Final answer:
During the Renaissance, mathematics was revered by intellectuals as both a philosophical framework for understanding the universe and a tool for artistic advancement, influencing significant progress in science and art.
Step-by-step explanation:
Renaissance intellectuals held mathematics in high esteem, considering it a key to understanding the universe's fundamental truths, as well as a tool for artistic innovation. The era's philosophers, particularly the Neoplatonists, believed in the superiority of mathematical thought over sensory observation for gaining knowledge about the world. Galileo inherited this perspective, recognizing that the underlying reality of the world is essentially mathematical, which led to the development of what would later be known as the New Science of Nature.