Anne-Maria Ernvall-Hytönen is the Professor of Mathematics for subject teacher training. Her research focuses on transcendental number theory through mathematical analysis.
What are your research topics?
In essence, I'm a number theorist. Number theory is a mathematical field founded on the characteristics of integers. I am particularly interested in questions related to transcendence. For example, I have worked on estimating the transcendental measure for the number e and its power series. A transcendental number is one that is not a solution to any non-zero polynomial with integer coefficients. I use the methods of this analysis for questions of number theory, which in practice means analytic number theory, focusing these days on questions arising from, but not limited to, transcendental number theory.
In addition, I study mathematics learning using quantitative methods.
I am also the deputy chair of the Finnish Mathematical Society as well as the chair of the mathematics division and the A2 committee of the Finnish Matriculation Examination Board. Moreover, I am involved in training for the mathematical olympiads and I popularise mathematics as the editor-in-chief of the Solmu periodical.
Where and how does the topic of your research have an impact?
My research in number theory is mathematical basic research, so not all possible applications are known at this stage. What is very fascinating about it, however, is the degree to which it has links to a range of topics. For instance, in a project focused solely on transcendental number theory, we ended up considering the accuracy of certain approximations by assessing a Laguerre polynomial. These polynomials are connected to aspects of number theory, including the Riemann zeta function theory. They also arise in other domains, such as in the wave function of the hydrogen atom.
In contrast, research on mathematics learning provides new knowledge of misconceptions and challenges in studying mathematics, as well as the factors that can support people's understanding.
What is inspiring in your field right now?
I am particularly fascinated by the linkage between things, or how the same ideas, methods and objects arise in different contexts, and in the connections between things overall.
