"A fifteenth century trend toward Platonic and Pythagorean mysticism, accompanying the growth of humanism over... earlier Scholastic philosophy, encouraged the previously denied use of the infinite and infinitesimal in geometry. As a result... mathematics was viewed as independent of the senses, not bound by empirical investigations, and thus free to use the infinitite and infinitesimal, provided that no inconsistencies resulted. By the early seventeenth century this view opened up bold new approaches."