Is "Creative Subject" of Brouwer a Designer? An Analysis of Intuitionist Mathematics From the Viewpoint of C-K Design Theory
Editor: Norell Bergendahl, M.; Grimheden, M.; Leifer, L.; Skogstad, P.; Lindemann, U.
Author: Kazakci, Akin Osman; Hatchuel, Armand
Section: Design Theory and Research Methodology
The paper considers one of the main constructive mathematical theories - the Intuitionist Mathematics. Brouwer, the father of Intuitionist Mathematics, describes mathematics as the study of mental mathematical constructions realized by a creative subject. This perspective on mathematics represents many similarities with more conventional design processes. By analyzing Brouwer work and mathematical philosophy, we identify the reasoning process Brouwer explains as a conceptive reasoning process. We point out some interesting parallels and similarities between Brouwer's work and another theory of creativity as conceptive reasoning process coming from design research ? namely, the C-K design theory. We argue that, even though the concept space of C-K theory is not explicitly represented, Intuitionist Mathematics authorize, and even welcome, concepts and the reasoning process of the creative subject implicitly makes use of them. This, result combined with many parallels between the C-K theory and Intuitionist Mathematics, opens up interesting research perspectives.