How did the mysticism get into science?

In the 1500s, when modern science was emerging, for the first 60 years or so most of the major thinkers in the field did not want math involved. (1) Science is empirical, hypothetical, and contingent, whereas math is rationalistic, categorical, and absolute. Put simply, scientific truth can change with new evidence, while at best have experiences that merely suggest mathematical concepts, and those concepts are universal (for instance, the definition of a triangle applies to all triangles). Thus, scientific thinkers of the time felt including math would be adding a mystical element to an otherwise objective pursuit. Even today it remains a mystery how something discovered within the mind can help explain matter, much less help us find previously unknown matter (as in theoretical physics). (2) Did it get accepted simply because it worked?