The Problem Solver

When Idun Reiten was only 12 years old, a radio show from the Norwegian Broadcasting Corporation held a math competition, presenting 10 problem sets over a span of 10 weeks. Only five people in all of Norway solved every single problem set, and 12-year-old Reiten was one of them. Her 16-year-old brother was another one.

Reiten received an inscribed pewter bowl for her accomplishment, but that was only the beginning of her math prizes and honors. Reiten, an LAS alumnus, turned 70 on New Year’s Day, and her birthday is being recognized in March with a special conference in her honor, drawing mathematicians from Norway, Illinois, and other parts of the world.

It is a fitting honor for someone whom LAS math professor Robert Fossum describes as a truly great mathematician and “one of the best PhD students to ever attend the University of Illinois.” Reiten received her PhD from Illinois in 1971, becoming only the second woman ever in Norway to receive a PhD in math.

Reiten grew up in Klaebu and Heimdal, small communities in Norway, where she found numerous possibilities for physical activity on her uncle’s nearby farm. She says both of her parents had a strong interest in mathematics. Her father taught elementary school, but her mother had only eight years of schooling, due to financial constraints. Nevertheless, she says her mother “could solve problems that normally required knowledge beyond her education.”

With such a firm family foundation in the world of numbers, Reiten says she always loved math, even before she was old enough to attend school. As she puts it, “I found the joy of solving problems when I was young, and this later grew to an admiration of its beauty.”

Reiten met Fossum when he was a visiting professor in Oslo, Norway, during the late 1960s, and this contact inspired her to come to the U of I to pursue her PhD in math. Illinois became a turning point in Reiten’s life, for she met American mathematician Maurice Auslander on campus when he was giving a series of lectures. She went on to forge a long collaboration with Auslander that lasted until his death in 1994. The duo is best known for developing the theory of “almost-split sequences” (Auslander-Reiten sequences) and irreducible maps.

The Auslander-Reiten theory has had a major impact on the representation theory of Artinian algebras and beyond. “It has been extremely important throughout the mathematical world and has many applications within the realm of mathematics,” Fossum says.

Since Auslander’s death, she has embarked on other critical collaborations, producing important work such as the theory of cluster categories and cluster tilted algebras.

Fossum, who advised Reiten when she was at Illinois, says: “She is persistent in attacking a problem. She is goal-oriented and can stick to a project and drive it to completion. She also picks up quickly on new ideas and can develop them in a very short time. It might take her only weeks to work through a problem that would take several months for someone else to solve.”

Reiten has been teaching and doing research at the University of Trondheim in Norway since 1974, and she became a professor there in 1982. She says that being a female PhD student in math is no longer a rarity in Norway, for seven of the 13 doctoral students in the university’s algebra group are female.

Over the years, Reiten has garnered many honors, including the Mobius Prize in 2007 from the Research Council of Norway for her total contributions to algebra. In 2007, she was elected as a foreign member of the Royal Swedish Academy of Science; in 2009, she received the Nansen Medal for outstanding research; and in 2010 she was invited to give the plenary lecture at the International Congress of Mathematicians in Hyderabad, India.

She has come a long way since receiving an inscribed pewter bowl at age 12.