I think the opportunities of computer experiments are absolutely vast. It’s like the situation about three hundred years ago with physics experiments. Even the easy stuff hasn’t been done. I’ve spent some of the past 15 years trying to do a bunch of the easy computer experiments—and I’ve discovered some incredibly interesting things. There’s amazing stuff out there to find.

But here’s a question for your audience: will mathematicians consider what’s done to be mathematics? What is mathematics these days? I think it’s become defined—like so many other areas of science—more by its methodology than by its content. Mathematics is not about general questions concerning abstract systems. It’s about what you can investigate and prove theorems about. That’s very limiting. In fact, almost by definition it means you can’t find things that are really surprising.

It’s worth noticing that in most fields of science, the number of experimentalists is far larger than the number of theoreticians. Mathematics is pretty much unique in having very few experimentalists. My guess is that one of the big things that will happen in mathematics—whether everyone in the field likes it or not—is that there will be a big shift towards experimentation as the methodology to use. I think one of our big contributions with Mathematica is to make that experimentation easy enough that one can do it without being sure one knows what results will come out—so one is really exploring.