Two mathematics students from Stellenbosch University (SU) have made mathematical history when their week-long internship with a mathematician at the University of Johannesburg (UJ) resulted in a paper accepted for publication in the Journal of Algebra and its Applications.
Dr Amatya Goswami, an expert in associative rings and algebras, general topology, order, lattices and ordered algebraic structures at UJ, says it is an exceedingly rare event for undergraduate students to produce publishable research in a reputable journal in mathematics.
He was visited in November 2023 by SU students Ms Kerry Porrill (then a second-year mathematics student) and Ms Danielle Kleyn (then third year mathematics) as part of an internship initiative managed by the National Institute for Theoretical and Computational Sciences (NITheCS).
“Initially, I intended to assign them some routine exercises in Ring Theory. However, I quickly realised that they were far too advanced for such tasks. I therefore set aside my original plan and proposed that we work on a research problem.
“To my utter surprise, within just one week, a substantial number of highly non-trivial results were proved. These developments subsequently culminated in a research paper. While the process of writing and submitting the paper took some time, the essential mathematics was almost entirely completed during that one week of their visit. Yesterday, I received official confirmation of the paper's acceptance in the Journal of Algebra and its Applications," he wrote in an email to NITheCS recently.
The two SU students say while ring theory was very new to them at the time, they both found the challenge “quite interesting": “It was quite challenging at first, especially since a lot of it was new. We spent the whole week just thinking about the ring we were studying and bouncing ideas off each other," Kerry commented.
The exposure to this field of mathematics certainly sparked their interest in algebra in general. Kerry is currently doing a BSc Honours in Mathematics, planning on specialising in algebra, while Danielle is doing her MSc in Mathematics in lattice theory and universal algebra under the guidance of Dr Michael Hoefnagel.
The paper, titled “On Structures of the Ring of Arithmetical Functions: Prime Ideals and Beyond", is available online at arXiv.
The NITheCS Internship Programme provides aspiring mathematicians with an opportunity to engage with research-level mathematics early in their academic journey. According to Dr Goswami, such an initiative is both profoundly beneficial and urgently needed, especially in the South African context.
