Exchanges of learning and controversies between engineers and mathematicians were important factors in the development of early modern science. This theme is discussed by focusing, first, on architectural and mathematical dynamism in mid 16th-century Milan. While some engineers-architects referred to Euclid and Vitruvius for improving their education and argued for an institutional reform of their profession, Girolamo Cardano and other mathematicians explained the "De architectura" and studied the inventions of the arts. Attention is drawn, then, to the entrance in the field of hydraulics of Benedetto Castelli, a Galilean mathematician who criticised some basic engineering methods but also relied on engineering experience. This mix of criticism and appropriation of engineering notions was particularly highlighted by Domenico Guglielmini, who saw in the study of the nature of rivers the key for their control and improvement. A further facet was the growing distinction among the practitioners. In 16th-century Milan professional distinctions appeared in a grand scale cadastral survey of the whole state and in the establishment of a professional body of engineers-architects and land surveyors. It was not a peculiarly Italian trend. In the postscript some remarks are added to show that a partly similar differentiation was also taking place among E.G.R. Taylor's mathematical practitioners of Elizabethan England. (Contains 3 figures and 117 footnotes.)