Lowenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Lowenheim's theorem. For example, the very result that scholars attribute to Lowenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Lowenheim--appears to have attributed to him. In The Birth of Model...