Physics was early in using computers to aid in working with its existing paradigms, and I would like to think that Mathematica helped with that. The biggest growth directions, I think, will be in the use of computation as a paradigm for physics. Part of this involves using computational models for physical systems. But part of it also involves understanding computational concepts like computational irreducibility, and seeing how they relate to phenomena in physics.

It’s hard to know what might crack the problem of finding a fundamental theory of physics, but perhaps it will be computation. Certainly, the intuition that we now have from exploring the computational universe of simple programs is something completely new—and it seems potentially highly relevant to questions of fundamental physics. I’ve been thinking about these kinds of things for a long time, and I’m finally about to mount a serious project to see whether there’s a computational way to approach fundamental physics that will get further than the quantum field theory and general relativity approaches that we’ve been trying for the last hundred years. Of course, it may be the wrong century—or the wrong approach—to crack the problem. But there’s definitely a lot of interesting theoretical structure to investigate.