2026 Wolfram Summer Research Institute: Opening Keynote

**Stephen Wolfram** (0:00)
So I guess the, you know, what do I see as being the objective?
We've kind of developed a certain way of doing science and technology that had been pretty productive over the last four or so decades. And I guess I see one of the main objectives here, to try and communicate what we can, methodology and ideas that we developed over that period of time for you guys. So you can do even better things with that methodology. And I guess for me, it's kind of a, it's a mixture of sort of science and technology, that term, and I myself kind of alternatively have been really concentrating on basic science and concentrating on technology about five times in my life. Right now, many things that I have long been interested in science, have sort of been coming to fruition, exciting. Many things that I've been sort of building towards in technology, are also coming to fruition at more or less the same time.
It would have been nice if these things had been spaced out by a few years, but they haven't.
So maybe I should talk a little bit about kind of science, doing science.
I'll talk a little bit about some of the projects I've been interested in, we've been interested in. We'll talk a little bit about technology and the things that I think I can sort of see going on there and ways to think about those kinds of things. So in terms of science, we are in a very interesting moment because I think that we kind of have a paradigm that lets us sort of see foundational things about a bunch of areas of science that have been where there haven't been foundational things to say for a long time. So I talked to the folks who are involved in physics, and I was talking to you last week, the kind of thing. What's the big picture? The big picture is, computation is a paradigm for thinking about formalizing things. So if mathematics was, 1600s was the big moment for mathematics to arrive as a way of formalizing things in the world.
I think these times are the big moment for the arrival of computation as a way to formalize things in the world. I think my view of what is competition, it's that you are defining rules for systems and then letting those rules run and seeing what happens. It's a bit different from mathematics. Mathematics, the goal is, at least mathematics from 1600s and so on, the goal is find a formula for what's going on, which is a little different than saying, we've got some underlying rules, now we have to run those and see what happens and understand that process. I think one of the things that has been interesting to me in sort of understanding the foundations of a bunch of fields, is a sort of methodology that I might call meta-modeling. So, you know, when you're studying some particular field in biology or whatever else, there are specific models where you say, this is what the actual cell looks like, this is what some particular detail of how things work. It is. But the question is, what's the underlying, you know, what's really the essence of what's going on? And, you know, I remember from years ago, trying to study snowflake growths and trying to think about, what are the detailed equations that govern, you know, the way that water vapor kind of accretes to the surface of a snowflake and so on? Okay, you can do a bunch of stuff at that level. But what's really going on? And what's really going on is something that in a sense, it's much simpler about kind of you're aggregating pieces to the snowflake and there's some inhibition to growth. It's something that is in a sense, the essence of what's happening is much simpler than that. And turns out that if you can model things at that sort of essential level, that you can reproduce sort of the essential features of what's happening. Snowflakes make sort of fluffy shapes and so on. You don't necessarily reproduce the details of how fast the arms grow in meters per second or whatever, but you do get sort of the essence of what's going on. I think that's sort of a methodology that is a little different from the methodology that we're used to with mathematical modeling and mathematical equations and kind of, can we find numbers to represent this or that thing? So in any case, I think the sort of the exciting thing about times is this computation is a paradigm for sort of formalizing things in the world and among other things, doing science. I guess that the path for me was from the early 1980s, kind of studying sort of the basic science of what do simple programs do, which you would have thought. So two things were sort of, I had kind of assumed that if you have a simple enough program, it would only do simple things. But then I actually did the experiments and found out that wasn't true, and that things like the Rule 30 phenomenon happened, and that even though the rules are simple, the behavior can be very complicated, and that kind of, you know, that launched, well, but I think I've done a bunch of things other people have done in the world under the banners of complexity and things like this. I'm not actually right. I'm not a great believer in a lot of what actually had been done there, but the sort of key phenomenon is out in the computational universe of possible programs, possible rules for things, it's quite generic for it to be the case that even very simple rules produce very complicated behavior. That's an intuitionally difficult thing to accept. If you haven't done a bunch of experiments along those lines, you simply won't believe it. I see this from over and over again, people saying, but look, there's this complicated phenomenon here. There's got to be a complicated explanation for it, but I think it's such a complicated phenomenon. This is the intuition is just wrong about that. I have to say, it's a lesson takes a long time to learn. It's now 45 years later, and I do lots of computer experiments on lots of things, and it is a routine experience for me that I'll have some kind of system, I'll have some hypothesis about what happens, I'll actually do the experiments, and it's like the thing does something I didn't expect.