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My response can be very simply stated as the well-known adage - Profile Before Optimizing

I am not completely discounting Numerical Analysis here. Mathematicians can make entire mathematical models of a machine but it will be at a certain level of abstraction. In practice there will be abstraction leaks due to some quirks of the implementation or real world dependencies.

So one should not merely depend on the mathematical model.

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A more important and often overlooked adage - make it correct before you try to make it fast.

My confusion at your (and others, not meaning to pick on this one) response is more fundamental than that. There is no way in which thinking about these things is somehow divorced from thinking about things mathematically.

To me "Merely depending on a mathematical model" isn't a problem that actually happens much. Failing to think about these things, on the other hand, very much is.

>My response can be very simply stated as the well-known adage - Profile Before Optimizing

Well, profiling IS also math.

If anything, it would be "optimizing" which is programming proper.

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