To the Ends of the Earth and Beyond

Lassi Päivärinta: Centre of Excellence in Inverse Problems

As a young boy Lassi Päivärinta found mathematics totally fascinating. An abstract field that seemed detached from everything else. Later he started to wonder what it all meant. And then he got to hear about inverse problems.

– Inverse-problem research showed that, with the help of mathematics, problems of great significance for society can be solved, says Päivärinta now – both as a professor and head of the Centre of Excellence in Inverse Problems Research.

In layman’s terms, an inverse problem can be described as a problem turned on its head. In a normal i.e. conventional mathematical problem the causes that affect the phenomenon in question are known and it is the consequences that we are trying to determine. In an inverse problem the consequences are known and we are trying to deduce the causes from the consequences.

For example, some cancerous tissues differ very little from healthy tissue when it comes to their density but a lot in terms of their electrical conductivity. By measuring the electromagnetism, we attempt to discover the tumour without the need for any biopsies or surgery.

– With inversion we can see beyond our own senses, says Päivärinta.

According to Päivärinta, the same principle can be used to study the soil. Many ores have different electrical and magnetic features than the soil surrounding them, and any deviation can be detected by monitoring the scattering of electromagnetic radiation. By applying similar mathematics we can also look for fractures in nuclear power plants. And, Päivärinta points out that the Centre carries out research from extremely theoretical starting points to extremely practical ones. Some of the researchers are developing software, some are then applying it in their research and the rest study purely mathematical theories.

In addition to the University of Helsinki, the Centre includes the universities of Oulu, Jyväskylä and Eastern Finland and the technical universities of Tampere and Lappeenranta. Päivärinta praises the exceptionally good team spirit. Some of the Centre’s founding members have collaborated since the mid 1980’s.

The Centre’s interest isn’t limited to just the contents of the human body or the soil. One of the most significant discoveries of this unit – up and running since 2006 – has to do with space. In 2006 the group led by Mikko Kaasalainen, Professor of Mathematics in the Tampere University of Technology, managed to define the forms of asteroids by measuring their luminositydistribution. This way they also discovered that the radiation from the sun affects the rotational velocity of the asteroids.

– Ever since Newton came along, people were convinced that the only thing affecting moving objects was gravity. Now, for the first time, we saw that other things affect even objects this big. It was a scientific sensation, says Päivärinta.

Despite the accomplishments of Finnish mathematicians, Päivärinta feels that the level of expertise of upper secondary school graduates has dropped and the standards of the schools have slipped.

– We should worry about this. Maybe there are too many subjects in upper secondary school – and they want to add more all the time. This is how the traditional subjects like mathematics could suffer, stated Päivärinta, who has been a member of the matriculation examination board for 20 years.

Centre of Excellence in Inverse Problems Research » »

Text: Tuomo Tamminen
Photo: Veikko Somerpuro
Translation: first-year students of English, rev. John Calton