Of course the first thing that comes to mind when confronted with the title of this book is John Updike's Rabbit Redux, where the protagonist (anti-hero?) Harry "Rabbit" Angstrom, of Updike's Rabbit Run, is brought back for more. Krantz's choice of this allusion to Updike's famous (or notorious) pair of books hits the target on many levels: choices of words are often charged with levels of meaning (as Updike's main character's pun-laden name already illustrates), the stories pull no punches and deal with topics that once raised many an eyebrow (yes, even mathematicians are involved in sex scandals), and we tend to measure the behavior of the characters populating the pages with our own — Krantz' objectives correspond perfectly. And just as Rabbit is many things, not all laudable by any means, the mathematicians and scientists whose tales Krantz tells are also three-dimensional men and women (or four-dimensional: Einstein makes a lot of appearances), with all the human flaws and foibles. However, in Krantz' book the vast majority of tales are funny rather than tragic: non-serious nonfiction in contradistinction to Updike's serious fiction.
Mathematical Apocrypha Redux should be read right after its predecessor, if one possesses a voracious appetite for stories about mathematicians; if, on the other hand, one prefers small servings every so often, well, both books are still required reading. Comparing the two, it's not inaccurate to say that the quality spectrum of tales in the first book has a higher infimum than that of tales in the second book, but that the suprema are about the same. In fact, already on p. 2 of MARedux a longish anecdote about Donald Knuth hits within epsilon of the sup, so to speak (and let's just say that epsilon is very, very small indeed: this is a terrific tale I'd never heard before!). Another set of wonderful tales (p. 177 ff.) concern none other than Alexandre Grothendieck, including his famous misidentification of 57 as prime; I'd heard the tale with 27 instead… no matter, of course: it's clearly funnier with 57. (There's strong evidence to believe that, presque partout, Grothendieck tales are worth telling and re-telling.)
There are any more examples I could cite, many known to many of us, to differing degrees of trustworthiness, many more obscure, some idiosyncratic, shall we say. I can't imagine a mathematician who wouldn't want to own both of these books.
Michael Berg is Professor of Mathematics at Loyola Marymount University in California.