I got out of the library a book with the above title. It is, unsurprisingly, about the famous conjecture made by Henri Poincaré in 1904 and the recent proof by Perelman of that conjecture. The main body of the text is intended for folks who had some geometry in high school and can barely remember it (or words to that effect from the preface). For those of us who want more mathematical depth, it has extensive end notes and a glossary of mathematical terms.

I'm not particularly satisfied with the glossary of mathematical terms. For one thing, there are than many terms, and the definitions are rather shallow. But the biggest thing which caught my eye was some sloppiness -- in a book which repeats the trope about mathematicians being very interested in rigor and correctness.

Here's an example of the sloppiness. In the glossary on page 243 the following terms are defined (in this order): metric, n-space, negative curvature, Poincaré Conjecture, positive curvature, Pythagorean theorem, Ricci flow, Riemann curvature tensor, round sphere, simply connected, and sphere (the first half of the definition, at least). On page 244, it continues with the conclusion of the definition of a sphere, then partial differential equation, postulate, proof, proposition, Ricci flow, surface, tensor, theorem, three-dimensional manifold, three-sphere, three-torus.

Aside from being a somewhat random collection of mathematical terms with some odd definitions (a proposition was defined as a statement derivable from postulates and previously proven propositions, while a theorem was defined as "an especially important proposition"), the alphabetization is horrid; it exists on each page, but not across both pages. At least both definitions of "Ricci flow" appear to be consistent with each other. Not identical, but consistent.

It makes me wonder about the editing in the rest of the book.