However, I agree that industry and mathematics are not best friends. That's because mathematicians righteously demand and require a level of freedom and support the industry is not always willing to give because of the social problem it creates with other employees and because the value of the work of a mathematician can be too hard to judge.

From my experience, the fight to get the working conditions you need is not worth it. My advise to fellow mathematicians is that — when you want go into the industry — to go where there are already mathematicians.

At the human layer, one expression of this idea is the principle of least astonishment: "People are part of the system. The design should match the user's experience, expectations, and mental models." (Wikipedia). A system involving people is not efficient if the people are often surprised by its design, implementation, or behavior.

Efficient software solutions also tend to involve elegance. Take Git for example as an improvement over other source control systems. The conceptual primitives that Git is built upon are elegant and recognizing them as the correct basis for source control (along with a strong implementation) resulted in Git's efficiency and power.

Granted, software is different from mathematics, but I find the parallel interesting. I suspect that a mathematician's desire to find an elegant formulation, and appreciation of it, is very similar to the software engineer's.