An intractable problem is one of those sticky types of problems that seem to defy an easy solution. These essays are a slightly humorous look at typical problems which computer analysts regularly face, but which never seem to be properly appreciated by many other people.  Dunham[1] had an interesting perspective on this.  He said:

“Why is this so? Does it have something to do with the eclectic communication skills of a computer scientist or mathematician? Why is it that if, during a lull in a dinner party conversation, a mathematician remarks that:

Conversation ceases. People show signs of terror. The party is over. Yet this equation is essential for our understanding of the normal probability distribution upon which luck and fortune are based.  Clearly, good luck has influence over a large part of our daily lives. People should want to talk about it.”

It is my belief that people do want to talk about this.  But, to communicate without ambiguity, one needs a precise language.  Mathematics is one language that endeavors to be precise but regretfully it is a difficult language to learn.  Teaching mathematics may be an intractable problem.

Someone once said, “In the land of the blind, a one-eyed man is king”.  It is only by learning to communicate our problems to others that we can open our eyes and become wise.

[These essays were originally published in 1995 and revised in 2010]

William Miles



1. Dunham, W. The Mathematical Universe, John Wiley & Sons, 1994, pp. 159-166.