Stephen Wolfram
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
Well, the first thing to say is that we've worked hard to maintain compatibility, so that any program written with an earlier version of Mathematica can run without change in 3.0, and any notebook can be converted.
There are a few very small incompatible changes - I really doubt most people will ever run into them.
The typical kind of thing would be the kind I found particularly easy to display graphically and so on are things called cellular automata. So a typical way that's setup is a line of cells, each cell is either black or white, and let's say you start off with just one black cell in the middle and all the other cells are white.
The thing that I realized was, well, if you are going to do theoretical science at all, you have to assume that nature operates according to some kind of definite rules. These rules have to be based on the same constructs we have set up in human mathematics, things like numbers, exponentials, and integrals and so on.
The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?
The most important precedents deal with the whole idea of symbolic programming - the notion of setting up symbolic expressions that can represent anything one wants, and then having functions that operate on both their structure and content.
The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general.
That idea has led to lots of the advances that we've seen in science in the past 300 years, but there are also places where science has not so far been able to make exact progress and where one sees lots of complex phenomena in nature, one is confronted with the same kinds of problems over and over again.
So the thing I realized rather gradually - I must say starting about 20 years ago now that we know about computers and things - there's a possibility of a more general basis for rules to describe nature.
I guess the good news is that we didn't make any big mistakes in the design of earlier versions of Mathematica that we'd have to go back on now.