The Icelandic Centre of Excellence in Theoretical Computer Science (ICE-TCS) at Reykjavik University celebrates its 20th anniversary this year. Magnús Már Halldórsson, a professor at RU’s Computer Science Department, is the head of the centre and one of its founding members. But what exactly is theoretical computer science? What kind of research is conducted at the center, and who is Magnús? In honor of the anniversary, we delve into these questions.

“I attended MH (Menntaskólinn við Hamrahlíð) back in the day. That’s where I first encountered computers. I was completely fascinated, and knew this would be my future path,” says Magnús, who went on to study in the United States, earning a bachelor’s and master’s degree in computer science and mathematics, as well as a PhD.

“My doctoral studies took a slightly different turn than I had originally planned. I started experimenting with computers and programming because I saw the potential to do practically anything with them. It wasn’t hard to foresee much of the future—although I didn’t quite anticipate the communication revolution. But in terms of what computers as tools could accomplish, that was clear. Initially, I thought of it in terms of programming and making software more powerful. However, during my graduate studies, I started working on theoretical questions, and eventually, I fully transitioned into that field,” he explains.

Magnús earned his PhD from Rutgers University in the United States in 1991 and then moved to Japan with his Japanese wife and their first child. The family lived there for four years while Magnús worked at two Japanese universities. Later, they relocated to Iceland, where he joined the University of Iceland’s Science Institute. In 2007, he started working at Reykjavik University, but as previously mentioned, he had been part of RU’s ICE-TCS since its founding in 2005, as its activities have always extended beyond RU.

Algorithms: Recipes for Problem-Solving

When asked what constitutes theoretical questions in computer science, Magnús describes his work:

“If I focus on what I do, we use computers to solve specific tasks. A program is supposed to perform a certain function, and there are technical aspects to how it is implemented. But at its core, there is always a problem-solving method—an algorithm, if you will, which acts as a recipe for what needs to be done. It must be implemented in specific programming languages because computers require precise instructions, and there are different programming languages, technologies, and tools. But beneath all that is the algorithm, which is independent of the specific technology, computer, or programming language. That’s what I’ve been working on—creating algorithms that allow problems to be solved efficiently, regardless of the computer being used.”

Magnús finds this work exciting, and the questions he deals with are generic and abstract.

“The key question is: what are the most complex problems? What are the fundamental questions that form the core of problem-solving? While practical applications may be specific to certain individuals or situations, we focus on the underlying question: how do we tackle this type of problem in general?”

Thus, researchers at ICE-TCS study the science behind technology.

“Computer science is a blend of science and technology, and we consider ourselves part of the fundamental scientific base of the field. Our group consists of four different subgroups, but we all focus on mathematical properties, concepts that can be mathematically described and form the foundation of computer science. If you want to guarantee that something works, you need to prove it mathematically. That’s what we strive to do—not just say that a program works most of the time, but ensure that it always solves the problem correctly,” Magnús explains.

Research Topics at ICE-TCS

A significant part of the centre’s research focuses on ensuring software correctness, that is, making sure there are no errors, bugs, or unexpected failures.

“This is one of the toughest challenges in computer science: ensuring that software does exactly what we want it to do. Usually, this is addressed through extensive testing to build confidence that it works. But sometimes, testing alone isn’t enough. You want to be sure that even on the thousandth run, no unexpected bug suddenly appears, especially when working with critical systems, such as nuclear power control, medical technology, or aviation software. In such cases, proving mathematically that the software behaves correctly is crucial. That’s what one of our research groups specializes in: analyzing software properties and developing techniques to verify correctness,” he says.

Another group at the centre works on automating mathematical proofs.

“This involves taking mathematical knowledge that has traditionally been derived manually and automating the process of proving mathematical theorems within software. This has led to significant advancements.”

Since its inception, ICE-TCS has been highly active, with a relatively large founding team. The research activities have expanded significantly, with an increasing number of postdoctoral researchers and PhD students joining over the years.

“We host weekly seminars, organize an annual conference, receive many visiting researchers, and have always had a strong presence of young researchers, whether postdocs or PhD students. So, there has always been a lot of activity here,” Magnús says.

The Importance of Fundamental Research

When asked about the significance of conducting fundamental research, like that at ICE-TCS, for Iceland’s scientific community, Magnús emphasizes its importance.

“We should aim to be internationally competitive. Of course, we’re a small country and can’t do everything, but whatever we undertake, we should strive to do it as well as possible. That has been our goal, and we’ve been successful in establishing a strong international reputation, as evidenced by various metrics. I believe this should be a universal goal—not just focusing on what matters to Iceland but ensuring that our work has broader relevance.”

He continues:

“In general, you want expertise at all levels of the technological stack. You don’t just want to operate on the surface; you need people who understand the deeper layers. And we’ve seen practical benefits from this. For example, Icelandic biotech company deCODE Genetics leveraged our expertise in certain data structures for their software. As society becomes more complex and interconnected, we can’t afford to be isolated. We need to stay on top of cutting-edge developments, especially in security. Ensuring that systems are correct and secure is crucial, and we need a solid foundation in that area.”

A Creative Field

Finally, Magnús emphasizes that theoretical computer science is far from dry or boring—it is, in fact, a highly creative field.

“As a colleague of mine put it: ‘I can’t stop doing this kind of math because I need something creative in my life.’ Some might think theoretical computer science is far from creative, just formal logic. But the process of solving these problems is incredibly creative. The best part of my work is that I can take it anywhere. Whether I’m hiking or in the shower, I can think about these problems and often get new ideas in those moments. It’s a form of meditation—grappling with theoretical questions. I suspect many people don’t realize just how fulfilling and intellectually stimulating it can be,” says Magnús Már Halldórsson, head of RU’s ICE-TCS.