Sometimes that's true: that there's a math way and an engineering-way and the two are fundamentally different.
For example, simply assuming that all 256 bit (genuinely!) random bitstrings will be different from each other is sound engineering, but invalid math. (the engineeer might worry if the bitstrings are *really* genuinely random, though)
If there's 1:2^80 odds that a cosmic ray will strike your hardware and flip a crucial bit, but a 1:2^128 odds that two random strings will collide by accident, the engineer worries most about the first possibility, while the mathematician worries about the second possibility.