> I don't care about proofs or theoretically problematic corner cases that "real mathematics" seems to be almost exclusively interested in.

That is a rather strange take for a software engineer.

When implementing something I do need to know what the corner cases are, whether the runtime can enter such a state. I need to think how to put in checks so that they cannot be reached, or alternatively, how to recover gracefully. That's my job after all, why would anyone pay me if I didn't.

Perhaps a topical example is a gimbal lock. I need to be aware that it can happen and I need to know how to prevent it.