One of the most basic questions with regard to mathematical thinking is “What is mathematical thinking?” This question Is not the kind that is readily answered by empirical research. However, research can provide some perspective on the nature of mathematical thought if the question is rephrased: “What characterizes the thinking of individuals who have demonstrated a high level of ability in mathematics?” Research that compares the abilities of very capable mathematics students with those of less capable students or the problem-solving processes exhibited by experts and novices otfers some insights into this question.