Paul M. Weichsel, Professor Emeritus, Department of Mathematics, UIUC
As I was beginning to play with Mathematica in the early nineties, a colleague of mine in the Mathematics Department and I were working on a problem that required us to look at some examples of graphs. We had essentially built a “machine” whose inputs were graphs of relatively small order, n, and the outputs were graphs of order approximately 2n, very daunting to do by hand. I remember inputting the data in my Mac Classic early in the evening and finding the results waiting for me in the morning. We found, surprisingly, that given a very large number of quite different input graphs, the outputs were a very restricted set of graphs. Examining these outputs gave us the crucial clue that we needed and we were led to a rather unexpected result. As so often happens, our final published paper made no mention of the machine calculations that we had done or of the fact that Mathematica was the primary tool.
I continue to use Mathematica in my current research.