(Published - 8 April 2020)
Topology is, broadly speaking, the study of shapes and forms - but it’s not all circles and squares. It’s a branch of pure mathematics concerned with properties of geometric forms that remain invariant under certain transformations, such as bending or stretching, and it’s been labeled as one of the most challenging fields in pure mathematics.
That challenge is part of what drew Mbekezeli Sibahle Nxumalo to pursue his MSc in Pure Mathematics in Topology and Category Theory from the University of the Western Cape - and to become one of the first to do it cum laude (passing with 82%) for his thesis. Ultrafilters and compactification. This follows from the Cum Laude (80%) average he received in 2017 for Bsc (Hons) Physical Sciences.
“Topology is used in a number of fields, such as Biology (to study the effects of certain enzymes on DNA), Physics (condensed matter physics, quantum field theory and physical cosmology), Data analysis, Robotics, Games and Puzzles and Fiber Art,” Mbekezeli explains. “Category Theory is a toolset for describing the general abstract structures in mathematics. And as someone who likes a mental challenge, how could I resist it?”
The proud Zulu youngster has come a long way from rural Ntumbane, Pongola, North of KwaZulu-Natal, where he was raised as the son of struggling parents.
“My father used to sell snuff (Intsu). My mom used to gather wood from a mountain and sell them for our survival, and she used to work in other people's maize fields,” he recalls. “I never wore a new uniform until I finished matric. I can't even mention having Christmas clothes.”
Mbekezeli isn’t done with maths just yet. He’s recently been appointed as an associate lecturer at UWC’s Mathematics Department, and plans to enrol for his PhD in Pure Mathematics in the second semester.
Mbekezeli talks about his achievements, his undying love for mathematics, and his plans for the future.
Why - and how - did you switch to pure maths after doing so well in physics?
I’ve always had an undying love for Mathematics. I ended up doing physics because of funding, and because it was the next best thing (there’s a lot of maths in physics, if you didn’t know). Dr Razafindrakoto from UWC’s Department of Mathematics took a big risk by offering me a chance to do a Msc in Pure Mathematics without having gone through Honours in Mathematics - but it paid off in the end, I think.
Why Topology and Category Theory?
I chose to study pure mathematics since it improves one's logic and analytical skills. And in Topology and Category theory, in particular, you get to do a lot of analysis and logic, while touching on a number of different fields of pure mathematics. There’s so much to learn and explore! So far, I am still enjoying it, and I don’t regret my decision at all.
What do you do when you’re not exploring the mysteries of mathematics?
Well, I do like to play games - especially Candy Crush or Sudoku. And I watch pretty much anything that has to do with lions. They’re awesome.
So what’s next?
I have a number of projects to explore as a way of giving back to the community through my mathematical and physical skills, and I’ll probably pursue some of them while I’m doing my PhD. My dream is to become one of the best pure mathematicians in the country - and to use everything that I’ve learned to improve other people’s lives and make a difference.
Any role models who’ve made an impression on your life?
Funny enough, both of my main role models are Mr Dube. The first Mr Dube taught me Mathematics in Grade 12; he motivated and encouraged me to always work hard and not lose focus, and he was one person who always saw the best in me. And then there’s Professor Dube from UNISA, whose hard work and dedication have made him one of the most prestigious South African professors of Pure Mathematics, and motivate me to do better every day.
What advice do you have for other students who want to achieve success?
To people who are in my situation, I say, believe in yourself. Your background will always be part of your journey, but it shouldn't define you. Fight against all the negative powers that your background brings to block you. If I could do it, what can stop you?