A junior lecturer and PhD student in Mathematical Sciences, Jacques Rabie, rubbed shoulders with some of the top researchers in his field at the Heidelberg Laureate Forum (HLF) in Germany recently. He was one of 200 young researchers from more than 50 countries worldwide who were selected for this honour.

The HLF is modeled on the concept of the Lindau Nobel Laureate Meetings, which annually provides young researchers the chance to engage with Nobel Laureates. As there are no Nobel Awards for computer science or mathematics, the HLF has since 2013 provided young mathematicians and computer scientists the opportunity to interact and learn from laureates in their fields too, all of whom have been winners of prestigious prizes such as the ACM Prize in Computing, the ACM AM Turing Award, the Fields Medal, Abel Prize and the Nevanlinna Prize.

The 2022 edition is the first in person event since the Covid-19 pandemic, as virtual events were held in 2020 and 2021.

At the opening event, held on Sunday 18 September 2022, HLF chair and managing director of the Klaus Tschira Foundation, said that the passion and dedication to research of the laureates and young researchers attending is the lifeblood of the Forum. She urged the participants to spend as much time networking as possible, and to learn from each other.

Workshops, panel discussions and seminars by laureates are par for the course of the HLF, as are social events aimed at providing the attendees enough time to have meaningful conversations. A boat trip down the Neckar River, a visit to the Speyer Museum of Technology, a Bavarian evening and a visit to the Heidelberg Castle are always among the highlights of the weeklong event.

Rabie says he is indeed taking the opportunity at HLF to network as much as possible with others in the field of algebra, and also to look for new lines of thought and research to explore.

“It is also interesting to chat to others about the world of work, and to hear how they experience it," he adds.

Although Rabie admits it is not always easy to do, he believes in having conversations and sharing about the work that one does, and the value of working together with others. In this sense, he admires the example set by the Hungarian mathematician Paul Erdős, whose mission it was to collaborate with as many fellow researchers as possible.

“If you do not share the work that you do, you are actually limiting the field that you are working in," adds Rabie, who authored an article on the topic of competition and collaboration in the maths field for the online publication Wisaarkhu.

Rabie recently submitted his PhD and hopes to graduate at the end of 2022. His thesis focused on the field of near vector-spaces, and through it he contributed his own ideas on its theory, geometry and hyperstructures.

He is also in the midst of his first year as a junior lecturer at SU, and is now looking for postdoctoral opportunities.

It's so far been a good 2022 for the young mathematician from the Class of 2015 at Linden High School in Johannesburg. His first paper, co-authored with his supervisor Prof Karin-Therese Howell of the SU Department of Mathematical Sciences, was published in January in the journal *Quaestiones Mathematicae**.*

They wrote on the geometries with non-commutative joins and their application to near-vector spaces. The duo has contributed to the theory of the geometry of near-structures by defining a near-linear space, proving some properties and showing that by adding some axioms they could arrive at a nearaffine space. They used some of the geometric results to prove an open problem in near-vector space theory, namely that a subset of a near-vector space that is closed under addition and scalar multiplication is a subspace.

“A nearaffine space is a generalisation of the traditional affine space, for which the line joining two points generally depends on the order in which the points are joined, i.e. the map sending a pair of different points to their common line is noncommutative," he explained during a recent talk in his home department.

Rabie enjoys teaching, and helping others to understand difficult concepts. It is a role that he had already taken on at school, often helping others who were struggling with mathematics in afterschool programmes. At SU he started tutoring and working as a teaching assistant in his second year. During the Covid-19 lockdown period, he incorporated cartoons and jokes into his learning material to try and make the experience of online classes and tutorials a bit less daunting for his students.

During 2020 helped to remodel teaching material for Mathematics 114 and 144 at the start of the Covid-19 pandemic, and subsequently to prepare the courses for the Augmented Remote Teaching, Learning, and Assessment (ARTLA) model followed by SU in 2021.

About his teaching philosophy, he says: “I believe there is no better substitution to independent practice when it comes to mathematics learning. However, this does not mean that students should be left entirely to self-study. The most important task of a lecturer is to create an environment most conducive to independent learning. This can for instance be achieved by giving some introductory problems before lectures to introduce the topics to be discussed in the lecture, and then some further problems designed for reflection after the lecture."

He believes increased student engagement can be achieved by encouraging student questions and participation in lectures, and using lecturing material that is visually stimulating.