The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection problem, the "fifteen" puzzle, the "64" puzzle, doubling the cube, squaring the circle, and perpetual motion machines. The latter problem extends from geometric construction to involve rules of nature. (JBW)