Mathematical mathematical user interfaces
Abstract:
All Turing Complete calculators are mathematically equivalent,
and therefore mathematical user interfaces need not innovate beyond
what is absolutely necessary. Typically, user interfaces are
character-based and imperative, with mice used to select windows,
and modes used to control the hidden complexities of the system.
Using Mathematica and xThink as representatives of the state of the
art in interactive mathematics, we show 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, then we compare the conventional
approach with our highly interactive approach, as exemplified by TruCalc.