They refuse to relate outward, to take reality for arbiter. This is the source of their witchery. The American Mathematical Monthly , v. 101, no. 9, November, 1994. Steinmetz, Charles P. Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions.
All mathematical truths are relative, conditional.
It is customary to sneer at Kepler for this. Stewart, Ian The successes of the differential equation paradigm were impressive and extensive. Many problems, including basic and important ones, led to equations that could be solved. A process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could. The Mathematics of Chaos.