2026 Wolfram Summer Research Institute: Opening Keynote

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, you know, 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, you know, computation is a paradigm for thinking about formalizing things.

So, you know, mathematics was, you know, 1600s was the big moment for mathematics to kind of arrive as a way of formalizing things in the world.

I think these times are the big moment for the arrival of commutation as a way to formalize things in the world.

And I think My view of what is computation is 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 the 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 else, there are specific models where you say, this is what the actual cell looks like.

This is what, you know, some particular detail of how things work.

It is.

But the question is, what's the underlying, what's really the essence of what's going on? And I remember from years ago, trying to study snowflake growth and trying to think about what are the detailed equations that govern 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, is much simpler about kind of 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 it turns out that if you can model things at that sort of essential level, that you can reproduce things.

sort of the essential features of what's happening.

You know, snowflakes make sort of fluffy shapes and so on.

You don't necessarily reproduce the details of, you know, 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, you know, can we find numbers to represent this or that thing? So...

In any case, I think the exciting thing about times is this computation as a paradigm for formalizing things in the world and, among other things, doing science.

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, you know, 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, you know, computation is a paradigm for thinking about formalizing things.

So, you know, mathematics was, you know, 1600s was the big moment for mathematics to kind of arrive as a way of formalizing things in the world.

I think these times are the big moment for the arrival of commutation as a way to formalize things in the world.

And I think My view of what is computation is 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 the 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 else, there are specific models where you say, this is what the actual cell looks like.

This is what, you know, some particular detail of how things work.

It is.

But the question is, what's the underlying, what's really the essence of what's going on? And I remember from years ago, trying to study snowflake growth and trying to think about what are the detailed equations that govern 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, is much simpler about kind of 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 it turns out that if you can model things at that sort of essential level, that you can reproduce things.

sort of the essential features of what's happening.

You know, snowflakes make sort of fluffy shapes and so on.

You don't necessarily reproduce the details of, you know, 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, you know, can we find numbers to represent this or that thing? So...

In any case, I think the exciting thing about times is this computation as a paradigm for formalizing things in the world and, among other things, doing science.