- Menso Folkters, Barnabas Hughes, Roi Wagner, and J. Lennart Breggrenby Victor J. Katz
Eurocentric history has been criticized for several decades, and a "global" approach to the writing of history is now widely encouraged. Victor Katz's first sourcebook The Mathematics of Egypt, Mesopotamia, China, India, and Islam(Princeton, 2007) contributed much to the global history of mathematics. The present volume adopts the same approach, but the scope of the book is defined geographically: it offers a comprehensive history of mathematics in medieval Europe that includes mathematical texts written in Latin, Hebrew, and Arabic. The interaction between Muslims, Jews, and Christians in Europe during the Middle Age promoted the advancement of the sciences, so it is reasonable to present their achievements together. The geographical definition of the scope of the book, however, raised some difficulties. As Victor Katz tells us in the introduction, "as the book developed it became clear that confining the geographical locus to European soil was too restrictive." Consequently, North Africa was included in the title and an appendix on Byzantium was added. Another disadvantage of the geographical definition is that Arabic mathematical texts that were written in the East and those written in the West are divided between the two sourcebooks, although they belong to basically one culture. The chapters on Arabic mathematics in both sourcebooks were edited by Lennart Breggren; it is recommended to read his introduction in the first book before approaching the chapter in second. The two volumes thus illustrate the great advantages of the writing of global history, as well as the "logistic" difficulties associated with it.
The "European Sourcebook" is divided into three chapters: "The Latin Mathematics of Medieval Europe" (divided into two parts: until 1140 and after 1140), "Mathematics in Hebrew in Medieval Europe," and "Mathematics in the Islamic World in Medieval Spain and North Africa." As in the "Eastern Sourcebook," the chapters were separately edited, each by an expert in the relevant field, include separate bibliographies, and with few comparisons or cross-references. In the European scene, however, the three cultures are more [End Page 279]closely related. The book apparently aims not only to offer clever episodes to amuse the mathematicians among the readers, but also to provide a picture of the state of the art for the historians among them. The historians are naturally interested in the channels of transmission of mathematical knowledge, which in some cases are well understood and in others remain unknown. For instance, we know a lot about the translations and distribution of canonical texts such as Euclid's Elementsor Archimedes' Measurement of the Circle, but how a Jewish scholar who lived in Castile in the fourteenth century learned about Hippocrates' squaring of the lunes or Nicomedes' conchoid is still far from clear.
Let me now address more closely the second chapter, which may be of special interest to the readers of Aleph. To date, medieval Hebrew mathematical texts have scarcely been known outside the community of Hebrew readers. General books on the history of mathematics either give a brief mention to a Jewish name in the chapter on Arabic mathematics or, more often, not at all. In the present volume Hebrew mathematics receives a very respectable presentation.
The chapter is cautiously titled "Mathematics in Hebrew"; in the introduction the editor, Roi Wagner, remarks that "the term 'Hebrew mathematics' risks conferring an illusory unity on the corpus presented," whereas in fact "the mathematical works covered in this section are strongly rooted in the non-Hebrew scientific traditions around which they evolved" (p. 224). Hebrew mathematics was indeed strongly dependent on Arabic learning, but still developed its own vocabulary and identity. This mathematical culture is well represented by a good selection of texts. Side by side with the well-known work of established scholars like Bernard R. Goldstein, Tony Lévy, José Luis Mancha, Shlomo Sela, and Shai Simonson, the chapter includes several texts taken from relatively recent dissertations, including those by Naomi Aradi...