The project is interdisciplinary – it will be implemented at the intersection of cognitive science, psychology, philosophy of mathematics and methodology of science. Mechanisms of spatial orientation, results of developmental psychology research concerning acquisition of geometric skills, language of geometry characterized by the repetition of certain formulas, mechanisms of abstraction, as well as mechanisms of precision and conceptual stability in geometry will be analyzed in succeeding stages of the project. In the last stage of the project links between the mechanisms of geometric and numerical cognition will be examined.

Modern cognitive science of mathematics has its origin in the psychological studies of the representation and processing of numbers, which have been conducted since the sixties. On the other hand, geometry is an area neglected by cognitive scientists. This state of research is unsatisfactory if only due to the fact that geometric thinking is extremely important in modern mathematics, and it played an important role in the development of this discipline.

Implementation of the project can contribute to initiation of fruitful interdisciplinary discussions between cognitive scientists, philosophers and mathematicians themselves. The latter often are skeptical about the psychological and cognitive theories explaining the nature of mathematical cognition. Mathematicians point to the gap resulting from the fragmentation of theories that have concerned the numerical structures, at the same time neglecting geometry. In a wider perspective, the project may be valuable for the whole cognitive science, shedding new light on relations between the phylogenetically old spatial skills and language.