Have you ever worked into the small hours of the morning on an algebra or some other mathematical problem, and yet been unable to get your answer to agree with the one given in the back of the book? No doubt sometime during this struggle you were almost convinced the answer in the book was wrong.
What was wrong with your solution? It was just that you were entertaining a false belief about the principle and rules of mathematics, was it not? How was the problem finally solved? By overcoming inertia and carefully consulting that part of the textbook which explained the particular mathematical principle underlying the solution of the problem. Upon doing this, you may have suddenly discovered that you had not been following the rules because you had not fully understood the principle involved.
The instant the mathematical principle was understood, all you had to do was to follow the rules, and you soon had the correct answer to the problem. What had changed? Surely not the problem, nor the mathematical principle. But your concept of the problem and of the rules of mathematics had changed from one of false concept or belief to one of understanding. When you had a right understanding of the mathematical principle and applied it, your problem was solved, and you rejoiced. In other words, the error was entirely in the human mind, and as soon as it was corrected there, the problem was solved.
