One of our principal aims when designing AsTeR was to produce clear and succinct audio renderings for mathematics. In designing a concise audio notation for mathematics, it is interesting to note that the written mathematical notation that we have come to accept is relatively new. For an in-depth survey of the evolution of written mathematics, see [Caj30].
There is little similarity between developing a written notation and its audio counterpart. However, the evolution of written notation shows the following. Any notational system is a combination of conventions and an intuitive use of the various dimensions that are provided by the perceptual modality and the means available to produce output appropriate for that modality. In the case of visual notation, these dimensions are font size, changes in baseline, use of different delimiters, stacking of sub-expressions to build up layout, and the use of characters from different scripts. This insight enabled us to develop a concise audio notation for spoken mathematics that exploits the various audio dimensions that are currently available -see s:math_readings for details. It is conceivable that the number of audio dimensions will increase with the improvement in audio hardware, leading to a more sophisticated audio notation.