In what sense is the passage a challenge to medieval views and methods? galileo used mathematics to understand the universe, but scholars of the middle ages believed that knowledge came from god. galileo used books for understanding, while scholars of the middle ages considered the use of books for knowledge to be dangerous. scholars of the middle ages said that one could not understand the universe, while galileo said that this understanding was possible. galileo saw science and philosophy as one and the same, while scholars of the middle ages saw them as two different things?

The answer is: Galileo used mathematics to understand the universe, but scholars of the Middle Ages believed that knowledge came from God.

During that period, scientific knowledge still hasn't been recognized by the majority of the people. The religious teaching that being taught  by the churches during that period was always regarded as a universal truth.

Galileo on the other hand, is one of the few people that was brave enough to challenge the church's authority. Due to his knowledge in Math and astronomy, he managed to disprove the church's narrative that always conveys that Earth is the center of the universe.