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however, it might take more discipline to learn other ways of solving problems rather than just resorting to the way that you think the problem should be solved.
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The beauty about math is that either your solution is right or it isn't.
That one of the reason why college is good because you have a teacher who will tell you when you have made an error somewhere.
Often multiple right ways to solve a problem and the goal is to find one of them.
That what mathematicians are for:
Finding ways to solve mathematical problems of other people (well sometimes the other people are mathematicians as well
).
When a mathematican produces a forumla a chemist might use that formula in his work.
Most chemists aren't good enough in math to create the mathematical toolkit that they use themselves.
And when the mathematican proved that the formula works the chemist doesn't have to brother about the math and can concentrate himself on chemistry.
The chemist can get away if he simply memorizes the forumlas.