Until now spontaneous analogies has been refused as possible candidates for fruitful analogical sources. Recently some researches has manifested the importance of spontaneous analogies, even literal similarities, in scientific problem solving and discovery. Focusing in the first creation and subsequent transformation of the source I will choose three significant examples, two of them relevant historical discoveries, of analogical inference in physical-mathematical thinking. These paradigmatic examples will be accompanied and strengthened in their nature with deep ideas in the history of science. The spontaneity/construction of a imagined entity and the theory dependence/independence will be the criteria in order to propose an elemental classification illustrated by these historical ideas. Under this classification the heuristic and pedagogical role or the importance of visual representations will be also studied. Thus history of science is a rich land of genetic ideas in order to implement a “teaching by problems” didactic.

Keywords: mathematical creativity, heuristic, analogical reasoning, literal similarity, imagination, visual representation. L?pning & Utbildning