This chapter concentrates on the nature of intelligence and the nature of domain expertise. It examines three alternative positions on the nature of cognitive ability: unified intellect, diverse intellect and hierarchical intellect. Historiometric studies suggest that historiometric genius correlates at between.25 and.35 with estimates of psychometric genius. Whether intelligence is unified or multiple, all budding geniuses must go through some sort of apprenticeship period in which they acquire the expertise that will enable them to make original and exemplary contributions to their chosen domain of achievement. To understand the difference between algorithms and heuristics, and to appreciate their relevance to an understanding of the nature of genius, the chapter takes a glance at two kinds of computer programs that engage in problem solving of a rather high order: expert systems and discovery programs. In any case, most expert systems operate according to algorithms rather than heuristics.