The quarterly of the University of Helsinki

Leena Itkonen

Back to summer issue 2004

Fifteen years have elapsed since the last major Cultural Foundation prize to mathematics, and the professor thinks that in the intervening time, the share of mathematical thinking in our worldview has eroded. In the spirit of Alan Sokal, Kupiainen has defended the honour of his branch of science, refuted criticism and infused faith in the capacity of natural sciences to generate knowledge and explain phenomena. He is also a Finnish pioneer in using mathematical methods to study problems presented by other disciplines.

Chaos theory brings new problems

Professor Kupiainen becomes enthusiastic when interaction between disciplines in mentioned, "In the last 20 or 30 years, mathematics has gained many ideas from the outside, from physics and other sciences. Interaction between the fields has been fruitful. This has benefited mathematics and promoted its internal development."

The development of computers had a significant impact on the dialogue between sciences when it became possible to numerically process many phenomena in a way that would previously have been too laborious. One of the most important objects of study was weather, but population variation in biology, certain chemical reactions in chemistry and the movement of heavenly bodies in physics are also examples of research topics that were modelled. A phenomenon called chaos emerged with the precise calculations. "A simple, easy-to-formulate law could have complex implications and a tiny mistake in the calculations could be reiterated and lead to fateful consequences. Sensitivity to small variations in the initial conditions is called the butterfly effect. It proposed that a butterfly flapping its wings in the Amazon could trigger a tornado somewhere else," Kupiainen says.

Mathematicians were inspired by the new opportunities. "Mathematics received an impetus from the outside to study these phenomena. This is how mathematics has often evolved. The field is completely free to conceive new problems, but if it is too free, not being able to conceive of problems that are sufficiently fruitful could become a problem."

Concern for mathematics skills

Recently, interesting questions have emerged in the field of biology. "The younger generation of doctors in mathematics and physics have begun to apply their knowledge in biology, as it presents interesting problems," says Kupiainen. In the Department of Mathematics and Statistics of the University of Helsinki this is evident as investment in biomathematics. Then there is also the fact that in a small country such as Finland, the demand for pure mathematicians is not great, so applied mathematics is an important line of education. Kupiainen thinks the university administration should encourage interaction between different sciences more than is now the case. Currently, the way money is distributed creates structural obstacles and can hamper co-operation between different sciences.

But this co-operation can also be hampered by old images. This spring, four professors from the Department of Biology at the University of Helsinki expressed their concern over the fact that schools might not be able to give a true picture of modern biology. Research into the most complex interaction systems known to science require a quantitative approach, so the professors wished for more mathematically gifted students interested in physics to study biology.

Kupiainen thinks the view, expressed in Finland's largest daily newspaper, is interesting, but he remarks that mathematics has also had trouble attracting enough students. Kupiainen says finding reasons for this is difficult. "Our students easily find jobs, but perhaps that is not enough to motivate school students. Something's wrong, when only a select few are interested in mathematics." Kupiainen feels the most important factor would be for the students to find the motivation and teachers to be inspiring. "For most people, mathematics is only a question of motivation. It is a myth that some genius could think about mathematics only an hour a day and that's it. One must work hard, top mathematicians work hard all the time. There are only a few special talents even among professional mathematicians," says Kupiainen and points out that the change should begin in primary school, among young school children.

Bringing together the humanist and scientific cultures

Naturally, mathematics is not needed for everything under the sun. "For instance, mathematics is no good in describing human relations," Kupiainen says with a laugh but adds, "But those who are able to explain things in a mathematical way are sure to benefit from it. Integrating mathematics into social sciences and psychology, for instance, would surely provide advantages, because the explanatory power would be greater," says Kupiainen.

But how to filter the scientific worldview into the rest of the culture? Kupiainen sees the popularisation of science as one possible answer. He wishes popularised science would, also in Finland, provide relevant information on the significance of the natural sciences on the way we see the world. Popularisation could also bridge the gap between the two cultures of science, the natural sciences versus the social sciences and humanities. "Bridging is needed and, in fact, it has been going on for some time now, but the general public sees what is going on in science only after a lag in time. Newspapers and magazines are gradually beginning to publish dialogue between the culture of the social sciences and biology, but more people are needed with an interest in both cultures," says Kupiainen and expresses a wish for a broader worldview.

Teaching hours the biggest problem for mathematics in schools

Markus Luoma teaches mathematics in Vuosaari lower secondary school. Students in the school can choose between three different lines: mathematics and natural sciences, humanities or music. Even with students interested in mathematics, the teacher has to struggle with limitations imposed by the number of lessons per week. "Learning with understanding is slow. The present contents of mathematics and the number of lessons do not allow it. Owing to haste, students are unable to construct the logical structure of mathematics. Instead, they try to memorise unconnected mathematical concepts and principles," says Luoma.

Mathematics is also commonly thought of as a difficult subject. "I believe students would change their view, if they were given time to understand numbers, operations, concepts and principles. In addition, mathematics is often seen in a one-sided light as routine performances in which students should beware of making errors. This view should definitively be abandoned with the help of learning with understanding."

Luoma says learning with understanding requires the teacher to have a reflective attitude and be open to dialogue and problem-based learning. "Nearly all the concepts taught in comprehensive schools are already there in the students' minds, only the name for the concept is missing. The same goes for mathematical principles. The way I see it, the teacher's role is to instruct the students with dialogue and questions. Almost the entire lesson is spent on thinking and talking about things, routine calculations receive less attention, which, on the other hand, is a bad thing, since without routine, studying mathematics in the future and using it in practice is not as fluent as it should be. With the present lesson allocation, one or the other has got to give," says Luoma.

Luoma thinks interaction between sciences comes across to students in the subject combinations of teachers. For instance, in the Vuosaari lower secondary school, maths teachers combine not only the usual physics and chemistry, but also woodwork, business studies or even home economics. "Personally, I think that the best feature of mathematics - which I also try to communicate to my students - is that it has so much to give to other sciences."

Luoma says students generally regard mathematics as an important subject and know that they will need it in their future studies. They, however, have quite a vague picture of what studying mathematics as a major can lead to. "I guess university courses that directly prepare you for a profession, such as doctor or lawyer, are the most popular fields of study. School kids might think that studying mathematics as a major offers only a narrow range of careers," says Luoma and places the ball in the university's court.