**The Secret Spiritual History of Calculus**In the 17th century Italian mathematician Bonaventura Cavalieri proposed that every plane is composed of an infinite number of lines and every solid of an infinite number of planes. One could use these “indivisibles,” he said, to calculate length, area and volume—an important step on the way to modern integral calculus.

Swiss mathematician Paul Guldin, Cavalieri's contemporary, vehemently disagreed, criticizing indivisibles as illogical. But the men argued for more than purely mathematical reasons.

They were members of two religious orders with similar spellings but very different philosophies: Guldin was a Jesuit and Cavalieri a Jesuat. The former believed in using mathematics to impose a rigid logical structure on a chaotic universe, whereas the latter was more interested in following his intuitions to understand the world in all its complexity.

http://www.scientificamerican.com/article/the-secret-spiritual-history-of-calculus/