Despite the many attempts, first by John Wallis and then by others, to argue his greatness, Thomas Harriot is usually treated as a significant but minor figure in the history of mathematics. It's likely, in fact, that many mathematicians have never heard of him. This book, which collects ten years of "Thomas Harriot Lectures" given at Oriel College, Oxford, offers us a chance to learn a little more about a very complicated man. Like many Renaissance scholars, Harriot had very broad interests, and the essays collected here reflect that breadth. They discuss Harriot's work as geographer and surveyor during his expedition to Virginia, his natural philosophy, his alchemical experiments, his religion, and yes, his mathematics.
A theme that resonates through all the essays is that Harriot left us a very large number of manuscript pages, many of which consist of nothing but mathematical calculations. Dealing with these unpublished papers is both challenging and dangerous, because it is all too easy for the historian to impose an interpretation on the material. Harriot's work on algebra is perhaps the best example: there are many handwritten pages on algebra in the Harriot papers, and there is also a posthumously published book. Unfortunately, the papers we have do not include a draft of the book, so that determining the relation between the two becomes an exercise in filling in the blanks. It turns out, for example, that the inequality symbols in Harriot's book (which are famous as the first instance of the use of inequality symbols that are somewhat like the modern ones) are not in Harriot's papers (he uses a pair of different symbols). On the other hand, the papers sometimes seem to suggest that Harriot actually understood things better than what is suggested by the book.
The fact that these lectures were given over a ten-year span by scholars with very different interests and points of view means that we see a wide range of opinions (including some strong disagreement) here. This is therefore not a comprehensive account of Harriot, but it may be an interesting place to begin to learn about him.
Fernando Q. Gouvêa (email@example.com) is the editor of FOCUS and MAA Online. He teaches both "History of Mathematics" and "Number Theory", among others, at Colby College. He is a number theorist whose main research focus is on p-adic modular forms and Galois representations.