Mathematical Rebuses

Mathematical Rebuses

Mathematical Mathematical User Interfaces

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...

Mathematical Wit and Mathematical Cognition

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...

Mathematical Wit and Mathematical Cognition

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 article 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 accomp...

Mathematical Discourse vs. Mathematical Intuition

One of the most uninformative statements one could possibly make about mathematics is that the axiomatic method expresses the real nature of mathematics, i.e., that mathematics consists in the deduction of conclusions from given axioms. For the same could be said about several other subjects, for example, about theology. Think of the first part of Spinoza’s Ethica ordine geometrico demonstrata ...