Basically that we’ve defined a whole new way for people to use computers—and that more than a million people have found out that it’s a good idea. For your audience, I’d say the most important thing is that lots and lots of people from all sorts of fields have now been exposed through Mathematica to issues about computers and mathematics—and have started to care about them.

I guess I have to say that I really don’t know all the effects Mathematica has had. Only a tiny fraction of our users ever explicitly tell us what they do with Mathematica. People have certainly told me that Mathematica has revolutionized all sorts of fields—including some I’ve barely heard of. It’s really a wonderful experience to build a tool like Mathematica, and then every year to see people doing more and more impressive things with it. I’ve put an incredible amount of work into Mathematica, and finding out that it makes a difference to so many people is really great.

From an intellectual point of view, I think one of the more important effects of Mathematica is that it has communicated advanced computer language ideas to a much wider audience than they ever reached before. There are a huge number of people who had only ever used languages like Fortran before, but who now understand symbolic expressions, rule-based programming and so on. I think that’s pretty important for the progress of computing as an intellectual endeavor.