Giuseppe Peano (1858–1932), professor of infinitesimal analysis at Turin and a prolific writer on a wide range of mathematical topics, contributed to the early development of both logicism and the formalism to which it is partly opposed. His first book, published under the name of a former teacher, Angelo Genocchi, was devoted to the calculus and featured a careful, systematic treatment of the subject that contrasted favorably with customary texts in rejecting loosely phrased definitions and theorems and in substituting rigorous proof for appeals to intuition. Peano was particularly insistent that the acceptability of a mathematical proposition should depend not on its intuitive plausibility but on its derivability from stated premises and definitions, and he devised a remarkable illustration of the way in which what appears evident to intuition may nonetheless be contradicted by formally incontrovertible considerations. This is his well-known space-filling curve, introduced in 1890 in the paper "Sur...