A Fable

Once upon a time, two young ladies, Melinda and Sheila, came to a town called Mathematics. People had warned them that this is a particularly confusing town. Many people who arrived in Mathematics were very enthusiastic, but could not find their way around, became frustrated, gave up, and left town.

Melinda was strongly determined to succeed. She was going to learn her way through the town. For example, to learn how to go from her dorm to class, she concentrated on memorizing this clearly essential information: she had to walk 325 steps south, then 253 steps west, then 129 steps in a diagonal (southwest), and finally 86 steps north. It was not easy to remember all of that, but fortunately she had a very good instructor who helped her to walk this same path 50 times. To stick to the strictly necessary information, she ignored much of the beauty along the route, such as the color of the adjacent buildings or the existence of trees, bushes, and nearby flowers. She always walked blindfolded. After repeated exercising, she succeeded in learning her way to class and also to the cafeteria. But she could not learn the way to the grocery store, the bus station, or a nice restaurant; there were just too many routes to memorize. It was so overwhelming! Finally she gave up and left town. Mathematics was too complicated for her.

Sheila, on the other hand, was much of a much less serious nature. She did not even intend to memorize the number of steps of her walks. Neither did she use the standard blindfold that students need for learning. She was always curious, looking at the different buildings, trees, bushes, and nearby flowers or anything else not necessarily related to her walk. Sometimes she walked down dead-end alleys to find out where they were leading, even if this was obviously superfluous. Curiously, Sheila succeeded in learning how to walk from one place to another. She even found it easy and enjoyed the scenery. She eventually built a building on a vacant lot in the city of Mathematics. (Smith, 1995, p.xv.)

Smith, K. J. (1995)., The Nature of Mathematics, Pacific Grove: Brooks/Cole Publishing Company.