the Jesuits tailoring the material to the imperial tastes and drafting carefully edited lecture notes. As has now become clear, these notes, annotated with Kangxi's vermillion ink, subsequently served as the basis for the Shuli jingyun (Essence of numbers and their principles), the mathematical portion of the Yuzhi lüli yuanyuan. Here, as throughout the entire book, Jami's description draws on the full wealth of available sources, including those that have surfaced only during the past few decades. These include Jesuit accounts in various languages, held by various European libraries, correspondence in Manchu between Kangxi and his sons, and renderings in Chinese of the emperor's doings by observers in his entourage. One particularly unforgettable example of the intimate insights these sources provide, reconstructed from three different extant accounts, is the Emperor's visit to the Southern Observatory in Nanjing and his pointed interrogation of the Chinese officials there present in order to show the inadequacy of their astronomical knowledge (a passage not suitable for readers with a fear of examinations).

Jami shows a superb mastery of these diverse sources in her well-ordered and efficiently annotated text. In the midst of a culturally heterogeneous and politically tense constellation of personalities, the emperor is shown using his mathematical knowledge as a tool for establishing his authority. His strategy also took the form of keeping this knowledge hidden within the Forbidden City, invisible to all but a select few. Not until the appearance of the Shuli jingyun were these new mathematical clothes displayed in full view, whereupon they set the dress code for the next century and a half. Thereafter, further interactions with Western learning had to wait until the mid-nineteenth century. The limits that this tight imperial control imposed on the transmission of knowledge are exemplified by the unsuccessful attempts by Jean-François Foucquet (1665–1741) first to introduce modern symbolic algebra and then to introduce an updated version of contemporary European astronomy. The former was barred because the emperor did not approve of it; the latter because Foucquet's fellow Jesuits objected to the idea of representing astronomy as a field of knowledge in progress. Although an older generation of positivistic scholarship might characterize this as an example of “failed transmission,” Jami commendably steers clear of imposing any value-biased interpretative framework on this intercultural circulation of knowledge. Instead, she lets the source texts speak for themselves, while supporting them with subtle interpretation and elucidation of terminology. Characteristic of this “show don't tell”' approach is her insightful choice to highlight the role of calculation and methods of calculation, rather than to emphasize geometry as previous accounts have done. It is arguably in the field of calculation that the encounter with Western learning led to the most interesting interactions, of which Jami gives several examples.

To conclude, Jami has produced a work of scholarly haute couture that is probably an almost definitive account of this first phase of the circulation of Western learning in China. The book is also highly recommended to those with a more general interest in the late Ming and early Qing periods, and to those interested in the transmission of scientific knowledge and its intercultural manifestations. Jami has done an exemplary job in making the book optimally accessible to a wide readership, and the amount of mathematical background needed to appreciate the arguments is kept to a minimum.