One question: How were those demonstrations programmed? I have a feeling they were developed by "manipulating abstract symbols." Math doesn't need a new interf

One question: How were those demonstrations programmed? I have a feeling they were developed by "manipulating abstract symbols." Math doesn't need a new interface, any more than a POSIX compliant shell does. Math is a beautiful and expressive language. Its strength is in communicating difficult, abstract concepts in a language that is manipulable. This manipulation is of the utmost importance in understanding the relationships between different concepts and even in developing new ones. Removing the single strongest aspect --the "abstract symbols"-- of mathematics is to neuter it.