Math in the service of insight and results
W. Edwards Deming and others used simple statistics to help companies improve product and process quality.
Virginia Postrel posted about the power of Bayesian statistics in getting drug test results more rapidly.
I and others have written about system dynamics, control theory applied to human, organizational, or ecological systems, as a way to make sense of and deal with those situations in which long time delays and the feedback of information play a strong role in determining outcomes.
Why is this important to mention? In today's fast-paced world, I think we often feel compelled to take the most direct approach to solving problems and making decisions: we use the experience we have already to make the decision that seems right, and we move on.
Sometimes that works well, but sometimes the result takes too long or the problem itself seems not to make sense. In those cases, check out the mathematical approaches! Perhaps there's a way to use the leverage of math to give you a better and easier answer than you might have gotten other ways.