# “Mathematics is art”

Sandra Di Rocco is a newly appointed professor of mathematics at KTH. When she speaks about algebraic geometry, she does so with a passion that sends shivers down your spine, and it even affects those who know very little about the subject.

Mathematics is about feeling and about language, says Sandra Di Rocco. Mathematics is the exact language which cannot be misunderstood.

“I would be lying if I said that I hadn’t always wanted to become a professor. So absolutely, my work has led to something which I wanted from the very beginning,” says Sandra Di Rocco.

She became a professor on 1st June this year, after six years as a senior lecturer. She views the role of professor as an important signal that KTH appreciates her research.

“There are very few occasions for a researcher to receive acknowledgement, in particular from his or her own department or university. But to achieve the title professor, well, it means that you have reached a special level. It is also recognition from other professors that my research is good enough. This makes you feel good,” says Sandra Di Rocco.

She carries out research on algebraic geometry. This means the rigorous study of geometric objects which are described with the use of algebra. Algebraic geometry is more than 200 years old and a classical area in mathematics.

“This is about studying geometric forms defined by polynomials. Polynomials turn up all over the place in mathematics, but they also turn up in physics, computer science and biomedicine.”

### A classical problem

Sandra Di Rocco’s research is not directly applied, but it is common that researchers in her field find areas of use at a later date for their research results.

She draws an example on a piece of paper: It depicts a robotic arm and represents a classical problem within kinematics, a so-called six-bar kinematic problem, she says.

“Which positions and how many positions are required for a robotic arm to reach from one point to another. That is what we are trying to work out,” says Sandra Di Rocco gesticulating fervently.

Despite her enthusiasm and pedagogical exposition, it’s not easy to keep up with her line of reasoning. It is obvious to me that I have long forgotten the maths I learned at school!

What I understand however is that the opposite of pure mathematics is not impure. Mathematics is divided up into pure and applied mathematics, and they complement each other.

### Traditional means of assistance

When I look around Sandra Di Rocco’s office, my eyes are drawn to an old-fashioned slate which is full of formulas and symbols. Why doesn’t she have a normal whiteboard?

“I love slates. Everything looks so much better on a slate, and it feels simpler and easier to use. It is difficult to say exactly why this is so, ” she exclaims.

And she is not alone among research colleagues as regards her passion for the old, traditional aids:

“We have two seminar rooms here: one with a slate and one with a whiteboard. You can guess which of them is always booked,” she says.

The slate is an instrument for communication, and this also applies to the subject of mathematics,” she means.

“I regard mathematics as the only way of being able to communicate scientific ideas in an exact manner. Quite simply, there can never be any misunderstandings,” says Sandra Di Rocco.

### How students view mathematics

This is also the way that students should regard mathematics, she says.

“Students should think of mathematics as a language without any misunderstandings, and not only as a set of formulas.

She has learned lots of things about problem solving through mathematics.

“Mathematics presents a clear description of the problem: Where is the beginning - where is the end - and what are the steps like between the beginning and the end? If I am affected by a problem in life it is not just about having the right tools, I must also able to analyse and break down the problem into smaller parts.

What is it that motivates you to conduct your research?

“If you ask an artist why he or she does what they do, you will probably receive the same response as you will from me. I like the feeling of having completed a job, in the same way as the artist does when he or she has just completed a work of art or a recorded a song. It produces a feeling of happiness and pride. I may have struggled a long time with something - perhaps months or years - and the final result is something really fantastic. Artists have their performances and researchers get published in scientific journals - it’s the same feeling I think.

She says that she may get a similar feeling when she listens to good music; she wishes she had been the person who had written the music.

“Mathematics is a form of artistry,” she says.

### The biggest moment

“I came to Sweden in 1996 and I was there as a postdoctoral student at the very prestigious Institute Mittag-Leffler, an international research Institute for mathematics in Djursholm, just outside Stockholm. The programme was arranged by, for me, some big names within mathematics, and that time was of great significance to me. And next term, spring 2011, I will be the one arranging a programme on the department, with several other promising young postdoctoral students. It feels great, and I believe and hope that they will appreciate it just as much as I did,” says Sandra Di Rocco.

As regards the objectives of her research, she has a clear image.

“I want to find interesting and smart solutions to geometric problems and also start new theories and research technologies which lead to new discoveries in geometry. But it is just as important to me to apply techniques from algebraic geometry in combinatorics and numeric analysis and vice versa.

Text: Peter Larsson

## Sandra Di Rocco

Age: 42 years

Family: Husband and daughter

Interests: I love music, sport (tennis and jogging) and friends. I play guitar, listen a lot to music and watch LOADS of films.