Joseph’s original (1991) book was an outstanding publishing event in the unexciting world of history of mathematics when it first appeared. As many readers — myself included — realized, the author had a new case to argue and argued it forcefully. The history of mathematics, he claimed, had been written in a way which systematically underestimated the often considerable contribution of non-European civilizations (preliterate, Egyptian/Mesopotamian, Indian, Chinese, Islamic). Without going into the reasons for this neglect, his book aimed to clarify the extent to which the ‘main stream’ of European mathematics as narrated by the standard histories was indebted to work from elsewhere. Much of his material was new or unfamiliar, and in suggestive diagrams he mapped the ‘classical’ Eurocentric version of mathematical transmission, and new more complex ways in which the interaction between a number of civilizations might have taken place.
In an evaluation of the first edition which Joseph courteously cites, I implied that the battle against Eurocentrism had not yet been won. Nonetheless, both the increasing volume and seriousness of research into non-European mathematics, and the changed tone of its evaluation in modern textbooks such as Katz’s standard work indicate that there has been a substantial change, for which Joseph’s book is in a large part responsible. (Joseph’s examples of the Eurocentric viewpoint are still taken from the work of Morris Kline, which I hope is now largely seen as outdated.) He now offers a substantially enlarged third edition. Have the changes in the text affected the message?
The short answer is no. To be explicit, the new edition differs from the old essentially by the addition of new material, in particular the research of the past twenty years. The author has also added chapter footnotes, which perhaps give the book a more academic air. However, as one might have anticipated, the research has not seriously affected the main thrust of Joseph’s original argument. It is becoming increasingly accepted that ‘mathematics’ cannot be confined in a single definitional framework, and that it has been practiced in widely different ways across cultures; that the classical European deductive model is not the only one; and that cross-fertilization has taken place at different places and times between these traditions. And the research, which is becoming heavily professionalized, has done nothing to contradict Joseph’s main arguments.
A particularly interesting example is the ‘calculus’ as developed by the Kerala mathematicians in the late medieval and early modern period; where the work itself is interesting; it clearly anticipates similar work in Europe two hundred years later; and there has been a great deal of research into a possible chain of transmission from Kerala to Europe. This is a particular interest of Joseph’s, and he discusses it thoroughly in a valuable entirely new section.
This is an excellent reframing of the original work, and I recommend it to new readers and old alike.
Luke Hodgkin is a retired lecturer at King’s College, London, and author of A History of Mathematics: Mesopotamia to Modernity (OUP, 2005).