i would disagree that math problems only have one strategy for getting to the answer. there are many things, particularly in more abstract math, which can be understood in multiple different ways. the first example that comes to mind is the fundamental theorem of algebra. you can prove it using complex analysis, algebraic topology, or abstract algebra. all the proofs are quite different and rely on deep results from different fields of math.

i think the same thing holds in the less abstract areas of math, it’s just that people are often only taught one strategy for solving a problem and so they believe that’s all there is.