Math is presented in a way that's supposed to be organized, compact, and categorical. If we taught math the same way math was proven and discovered, it would be so slow and inefficient that we would still be covering linear algebra in post grad.
As an analogy: The 1,000th person to climb Mt. Everest takes a well defined path that has already been mapped out as the most efficient path to the top. If every single person had to go through the treachery of finding the dead ends, cliffs, crevices, and death traps that the first few climbers endured, it would be a journey only a few could accomplish.
Most people (computer scientists, engineers, chemists, physicists) using math only need to reach the top and see the view from the peak. The few climbers that are really dedicated to climbing (ie, the math researchers who reach the frontier of math) will naturally learn about the rest of the jagged, unmapped landscape as they climb harder and unconquered mountains.
As an analogy: The 1,000th person to climb Mt. Everest takes a well defined path that has already been mapped out as the most efficient path to the top. If every single person had to go through the treachery of finding the dead ends, cliffs, crevices, and death traps that the first few climbers endured, it would be a journey only a few could accomplish.
Most people (computer scientists, engineers, chemists, physicists) using math only need to reach the top and see the view from the peak. The few climbers that are really dedicated to climbing (ie, the math researchers who reach the frontier of math) will naturally learn about the rest of the jagged, unmapped landscape as they climb harder and unconquered mountains.