> As a specific example, our high-school math curriculum taught a lot of calculus, but framed it incorrectly as being a useful tool that people would use. One day at FedEx the BoD (board of directors) was concerned about the future of the company and as part of that wanted an estimate of the likely growth of the company. In the offices there were several efforts, free-hand, wishes, hopes, guesses, what the marketing/selling people thought, etc., and none of those efforts seemed to be objective or with a foundation or rationality. We knew the current revenue. We could make an okay estimate of revenue when all the airplanes were full. So, the problem was essentially to interpolate over time between those two numbers. For the interpolation, how might that go? That is, what, day by day, would be driving the growth? So, notice that each day current customers would be shipping packages, and customers to be would be receiving packages and, thus, learning about FedEx and becoming customers. That is, each day the growth would be directly proportional to (1) the number of current customers creating publicity and (2) the number of customers to be receiving that publicity. So, for some math, let t be time in days, y(t) the revenue on day t, t = 0 for the present day, and b the revenue when all the planes were full. Then for some constant of proportionality k, we have y'(t) = k y(t) (b - y(t)) where y'(t) = dy/dt the calculus first derivative of y(t) with respect to t. A little calculus yields the solution. y(t) = y(0) b exp(bkt) / ( y(0)( exp(bkt) - 1) + b)) Seeing how the growth goes for several values of k, pick one that seems reasonable. Draw the graph and leave it for the BoD. That was a Friday, and the BoD meeting started at 8 AM the next day, Saturday. First thing at the meeting, two crucial BoD members asked how the graph was drawn. For several hours, no one had an answer. The two members gave up on FedEx, got plane tickets back to Texas, returned to their rented rooms, packed, and as a last chance returned to the BoD meeting. FedEx was about to die. I did all the work for the graph, the idea, calculus, arithmetic (HP calculator), but didn't know about the BoD meeting. Someone guessed that I did know about the graph, and I got a call and came to the meeting. The two crucial BoD members were grim, standing in the hallway with their bags packed, and their airline tickets in their shirt pockets. I reproduced a few points on the graph, and FedEx was saved. So, some math saved a business.