Two mathematics students from Stellenbosch University (SU) have made mathematical history. Their week-long internship under the mentorship of Dr Amatya Goswami at the University of Johannesburg (UJ) has resulted in a research paper accepted for publication in the prestigious Journal of Algebra and its Applications.
Mathematics often presents challenges that can be daunting for even the most seasoned scholars, yet what the two students accomplished in just one week is remarkable. Dr Goswami, a specialist in associative rings and algebras, general topology, and lattices, noted that it is exceedingly rare for undergraduate students to contribute publishable research to a reputable mathematics journal.
In November 2023, Ms Kerry Porrill, who was then a second-year mathematics student, and Ms Danielle Kleyn, a third-year mathematics student, embarked on an internship that is part of an initiative managed by the National Institute for Theoretical and Computational Sciences (NITheCS). Initially, Dr Goswami had planned to assign routine exercises based on Ring Theory. However, it quickly became evident that these students were operating at an advanced level far beyond his expectations.
“The challenge was quite interesting,” Kerry commented, reflecting on their first encounter with ring theory. “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.” The result was a significant number of highly non-trivial results demonstrated within their brief time together, leading to the eventual writing and submission of a research paper titled “On Structures of the Ring of Arithmetical Functions: Prime Ideals and Beyond”.
Both students have continued their academic pursuits in mathematics, ignited by the exposure to algebras and their research. Kerry is currently completing a BSc Honours in Mathematics with plans to specialise in algebra, while Danielle is pursuing her MSc in Mathematics, focusing on lattice theory and universal algebra under Dr Michael Hoefnagel’s mentorship.
With this achievement, the NITheCS Internship Programme has once again demonstrated its value to aspiring mathematicians. Dr Goswami remarks that this initiative provides a precious opportunity for students to engage with research-level mathematics early in their academic careers, a necessity in the South African context.
