 These longstanding paradigms were destined to be challenged from the sixteenth century onward, both from a speculative and an empirical perspective. Observation of stellae novae and comets condemned the crystalline spheres and raised doubts regarding the doctrine of the immutability of heavens. According to the traditional Aristotelian account, comets were phenomena in the sublunar atmosphere. The great astronomer Johannes Regiomontanus (1436–1476) did not challenge this vision of the cosmos when he calculated the distance of the 1472 comet by considering the angle of parallax, but about a century later, the Jesuit Christopher Clavius (1538–1612), observing a nova (1572), and Tycho Brahe (1546–1601), observing a comet (1577), both demonstrated that the suddenly bright star and the comet must lie beyond the moon, and that therefore the doctrine of the spheres was false. The demonstrated fluidity of heavens also compromised, more crucially, the doctrine of their immutability. Two factors made possible such an achievement: the availability of better measuring instruments, and a stronger emphasis on mathematics. This emphasis on mathematics was probably the most important contribution of Platonism to the development of natural philosophy, and in particular astronomy, during the Renaissance. Though it is true that Neoplatonic philosophers had proposed alternatives to the Peripatetic theories on the heavens (e.g., Marsilio Ficino argued that the heavens were made of spiritus and rejected the division of the universe into spheres), it was their insistence on the importance of geometry and mathematics that opened the way to the quantitative vision of the world which gradually replaced the qualitative paradigm connected to the Aristotelian tradition.