THE STRANGE FATE OF ABSTRACT THINKING
Alexandre V Borovik · 2013
the possibility of easy generation of concrete examples and encourages in students a bottom-up, inductive style of thinking. This increases the gap between mathematics as it is taught and the research level mathematics dominated by hierarchically structured top-down abstract thinking. Interactive representation of mathematics via user-friendly interfaces is made possible by thinking that far exceeds the one normally acquired by mathematics graduates. The paper discusses a possible remedy: the use of high level functional programming languages such as Haskell as a tool for handling abstract mathematical structures. Introduction and disclaimers This short paper belongs to a series of publications (see, for example, Borovik 2011) informed by my work in the Education Committee of the London Mathematical Society [LMS] and the