Artikel på engelska. 

Josefin Ahlkrona och Sofia Tirabassi utvecklar hur man kan förstå världen med matematik.

The president of Stockholm university approved the recommendation from the Faculty of Science in June, after the evaluation process of the applications for promotion had concluded.

Sofia´s research is in algebraic geometry, one of the most abstract areas of mathematics, while Josefin´s research on mathematical models contributes in the field of climate science. Her research is primarily about finite element methods for ice sheet modelling and ocean modelling.

- I´m working on the math behind the ice sheet models. This is connected to sea level rise. In order to understand what causes it, we need to know how fast the ice is melting. We need ice sheet models that are both more accurate and faster, so we have to look at the math behind it, says Josefin.

Sofia´s main filed of specialization studies geometric objects arising from algebraic equations.

- Despite the fact that it is abstract and of a classical nature, algebraic geometry has a deep impact on our everyday life, says Sofia. She explains that for example, the study of the geometry of elliptic curves—i.e., curves described by the equation y² = x³ + ax + b— has greatly improved the way in which we can protect ourselves while surfing the Internet:

Cryptography based on elliptic curves is used in a wide range of applications, from the safety of online transactions to the protection of sensitive data stored on hard disks. Some of the central objects of her research – abelian and semi-abelian varieties- can be thought of, under many aspects, as higher dimensional elliptic curves.

Different paths into math

Sofia Tirabassi and Josefin Ahlkrona had different paths into Mathematics. Sofia found out quite early that she wanted to pursue an academical career in that field, while Josefin was open for opportunities in the private sector as well:

- I haven´t identified as a mathematician in the past, I´ve looked for different opportunities. But I was sort of gradually realizing that math is what i find the most fun, says Josefin, who worked as an assistant professor with our institution for the last four years before being promoted to asscociate professor. 

- Before doing my master thesis, I thought to go to the private section. I actually had a dream of working on climate modelling but I didn't think it was realistic. Then I got the oppurtunity to do a master thesis on ice sheet modelling and naturally took it. I continued the topic during my PhD. After my PhD I was again open for both private sector and academia, she says.  

- I then got an email from a math-professor that I admire, about a postdoc position in germany. I took the position and then got my assistant professorship at SU in 2019. Then I had 4 years to work towards promotion, she says.

Sofia on the other hand, says she wanted to become an academic already in high school.

- I ended up studying algebraic geometry almost randomly thanks to a charismatic professor who gave me an undergraduate project in the area. And then I fell in love with the subject. Toward the end of my master studies, my supervisor asked me “what do you want to do afterward?” I answered, “I want to be paid for doing math”, to which he answered that I needed to get a PHD, which I did. I really wanted to stay in the academic world after that. I wanted to work for anyone who was willing to pay me for my research, so I applied for work all over the world, Sofia says.

Math and climate research

The ice on Greenland and Antarctica slowly moves towards the coasts, where it meets the warming ocean and melts. The ice can be seen as a very thick fluid. To model the flow of ice (or ocean) you consider the basic laws of physics that mass, momentum and energy must be conserved. From those principals you get get equations.

We want to solve these equations for velocity and pressure, but they are so complicated that doing so analytically with paper and pen is impossible. We therefore look for an approximated, "numerical" solution in many sample points spread out over the ice or ocean. In each point, we can solve a simplified version of the equations wtih some few calculations. The problem is thus transformed into doing simple calculations in many points.

- This is an excellent task for a computer. My job is about how to break the equations down into these simple calculations in a smart way, that gives as accurate answers as possible without requiring to much computational power, Josefin says.

Understanding the world with math

- Italian physicist Galileo Galilei once said that the book of nature is written in mathematical language, meaning that to understand the world around us we need to understand and being able to work with math. There are also many “unnatural phenomena” that can be described using mathematics, Sofia says.

For example, nowadays, mathematics is used to determine the premia of different types of insurances, and prices of bonds and other financial assets. We can also use math to model how much a new building will oscillate under the force of wind, and then know if the materials we have will allow it to stand.

To describe a phenomenon using mathematics is called mathematical modelling. It is one of the most concrete branches of mathematics and closely related to Josefin’s research. It could be said that she is working to uncover what in Galileo’s book of nature is written about ice melting.

Sofia’s research is different: it deals with abstract objects and has not a direct impact to our everyday life. But this could change in the future because we do not really know today which mathematical tools we will need then. Going back to cybersecurity, when Rivest-Shamir-Adleman wrote their robust encryption algorithm in 1977, they did it by leveraging on purely theoretical results almost two centuries old. Thus, we need to keep developing math, even the most abstract one, because it might be essential in the years to come. In addition - as Dante’s Ulysses (see Divina Commedia, Inferno, Canto XXVI) would have said - we are not made to live as brutes, but to pursue virtue and knowledge.

Math literacy

- Mathematicians are problem solvers, that´s why people hire us: not for what we know, but for the way we are trained to think during our studies. People are often scared of math and numbers, which makes it easy to cheat them in many ways, for instance when it comes to statistics. The world would become a better place if everyone learned a little bit to think as a mathematician and not be afraid of a few formulas, Sofia says.

She also shares her thoughts on how Sweden´s educational system may inspire more young people to become mathematicians:

- If you don´t choose an NO-program in high school, then you are not qualified to study math at the university unless you go through some komvux program. In order to want to study math, you have to discover that you actually like math when you are 14 or 15. Not everybody is so lucky. I became good at math – and so I started loving it - when I was 16, so if I would have lived in Sweden then, I might not have become a mathematician. Unless a primary school teacher can inspire students and nurture their love for math – beside their many other duties - Sweden will be missing on an incredible untapped potential, Sofia says.