# NTNU mathematician adds up to the best

On May 4, Idun Reiten, a mathematician at the Norwegian University of Science and Technology (NTNU), was recognized with the national Fridtjof Nansen Prize, for outstanding research in science and medicine. She has also recently learned that she will travel to Hyderabad, India, in 2010 to deliver the Emmy Noether lecture at the International Congress of Mathematicians – an honour that recognizes her as one of the world’s leading female mathematicians.

“This came totally out of the blue,” Reiten, 67, said. “I was pleasantly surprised.”

**Four decades as a theoretical mathematician**

Reiten may have been surprised, but those who are familiar with her four-decade-long career as a theoretical mathematician were not. Reiten has authored more than 100 papers and developed a theory that bears her name, the Auslander-Reiten theory.

In 2007, she was elected to the Royal Swedish Academy of Sciences, the group that awards the Nobel Prizes in Physics and Chemistry, the only woman in the mathematics group and the only Norwegian in the academy’s mathematics, natural sciences and technology disciplines.

**"Beautiful and elegant"**

Most recently, Reiten has worked in cluster theory, a branch of algebra that was introduced in 2000. Reiten’s namesake theory has been described as “beautiful and elegant” by colleague Gordana Todorov, Associate Professor of Mathematics at Northeastern University in the United States.

“In many fields of mathematics and especially in the many aspects of the representation theory, Auslander-Reiten quivers (a particular consequence of the theory) appear as convenient combinatorial tools,” Todorov says. Reiten’s collaborators work in the United States, Canada, Belgium, Greece, Mexico, Italy, Germany, Japan, Poland, England, France and Argentina.

But don’t worry if you find cluster theory a bit esoteric – Reiten herself acknowledges the challenge in giving the Noether lecture in India, even to a room full of more than 2000 international mathematicians, because any branch of mathematics is so specialized. “New theories are being developed all the time,” she said. “That is why it will be hard to give a lecture even to a general audience of mathematicians.”

**German, Latin, chemistry and... maths**

Reiten’s career developed somewhat unconventionally – she always loved mathematics, but was unsure if she should pursue a career as a mathematician. Instead, she specialized in Latin in high school, and studied German, mathematics and chemistry as an undergraduate at one of NTNU’s predecessors, the Norwegian Teachers College in Trondheim. She took her PhD in mathematics at the University of Illinois in 1971, and at the time was only the second Norwegian woman to be awarded a PhD in maths – with the first awarded in 1902. She says her interest in language and in mathematics grew out of a common fascination in finding patterns in things.

“I study abstract systems and find the properties that will apply elsewhere,” she says. “The idea is to see the similarities in things, to look for common structures.”

**Thinks in English -- and in symbols**

Reiten needs nothing more than a notebook and a pen to do her research, as she thinks out theorems and proofs. She writes in a small hand in unlined A4 notebooks, often diagramming her ideas with arrows to see if they will work. Reiten’s native language is Norwegian, but she thinks and writes in English. While she would encourage anyone who is interested to pursue mathematics as a career, she says it’s rare that she has to encourage higher level students. “Mostly people who study maths are people who really like it,” she says. “It’s rare that you say to someone, ‘you should study maths’. Generally, people know.”

The Emmy Noether lecturer at the International Congress of Mathematicians, which is held every fourth year, is now chosen by the International Mathematical Union to “honor women who have made fundamental and sustained contributions to the mathematical sciences”. Emmy Noether was a German mathematician who was forced to flee Nazi Germany in 1933. She came to the United States to teach at Bryn Mawr College but died in 1935, just two years into her new life in America. Albert Einstein described Noether in a letter to the New York Times as “the most significant creative mathematical genius thus far produced since the higher education of women began."