This article has an economics spin to it, which is interesting as only insiders seem to understand how much mathematics is required in that field. Greg Mankiw

This article has an economics spin to it, which is interesting as only insiders seem to understand how much mathematics is required in that field. Greg Mankiw lays out a similar defense of mathematics in what we might assume to be a more logic or intuition driven field. (http://gregmankiw.blogspot.com/2006/09/why-aspiring-economists-need-math.html http://gregmankiw.blogspot.com/2006/09/why-aspiring-economis...) His advice for aspiring Phd students in economics suggests as much mathematics as many undergrad programs require (http://gregmankiw.blogspot.com/2006/05/which-math-courses.html http://gregmankiw.blogspot.com/2006/05/which-math-courses.ht...). What's this mean about calculators and learning the basics? There are concepts that you can't mentally understand if your mind can't map the basics of math. I see it in real world examples (people can't make quantitative business judgements on the fly) as well as abstract reasoning. One of the critiques of Google is similar - by reducing what we need to remember, we reduce our ability to process certain ideas on the fly. Like many things, it's ultimately a trade-off. Are the things we mentally miss from utilizing calculators and Google more or less important than what we gain in added productivity? (Is it worth the health hit of driving 5 miles to work rather than walking? Can you mitigate it by spending half the saved time in the gym?)