Despite what it might look like, this is not a pop math book. Judging by the terminology that goes undefined, its intended audience excludes not just the intelligent layman but also the non-specialist mathematician. It focuses very much on the proper allocation of credit for the invention of proof theory.

Von Plato certainly doesn't pull any punches. For example, on page 174, we read that "the comments of Hao Wang to the contrary . . . reveal an embarrassing ignorance of intuitionistic logic", while on page 196 von Plato says: "The paper is on the whole a testimony to Hilbert's modest level of sophistication in purely logical questions."

At least to some degree, the book seems to have been cobbled together from von Plato's research articles. The fact that the book doesn't quite read as one coherent work is evidenced by the apparent introduction of topics in the middle of the book that have already been discussed. For example, on page 177 we read of "what is usually called the 'double negation shift'" and again on page 274 we read of "what today is called "double-negation shift'". As another example, on page 234 von Plato says: "Predicate logic is the logical language that forms the basis of the formalization of such parts of mathematics as arithmetic and elementary geometry" even though he'd been talking about predicate logic for the last couple hundred pages already.

Kudos to Princeton University Press for the sewn binding and the buckram cover. This puts them among the last handful of publishers who still seem to care about the physical quality of their books. ( )