Publication of important historical source material is always cause for rejoicing. This is particularly so in the case of the first volume of the Correspondence of John Wallis (1616–1703). I think Wallis has received less attention from the general histories of mathematics than he deserves. Partly, this is because he had the bad luck to have made substantial contributions to analysis and to physics that were later viewed mainly as pointing towards calculus and Newtonian mechanics. (Being a predecessor can be a formula for obscurity…) It may also have something to do with the fact that Wallis worked in so many fields (he did significant work in theology and cryptography, for example, in addition to mathematics). The fact that he had a rather prickly personality and was involved in many controversies (the most famous one being the one with Thomas Hobbes) probably has something to do with it too.
There is no doubt, however, that Wallis was one of the most important mathematicians of his time, and that his works contain a lot of fascinating material. In particular, he was attuned to the history of mathematics, and several of his books contain portions in which he gives historical accounts of the subject. These are notoriously partisan and polemical, but I find them fascinating.
This volume is the first in a series collecting all of Wallis’s letters (in their original languages). The letters have been collected from archives spread throughout Europe, and are presented here with careful textual notes. There are no translations or commentary except for a useful introduction summarizing Wallis’s life and interests. So this is a book for scholars, and its price makes it a book that only libraries (perhaps only the bigger libraries, in fact) are likely to buy. Still, it is good news that the letters are being published. I hope it’ll lead to more work being done on Wallis and his mathematics.
Fernando Q. Gouvêa is professor of mathematics at Colby College in Waterville, ME.