Emeritus Professor Michael Albert – problem solver and puzzle maker

Following 27 years of teaching and research, Emeritus Professor Michael Albert retired from Otago in December 2024.

Starting in the Department of Mathematics and Statistics, Michael transferred to the Department of Computer Science for the bulk of his tenure which included serving as Head of Department for seven years. In 2023, Computer Science was amalgamated into the new School of Computing.

A decade after completing his PhD in Mathematics as a Rhodes Scholar from University of Oxford in 1984, Michael moved into combinatorics, which became his field of research expertise.

“I think it was such a perfect fit for my personal way of thinking about problems,” Michael says.  “I enjoy the fact that it throws up a lot of problems that are accessible without requiring enormous amounts of background knowledge.”

Catching up with Michael during his early stages of retirement, Sciences Communications Advisor Guy Frederick obtains a brief insight into combinatorics and learns about a game he developed that now has its own Wikipedia profile.

What nurtured your path in mathematics?

Apparently, even before starting school I was intrigued by patterns in numbers and how they fit together. I always had a natural aptitude for mathematics, but also wonderful teachers who fostered that enthusiasm and provided enrichment for the subject. In 1970s Canada there was a rich ecosystem of maths competitions which provided further incentive for me to work on my underlying knowledge and problem-solving skills.

What was your link to computer science?

Largely that I’d recognised that computing provided the ability to create a ‘guess-checking laboratory’. When pursuing ideas for solving problems, technology can quickly find counterexamples because, unlike humans, computers don’t get bored of looking at 10,000 or 10,000,000 different cases.  Computing also provided the space and opportunity for me to write special-purpose software.

What is combinatorics in a nutshell?

My research area in combinatoricsis broad but at its core is the study of discrete structures that have a finite number of configurations and how these relate to one another. A classic example would be to ask: given a row of cards in some scrambled order, what’s the minimum number of adjacent pairs you need to exchange to get them in order? This applies to computer science because digital computers are fundamentally devices that manipulate discrete structures.

Applications of this field involve studying these structures at scale. For example, social networks are discrete structures and the algorithms that get applied to them are parts of combinatorial mathematics. Aspects of cryptography and security, genomics, and experimental design are also combinatorial in nature.

What was the game you designed with its own Wikipedia page?

Two-player games of perfect information, typically the kind where you have pieces on a board, are a classic example of combinatorial structures.  Clobber was a fortunate discovery of this type. It’s a capturing game, where your pieces can capture an opponent’s adjacent pieces and vice versa. It has the property that whenever one player has a move available so does the other. It proved to be surprisingly rich. It also makes it rather frustrating to play for humans since, unlike most piece-based games (such as chess) there’s little or no sense of cumulative advantage to provide strategic guidance in the early stages of the game.

Link to Clobber.

How has the field of computer science changed over your career?

The obvious change is the resurgence of AI that’s quite possibly going to fundamentally change the way we do research and teach. If my career still lay ahead of me, I’d engage with AI as quickly and deeply as possible.

Thinking about the future role of computing in society, we need to be conscious that it’s important to understand, and lead the development of, new tools and techniques. But we also need to see how they fit into the world, what social and ethical issues this raises, and what the specific circumstances of being in Aotearoa imply for their use.

How do you intend to start your retirement?

I will continue as co-editor-in-chief of the Australasian Journal of Combinatorics, an open access journal that has a boutique feel. Personally, I hope to do some writing, a little bit of web development, and most likely (and to no one’s surprise) plenty of puzzles and games.

Any career highlight that stands out for you?

Without doubt it’s the teaching I have done and the sense that I’ve been able to explain things clearly at a level that’s accessible to most students, while also showing that there’s much more out there for those who choose to pursue it.