He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd prime numbers.

The first problem in the first chapter is to guess the rule according to which the successive terms of the following sequence are chosen: 11, 31, 41, 61, 71, 101, 131, .

In the next chapter the techniques of generalization, specialization and analogy are presented as possible strategies for plausible reasoning.

In the remaining chapters, these ideas are illustrated by discussing the discovery of several results in various fields of mathematics like number theory, geometry, etc.

This volume attempts to formulate certain patterns of plausible reasoning.