Jacqueline Stedall's The Greate Invention of Algebra puts us all in her debt. The meat of this book is a careful edition of all the pages of Thomas Harriot's mathematical notes that have to do with algebra. To understand why this is important, we have to go into a bit of detail about Harriot's contributions to algebra.
Most of what we know about Harriot's algebra goes back to a book called Artis Analyticae Praxis ("The Practice of the Analytic Art"). This was published in 1631, ten years after Harriot's death. This was edited by Walter Warner, despite Harriot's wish that Nathaniel Torporley be the editor. Here is how Stedall describes Warner and his work: "Warner was not previously known as a mathematician, and never understood Harriot's work as well as Torporley did. Instead of editing the manuscripts as they stood, he chose to select and reorder the material... In doing so he not only destroyed the coherence of Harriot's treatise but made it appear considerably less sophisticated than in fact it was."
Thus, up to now, historians had to either use a corrupt edition of Harriot's work or to consult the actual papers (thousands of pages of papers!) and select out the algebraic portions. This is what Stedall has done for us: as she says, this book "offers, for the first time since 1632, a complete version of Harriot's Treatise on Equations."
Well, as "complete" as possible. The book contains a translation of all of the pages containing Harriot's notes for the planned Treatise. There is not a whole lot of connective tissue (in fact, there isn't very much text at all). But it is quite possible to make sense of Harriot's material, and therefore it is now possible to have a fairer measure of what Harriot actually did. (One can find Stedall's own estimate of Harriot's contribution in her book A Discourse Concerning Algebra: English algebra to 1685, to be reviewed soon on MAA Online. Stedall is an author to watch: I understand her edition of the Arithmetica Infinitorum of John Wallis is also forthcoming.).
The upshot is that this is a book that should be in any library that tries to have a complete set of historical source material.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He is fanatic about number theory, the history of mathematics, Christian theology, poetry, science fiction, comic books, politics, classics, and football (the real thing, not the American version).