The symbolic computation laboratory at UIUC

As I was leaving Erwin Engeler's office at the ETH during the summer of 1985, he casually asked me if I had seen their mathematics laboratory. Up to that point I had heard nothing about it, but as soon as I understood how it was organized and how it functioned, I realized that it was almost exactly what I had been looking for. Over the years, there have been numerous computer projects in the mathematics department at the UIUC, the most notable being George Francis' Apple Lab and the recently established Plato and Excel (IBM) labs. However, none of these seemed to conform with the kind of computer experience I imagined for students. I did not feel that it was the proper function of a mathematics department to teach students to program in traditional languages such as Basic or Pascal or Forth. But I did feel that algorithms were an important component of modern mathematics which deserved the same kind of emphasis that is normally accorded to proofs. What better way to understand the role of algorithms could there be than to try to implement them in computer programs? How could this be done unless it were done say in Pascal? Why not use Macsyma? I thought and still think that one could base a valid course just on this, but when I saw that the Laboratory at the ETH used projects in many different computer algebra languages, I realized that that was the methodology for which I was searching.