This viewpoint seems very common among programmers, for some reason. I don't often hear it in other fields. The point of employing someone with a particular s

This viewpoint seems very common among programmers, for some reason. I don't often hear it in other fields. The point of employing someone with a particular skill is that they know that skill, and can demonstrate that they know it. Otherwise, you don't know they'll be able to apply it when needed. Hiring for skills is pointless if you believe any person can pick up any skill sufficiently well on the fly. In many cases, if you lack a skill (mathematical or otherwise), you won't know it's possible, so you won't know to learn it on demand. It's not a tool in your toolbox, so you won't approach a problem knowing it's a feasible strategy. This is why it's so hard to talk to non-programmers about programming. They lack the foundation to know what's easy or hard. I've had managers try to assign me unsolved problems in the field, and sat in meetings where I was told we didn't have the time to fix a bug which could have been fixed in less time than holding that meeting.