QAMA - The calculator that makes you think

The guys at work think I have superpowers because I can do rough calculations in my head without resorting to a calculator. In the middle of intense discussions about systems architecture it's a real bonus to be able to get the numbers quickly and without suspending the discussion in order to punch things into a calculator.

They say that discussions go faster and are more free-flowing and productive because they don't have to stop and start constantly.

Of course, I work in an engineering-heavy field, so my experience won't be typical. Even so, your question carries overtones of the "when am I ever going to use this?" question that causes math teachers all over the world to despair of ever getting people to understand that it's not about the facts, it's about the ability to think.

Being able to do mental arithmetic effectively is one aspect of being able to break down problems into small parts, and retain some pieces while working on others. The skills involved are clearly related to those required in programming - seeing more than one way to do things, working through long chains of reasoning, combining tiny operations into large and complex calculations. It's plausible that practising those skills in small, concrete settings such as arithmetic can help foster the abilities required in larger and more abstract settings such as math and programming.

You'll never need trig if all you ever do is flip burgers, but I use it all the time in computing margins of error in safety critical operation of 30,000 tonne tankers and nuclear submarines. There is a middle ground.

But it's not really about the tools being used to learn, it's about the skills you acquire on the way.