If you are using math to model the world then the correctness of the model matters much more that the math itself. Below is a quote from a math educator. I guess my point the math should never be divorced from the model except at the highest levels.

Probably 40 years ago, I was an invited guest at a national summer conference whose purpose was to grade the AP Examinations in Calculus. When I arrived, I found myself in the middle of a debate occasioned by the need to evaluate a particular student’s solution of a problem. The problem was to find the volume of a particular solid which was inside a unit three-dimensional cube. The student had set up the relevant integrals correctly, but had made a computational error at the end and came up with an answer in the millions. (He multiplied instead of dividing by some power of 10.) The two sides of the debate had very different ideas about how to allocate the ten possible points. Side 1 argued, “He set everything up correctly, he knew what he was doing, he made a silly numerical error, let’s take off a point.” Side 2 argued, “He must have been sound asleep! How can a solid inside a unit cube have a volume in the millions?! It shows no judgment at all. Let’s give him a point.”

My recollection is that Side 1 won the argument, by a large margin. But now suppose the problem had been set in a mathematical modeling context. Then it would no longer be an argument just from the traditional mathematics point of view. In a mathematical modeling situation, pure mathematics loses some of its sover- eignty. The quality of a result is judged not only by the correctness of the mathematics done within the idealized mathematical situation, but also by the success of the confrontation with reality at the end. If the result doesn’t make sense in terms of the original situation in the real world, it’s not an acceptable solution. How would you vote?