One way to divide people on mathematics is to separate those who see it as a technology (have problem -> apply mathematics -> problem is solved) from those who see it as a way of interpreting the world (eg, the stock market /is/ a set of correlated random variables, adding things to a heap /is/ addition, geometry /is/ how the world fits together).
Usually there isn't a huge amount of difference between these competing philosophies, but it really rears its head in probability and statistics where a huge amount of damage is done, eg, p-value-hacking by people who think statistics is a technology rather than a perspective.
Usually there isn't a huge amount of difference between these competing philosophies, but it really rears its head in probability and statistics where a huge amount of damage is done, eg, p-value-hacking by people who think statistics is a technology rather than a perspective.