Women of Mathematics: Elisabeth Gaar

Country: Austria

Affiliation: Universität Klagenfurt, Austria

Field of Research: combinatorial optimisation, nonlinear optimisation

Formel_Elisabeth Gaar I (c) Chritina Supanz

1.) Why did you choose this formula?

This formula has been a major part of my research of the last few years. It is a very complicated formulation of a very simple problem. However, this formulation can be used in a highly elegant way to tackle a problem that isn’t possible to solve with easier formulations.

2.) What made you decide to study Mathematics?

At school I was very good at mathematics and especially at the mathematics competition “Känguru der Mathematik”. Because of that I started attending Mathematical Olympiad courses at the age of 14. At these courses, I found out that mathematics is much more than just playing with numbers, and is better compared to solving puzzles at a very high level. In the end it was a very easy decision to study mathematics.

3.) What do you like so much about Mathematics?

In mathematics, everything is purely logical and everything is either right or wrong. It may be that we don’t know yet which of the two possibilities it is, but exactly one of them is definitely true. The fact that it’s very often possible to reach the same result in several completely different ways is another thing that makes mathematics fascinating.

4.) How does Mathematics influence our lives on a daily basis?

Mathematics is everywhere. We are all lucky that some mathematicians took care of the complicated things and now we can benefit from their results and methods. Mathematics is used in the weather forecast, in the security measures of credit cards, in creating train timetables and deciding on the shortest route to your destination in Google Maps.

5.) Have you experienced a special Mathematics moment?

I really enjoy the feeling when I’m in the middle of proving some theorem and then I come up with the final idea that completes the proof. At this point you’re skeptical at first, so you reconsider and think about everything again. Eventually, you try to write up the proof and only then do you allow yourself to really believe that you have completed the proof.

6.) What advice would you give future mathematicians to help them on their way?

Getting started in the field of mathematics is always tough, because “real mathematics” is completely different to what pupils get taught at school. But it’s so much more exciting, fascinating and beautiful, so don’t let anybody discourage you.

Women of Mathematics: Michaela Szölgyenyi

Country: Austria

Affiliation: Universität Klagenfurt, Austria

Field of Research: computational stochastics, stochastic differential equations, stochastic optimal control, mathematical finance, insurance mathematics

Formel_Michael Szölgyenyi I (c) Christina Supanz

1.) Why did you choose this formula?

The “Itō” formula applied to a certain transformation G is used in my work to overcome issues caused by certain discontinuities in stochastic evolution equations caused by, for example, the optimal operation of energy storages.

2.) What made you decide to study Mathematics?

I considered several fields of study and, to be honest, studying mathematics was a spontaneous decision.

3.) What do you like so much about Mathematics?

The fact it is pure logic, but still surprises me from time to time.

4.) How does Mathematics influence our lives on a daily basis?

Mathematics is everywhere – we encounter it in our phones, when buying something in the supermarket, when receiving medical treatment, when there are changes in energy prices… the list goes on.

5.) Have you experienced a special Mathematics moment?

When I explained to my then 10-year-old second cousin what prime numbers are and asked him how many even prime numbers there are. Ten minutes later he came up with the correct answer and an explanation.

6.) What advice would you give future mathematicians to help them on their way?

Believe in yourself!

Women of Mathematics: Elena Resmerita

Country: Romania

Affiliation: Universität Klagenfurt, Austria

Field of Research: inverse problems (regularisation methods, image reconstruction theory and continuous optimisation)

Formel_Elena Resmerita I (c) Christina Supanz

1.) Why did you choose this formula?

This relates to the proximal point method, an optimisation technique introduced in 1962. The method has generated a number of efficient algorithms for inverse problems, for instance in signal and image reconstruction. About 15 years ago, I thought it was getting old and people would lose interest in it, but I’m happy that recent developments in applied mathematics have shown the contrary: it will continue to be a powerful tool in solving complex mathematical problems.

2.) What made you decide to study Mathematics?

Initially I wanted to study medicine, but I found it difficult to learn all of the biology needed for the entrance exam. However, I realised that the entrance exams for mathematics would be relatively easy for me. This, together with my passion for teaching (I used to give my friends, neighbours and other children private lessons) made me choose mathematics.

3.) What do you like so much about Mathematics?

In mathematics everyone is happy when a problem can be solved in some way, and even happier when there are several ways to solve it. If a solution cannot be found, we come across new problems when trying to approach the original problem, and these are sometimes more important than the problem we started with. So we keep on trying to solve problems…

4.) How does Mathematics influence our lives on a daily basis?

On a personal level, mathematics helps us to develop very structured thinking, whether it’s about efficiently planning your holiday or taking important decisions in life. On a global level, it provides a basis for all natural sciences: physics, chemistry, engineering, biology, and so on.

5.) Have you experienced a special Mathematics moment?

After finishing my PhD studies in Israel, I started to learn about another field of mathematics in Linz, Austria. I remember the sense of achievement I felt when I successfully published a paper of my own in this new field – incidentally, that has been my most successful publication so far.

6.) What advice would you give future mathematicians to help them on their way?

A career in mathematics has the same requirements for success as any other field. You have to enjoy the subject and feel comfortable working with it, but you also need to be committed and see the work through.

Women of Mathematics: Barbara Kaltenbacher

Country: Austria

Affiliation: Universität Klagenfurt, Austria

Field of Research: inverse problems, regularization methods, parameter identification in partial differential equations, optimization with PDE constraints, direct and inverse problems in piezoelectricity and magnetics, nonlinear acoustics

Formel_Barbara Kaltenbacher I (c) Christina Supanz

1.) Why did you choose this formula?

Because it is a formula I am working with at the moment. It describes the nonlinear propagation of high-intensity focused ultrasound, as can be seen when it is used to disintegrate kidney stones, for example. This model is what is known as a partial differential equation, which involves various physical parameters. I am currently looking into how the solution of this equation changes as the tau parameter (relaxation time) approaches zero.

2.) What made you decide to study Mathematics?

I always enjoyed studying Mathematics at school – and I definitely have my high-school teacher to largely thank for that as she helped and encouraged us a great deal. I wasn’t your typical maths geek, though! I was interested in a lot of other things at school and I had to work really hard when I first started studying. It only really all clicked into place properly after the first few semesters.

3.) What do you like so much about Mathematics?

I like the fact that there are definitive answers in the sense that a mathematical statement can only be true or false and a mathematical proof is absolutely watertight and cannot be disputed (provided that it is correct in the first place, of course). On the other hand, it can be extremely hard work to get to that stage and proofs have been known to haunt my dreams at times.

You’ve also got the chance to work with people from all around the world – and they are basically always like-minded people who are just as fascinated by Mathematics. There are also plenty of exciting fields of application, meaning that there is more or less always chance to learn something new.

4.) How does Mathematics influence our lives on a daily basis?

There are so many applications within my own field of research alone, including all medical imaging processes, which simply couldn’t exist without advanced mathematical algorithms. In actual fact, Mathematics is at the heart of all modern technology, ranging from algorithms used to process signals in telecommunications to the control systems for industrial facilities. It is often the case that mathematical tools are based on results from pure basic research, for which no real-life applications were considered when they first came about. And, of course, the process of actually applying them often requires close collaboration with colleagues from the fields of Engineering, Medicine, Business and so on. But there’s still lots of work to be done on pure basic research within Mathematics too.

5.) Have you experienced a special Mathematics moment?

Special moments happen all the time when the basic idea behind a proof comes to me or once I have added the final little part of the puzzle to finish it off. There are special moments like this in teaching too, such as when I realise that the students are taking on board and truly understanding what I am trying to tell them about.

6.) What advice would you give future mathematicians to help them on their way?

At the end of the day, Mathematics is a gender-neutral science – both in terms of the content covered and the ways of working. That makes it all the more crazy that there are still fewer female mathematicians than male ones. It’s certainly a positive and natural development that this difference in numbers is decreasing with every generation. But we need to reach a balance much more quickly. There are still girls and young women who simply don’t have enough confidence in themselves when it comes to Mathematics – and that comes across first when they are choosing what to study and then later on when they need to assert their position within the academic world. We are still sadly seeing way too many talented candidates slip through the net as a result.