Algebra uses letters, symbols and rules to describe states, processes and objects, for example in the form of equations. However, these do not always provide clear solutions. "It can happen, for example, that an algebraic curve has a 'kink', corners, peaks or intersections. Then there is more than one tangent at some points," says Faber, referring to one of her specialisms - singularities.
It is precisely this process - categorising and describing exceptional cases - that she finds exciting about her field of research: "When we see a singularity, we try to present it in a comprehensible way. But to do this, we first have to build up the vocabulary and develop the appropriate methods. It often feels like we're learning a new language," she explains
From the Olympics to science
Faber heads the Algebra and Number Theory research group at the University of Graz. After studying in Vienna, she returned to Austria two years ago after spending time in Canada, the USA, Sweden and the UK. She believes it is particularly important to teach students early on that university mathematics has little to do with the arithmetic they are familiar with from school. "I wasn't very good at maths at school at first. I wasn't interested in the subject at all," says Faber. It wasn't until the Maths Olympiad that the spark was ignited: "Suddenly it was all about working out and proving things together. I was much more interested in that than pure text problems," smiles the researcher.
Arithmetic = computer, thinking = human
It is precisely these skills that she wants to pass on to her students: "At university, we deal with definitions, structures and the question of what can be considered a mathematical proof. The computer does the arithmetic anyway. It is crucial to understand how and why methods work." And because everything has two (or more) sides, Eleonore Faber loves to visualise algebraic forms - in 2D on her Instagram account or, when time allows, in 3D paper models for her courses.
>> If you want to immerse yourself in the world of scientific computing, you can do so on the Bachelor's degree programme in Mathematics.