Abstract
Although scientific creativity has often been described as combinatorial, the description is usually insufficiently formulated to count as a precise scientific explanation. Therefore, the current article is devoted to elaborating a formalization defined by three combinatorial parameters: the initial probability p, the final utility u, and the scientist's prior knowledge of that utility v. These parameters then lead logically to an 8-fold typology involving two forms of expertise, two irrational combinations, and four "blind" combinations. One of the latter provides the basis for the definition of personal creativity as c=(1-p)u(1-v), that is, the multiplicative product of originality, utility, and surprise. This three-criterion definition then has six critical implications. Those implications lead to a discussion of various combinatorial processes and procedures that include a treatment of the No Free Lunch Theorems regarding optimization algorithms as well as the creativity-maximizing phenomena of mind wandering and serendipity. The article closes with a discussion of how scientific creativity differs from artistic creativity. Besides the obvious contrasts in the ideas entering the combinatorial processes and procedures, scientific combinations, products, and communities strikingly differ from those typical of the arts. These differences also imply contrasts in developmental experiences and personality characteristics. In sum, the formal combinatorial analysis enhances our understanding of scientific creativity.