Changing the Culture 2000:
April 28, 2000
SFU at Harbour Centre
515 Hastings Street, Vancouver
The advent of affordable computers with huge storage and communication capabilities seems to promise a golden age of mathematical visualisation. The question is to what extent it can relieve us of the laborious doodling and imagining that has always been an integral part of mathematical activity.
When asked about the nature of his thinking, Einstein once replied that it was a mixture of visual and kinesthetic elements. The plausibility of that reply is corroborated by any observation of people grappling with mathematics -- say, students taking an exam. When they are not busy writing or drawing, they tend to stare into space or at the ceiling, stab or stroke the air, drum or scribble with their fingers, and the like.
Our question therefore has two parts: (1) what exactly is going on there, and (2) how can computers be integrated into that process?