One of the biggest mistakes of research mathematics in America in the last 50 years has been to let computer science get away. If you look at what was done when computing was young, there was a strong and definite strand of computing that was essentially part of mathematics. The mathematicians rejected it: this was a big mistake. While there is a certain track of computer science which is basically computer engineering, the fact that computing and mathematics ended up being adversaries rather than being close intellectually was a big mistake of the mathematics community.

When Mathematica was quite young, and I talked to people in the computer industry about doing mathematics on computers, they said to me, “Why would anybody want to do that?” It’s quite ironic, considering that in the early days of computing with von Neumann, Turing and others, one of the original conceptions (at least one of the major tracks) was that one was building these machines to automate mathematics. There was another track saying that one was building these machines to automate what the census bureau does, which is a separate bookkeeping area. But by the time personal computers had come out in the late ’70s and early ’80s, the computer industry had this idea that what computers were used for was word processing, spreadsheets, etc., and the notion that one could use computers to do mathematics was bizarre.