Ryan Peterman

It lives in both spaces.

It is a mathematical field in the sense that most of what we generate are theorems and proofs in the mathematics sense.

On the other hand, it's related to computation because the kind of questions we ask ourselves, the problems we are trying to solve, are partly motivated by trying to understand computation.

So you can think of theoretical computer science very much like you can think about analysis and algebra and topology.

There are notions, in algebra you are trying to understand equations or systems of equations, and in analysis you are trying to understand, very generally speaking, inequalities and continuous spaces.

So there are these notions you are trying to understand.

Computation is one of these notions.

You are trying to understand what can you produce by an evolution of simple local steps to a given environment, the input.

And this can be a sequence of bits or it can be the DNA of a person from which you produce proteins using computation or you produce a new baby using the evolution of a fertilized egg or the weather.

So computation is sort of everywhere.

And we are trying to understand it in ways that are different.

We care about resources, how much resources are exerted in any such computation and trying to model it, trying to understand the algorithms that underline natural phenomena.

So we live in both spaces.

We have a lot of input of problems and models from industry, technology, systems, and so on.

And we have all the mathematics that is...

We have the rigorous side coming from, and the aesthetic side, I would say, like creating models of proof systems because they are nice, because they are interesting, not because they are implementable necessarily.

So living in these two spaces is extremely beneficial to this theory of composition.

Okay, so let me say one thing about the beginning of your question.

It says about solving problems.

I think that what we do more, much more, is modeling things.