Taking Mathematica and xThink as representatives of the state of the art in interactive mathematics, we argue conventional mathematical user interfaces leave much to be desired, because they separate the mathematics from the context of the user interface, which remains as unmathematical as ever. We put the usability of such systems into mathematical perspective, and compare the conventional app...

we study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. we discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. this second part continues to study the question of catecoricitytrans...

The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This paper analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompan...