The Broken God by David Zindell is a sci-fi novel about a universe in which the top ruling class is called "The Order of Mystic Mathematicians and Other Seekers of the Ineffable Flame". They have to go through extreme training in advanced math because they use topology to navigate through the universe using something called the Vild. To my knowledge it is the only work of fiction that uses the term "topology" in its mathematical sense in the first few pages.
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