The Hungarian mathematician George Polya (1887–1985) was a prominent twentieth-century mathematician. A founder of modern heuristics, he is especially known for writing a best-seller on "How to Pose and Solve a Problem" (see our feature "Mathematics and Psychology" in Tangente 159). He also wrote a two-volume book entitled The Discovery of Mathematics (Dunod, 1967). The second volume is devoted to a "general method," presented as an attempt to provide "a general method applicable to every kind of problem; […] while the variety of problems we may encounter is infinite, each of us has only one head with which to solve them, so it is natural to hope that a single method will suffice". Throughout the book, Polya illustrates these general ideas with a wide range of examples; several times, he refers to how animals behave when they encounter a problem…
The mouse and the cheese ------------------------
Here are two short stories inspired by passages from Polya's book (see pages 211, 252 and 254). To some extent, they may serve as models for solving mathematical problems.
Our first imaginary story takes place on a farm in the countryside. An old-fashioned mousetrap, consisting of a barred cage fitted with a trapdoor, has been placed in a corner of the kitchen. When the farmer sees that a little mouse has been caught in it, he carries his prize into the garden, then goes back inside calling for his cat. The mouse seems to understand these words, which foretell a grim fate. It begins to panic, darting from one side of the cage to the other and striking the bars with increasing force; in doing so, it creates a small opening through which it can escape from the trap as quickly as possible and scurry to the far end of the garden. On the way, it discovers the entrance to a maze and senses that a tempting piece of its favorite cheese lies at the other end. Naturally, it ventures into the passage, which is straight at first. Then it reaches a dead end and has to change direction. It struggles onward, turning now right, now left, trying several routes when necessary and sometimes having to retrace its steps. Eventually, however, it reaches the maze's exit and can at last savor the piece of cheese before disappearing into the surrounding meadows. The little creature is safe.