Prof Jan Harm van der Walt, who is hailed for his clear explanations of calculus on YouTube, chats about his foray into mathematics, his many responsibilities within the scientific community and his recently awarded NRF C1 rating.

Professor Jan Harm van der Walt is the first to admit that he isn’t in a discipline that lends itself to party conversations.

“I’m interested in vector lattices, convergent structures and spaces of continuous functions,” says the mathematician about these concepts that are not instantly recognisable to mere mortals. “I am also a mere mortal,” he adds with a smile.

Yet when Prof Van der Walt explains his work, he brings it to life in the clearest way possible, as proven by the comments on his YouTube channel about a calculus course at the University of Pretoria (UP), where he is an associate professor in the Department of Mathematics and Applied Mathematics.

“Hopefully you are doing well somewhere else other than YouTube with your great teaching skills,” one commentator says. “This video was really helpful, and the way you explain the process is very clear. I wish more teachers had this way to explain proofs,” says another.

The 84 videos he has posted have generated 35 988 views.      

“It has accumulated over the years,” Prof Van der Walt says modestly. “I haven’t made new ones in a long time. We made videos for some courses during the pandemic, but those aren’t publicly available on YouTube. Students say it helped them, so I suppose that’s good feedback.”

His explanation of his discipline is lucid: “Mathematics, you may have heard, is the language of science. Linguists study the structure of languages and how they evolve. So what mathematicians do, what is considered pure mathematics – I’m not overly fond of the distinction, but let's stick with that – is kind of akin to being the linguists of science. We study the language of science; we study the structure of this language. Within this language, there are various kinds of abstract structures, and the abstract structures in which I am interested are vector lattices, convergent structures and spaces of continuous functions. And these are all interrelated.”

They fall into a field known as positivity, which involves, among other things, he says, order in the sense of one object being bigger or smaller than another. This makes it useful to describe things like mathematical models of population sizes, and so some researchers use these structures in their studies of population dynamics.

In July, Prof Van der Walt attended a workshop on positivity and Banach spaces at the Chern Institute of Mathematics in Tianjin, China. He was a member of the workshop’s scientific committee. He regards travel like this as one of the fringe benefits of an academic career. These events also provide opportunities to communicate with like-minded colleagues, which is particularly valuable when you delve daily into a field that doesn’t make for light banter.

It is therefore no surprise that Prof Van der Walt enjoys collaborations. Internationally, he is involved with Prof Marcel de Jeu of Leiden University in the Netherlands in research on vector lattices of continuous functions. They also each coordinate the funding of close to R1.5 million that they have received from the European Union Erasmus+ programme for student and staff exchanges from 2022 to 2025. This four-year grant follows a previous one equivalent to just over R500 000.

Together with Dr Marten Wortel of UP, Prof Van der Walt also collaborates with two other colleagues from Leiden University, Prof Onno van Gaans and Prof Mark Roelands, on the compactness of order intervals in partially ordered vector spaces. And Dr Wortel and he have another project with Xingni Jiang of Sichuan University in China, dealing with vector-valued integration. Prof Van der Walt also has an ongoing project with Prof Vladimir Troitsky, Dr Michael O’Brien and Dr Eugene Bilokopytov of the University of Alberta in Edmonton, Canada and Dr Jurie Conradie of the University of Cape Town, on convergence structures.

Additionally, he is very active in mathematical circles locally. Prof Van der Walt is on the organising committee of the 67th annual conference of the South African Mathematical Society (SAMS) that UP is hosting from 4 to 6 December. About 200 delegates are expected. He is also on the editorial board of SAMS’ annual journal, Quaestiones Mathematicae. SAMS aims to advance mathematics in South Africa, though it is not one of those organisations that sounds good on paper only.

“They try to contribute and influence government policy as it impacts mathematics, both at research and tertiary education levels, and at secondary and primary education levels,” Prof Van der Walt says.

He has a keenly developed sense of responsibility to his discipline. He is eager to play his part and to do it to the best of his ability. Besides his involvement with SAMS, at UP, he is the mathematical sciences’ representative in the Faculty of Natural and Agricultural Sciences’ Teaching & Learning Committee, and was previously on its examination and (student) appeals committees. He also reviews grant applications for the National Research Foundation (NRF). He brings a strong sense of duty to these positions.

“It’s something that has to be done and has to be done well, and it’s part of your service to the scientific community,” he says.

Prof Van der Walt was recently awarded an NRF C1 rating, which means he is regarded as an established researcher who enjoys considerable international recognition or has contributed to a new thinking, new direction and/or new paradigm. He has advanced a notch with each rating, having received a Y2 in 2012, which recognised him as a researcher with potential to establish himself in his field, and a C2, or established researcher, in 2018.

“It’s good to know your work is recognised as valuable by your peers. That, for me, is the real value of the rating, that I am doing something that other people also consider meaningful and interesting.”

Prof Van der Walt is a UP person. He did all his studies at UP, which also happens to be the university his parents and his sister attended. And conveniently, it’s the university closest to his childhood home, having grown up outside Hartbeespoort on a smallholding until he was 14, when they moved to the town itself.

Staff in his department all “get along well and it’s a supportive environment”, he says. The department – one of the largest at UP and in Africa, with more than 20 000 students enrolled in mathematical modules – was ranked first in South Africa on the 2024  Quacquarelli Symonds (QS) World University Rankings.

Being an academic was always on the cards for Prof Van der Walt. He wanted to be a theoretical physicist, got roped into actuarial science, and when he realised while at university it was possible to have a career in maths, swopped to that in his third year at UP. He graduated with a PhD at the age of 27.

To relax, Prof Van der Walt enjoys working in the garden, and playing with his children, aged 10 and 12.

“They have not yet outgrown me,” he says with a smile. He also enjoys reading; right now, he is reading Charles Dickens’s Hard Times.

“Books like that, like the books by Tolstoy, are classics, and they're classics because the story remains relevant. It persists. It still has meaning. And of course, they are good writers.”