Recently I read an article in the New York Times that discussed the oldest known math puzzles ever found:  http://www.nytimes.com/2010/12/07/science/07first.html?_r=1&src=me&ref=general.  As this particular article and finding, about Egyptian school papyri from the Middle Kingdom, deals with a few interests of mine:  namely ancient near east texts, mathematics, education, and history, I thought it worthwhile to discuss.

Among the more curious features of the papyri discussed in the article is that they bear such a resemblance to chestnuts present in longstanding English math puzzles, despite the fact that the schoolbooks teaching the St. Ives problem presumably had no knowledge of analogous Egyptian math puzzles dating from around the time the Israelites were in Egypt (if you follow the early chronology, as I do).  The fact that these puzzles, despite their antiquity, are of a type still seen in math textbooks offers yet another reminder (if any were needed) that some aspects of human behavior, including textbook word problems, have not changed a great deal in the last 3600 years.  What that says about our methods of education is not for me to decide.

Why is that we give students puzzles to learn from?  I must admit myself that since childhood I have always been fond of puzzles, riddles, and enigmas.  I’m not precisely sure what that says about my turn of mind or personality, but such a tendency to seek to penetrate beyond the surface level of thought and to grasp what is really essential and important, to put the pieces together to make the right picture, to follow the clues to solve the mystery, is certainly an important quality for human beings.  One gathers that even relatively early in human history, it became important to develop the right sort of mental approach to solve problems, and not merely learn by rote memorization.

It is, in fact, the development of mental heuristics to determine the mathematical principles of ordinary life and behavior that make math puzzles so enduring and intriguing.  What particular reason was found to begin learning such matters is not entirely known–there is some speculation that math puzzles were needed to educate a society moving from a heavily centralized government to a more decentralized one (at least that is what the New York Times article speculated).  Ironically enough, if that is the case, it would appear that mathematics is one of the areas that a free society would need to be proficient in, while a socialistic society would not have to bother as much with such matters because only the technocratic elite would need such knowledge.  If freedom requires the development of the mind, then those of us who wish to be free need to focus on developing the mental skills to think wisely.

What is the value of such puzzles and enigmas?  One important value is the fact that a math puzzle has an answer.  We spend much of our time puzzling over problems that do not appear to have easy answers, if they have answers at all, and math puzzles offer a simplified way of solving problems that lead to a satisfying conclusion.  The same is true of jigsaw, sudoku, and crossword puzzles.  You follow the process and solve the clues and you eventually come to a satisfying conclusion.  There is a reward for one’s mental effort that one can see in having a solution.  Developing one’s skills and confidence in such matters gives one the mental and emotional confidence to tackle more difficult and less clear-cut puzzles by the same method.

Mental discipline leads to mental discernment, a lesson that is applicable on a lot of levels, in the same way that physical exercise and training precede athletic excellence or moral self-discipline leads to the development of virtue.  If we want the fruits of labor, we have to put in the labor and develop the right strategies.   The Egyptian math puzzles were simply a recognition of that fact and an attempt to impress that upon young and bright students.  We can learn from them just as well ourselves.