Prof Florian Luca from the Department of Mathematics in the Faculty of Science at Stellenbosch University delivered his inaugural lecture on Tuesday 27 May 2025. The title of his lecture was 'The Skolem landscape'. It can be viewed here.
Luca spoke to the Corporate Communication and Marketing Division about his passion for mathematics and how his research on Number Theory finds application in our daily lives.
Tell us more about your research and why you became interested in this specific field.
I was interested in mathematical riddles since I was a child. As I grew up, I learned that there are some techniques to tackle such problems. As a high school student, I enjoyed some success in problem solving – making it all the way to the International Mathematical Olympiad. So, I feel that I am still doing the same type of problem solving as in my childhood except that now I have a lot more tools in my bag.
How would you describe the relevance of your work?
As any scientist, most of what I do is relevant to the community of scholars to which I belong. We all do our best to advance our area and better understand the mathematics that we are studying. Occasionally, a small part of what we do finds application in other areas such as computer science, coding and cryptography (securing information by using codes to prevent unauthorised access).
Your research centres on Number Theory. Can you share a few ways it applies to our daily lives?
Number Theory is about finding patterns in the ocean of numbers. For example, there are many interesting palindromes (numbers that read the same from left to right). A Czech legend has it that the construction of the famous Charles Bridge in Prague started at 05:31 on 9 July 1357 with the first brick being laid by the King Charles IV himself. The exact time (1357 9/7 5:31) is a palindrome which was believed that it would bring additional strength to the construction. In modern times, we are surrounded by numbers from the driving directions in the GPS to price reductions in supermarkets. So, understanding numbers makes our daily lives easier.
You are the principal investigator in the DynAMiCs project. How do you see it contributing to advances in mathematics and computer science?
Discrete dynamical systems pervade the quantitative sciences and lie at the heart of central computational challenges in a wide variety of areas, from programme analysis and computer-aided verification to neural networks and theoretical biology. Such systems are typically simple to describe yet give rise to a rich algorithmic and mathematical theory that is replete with easily stated and compelling open problems. One such example is the famous Skolem Problem: Does the orbit of a given linear dynamical system ever hit a given hyperplane? The decidability of this question is a longstanding open problem going back nearly a century! Our project aims to makes progress on some of these difficult problems. Some partial advances will be described in my inaugural lecture which is on the Skolem landscape.
Higher education can be challenging. What keeps you going when things get tough?
The university community. We are not alone; we have collaborators, colleagues and students. We do research, attend conferences, lecture, mentor students and young colleagues. When something becomes hard in one aspect maybe we can put that matter to rest for a while and concentrate on a different aspect for some time. Once we make some progress there, we can come back to the previous challenge with renewed energy.
What aspects of your work do you enjoy the most?
Collaboration. I enjoy going to mathematics conferences, listening to what colleagues have been up to, learning about their tools and achievements and attempting to push matters forward.
As someone who is passionate about mathematics, what would your message be to young people who may find it challenging or intimidating?
Find your passion. Don't follow the crowd. Do what you like, even if it seems that perhaps what you like is not the mainstream. Be well-prepared but be original.
Tell us something exciting about yourself that people would not expect.
I like looking at maps and planning fantastic trips in my head.
How do you spend your free time?
I enjoy spending time in nature, hiking, and going places which are off the beaten track.
