In part 1 of this essay (see New Era edition of 10 November 2021), I shared my story of how I met Professor Günter Heimbeck for the first time in a public lecture at NUST. Professor Heimbeck’s lecture was deep and advanced, and it left me with questions. Three years later, I came across a book, The Geography of Thought that gave me a paradigm shift in terms of understanding the behaviour of great scholars.
As a result of this paradigm shift, I decided to have a talk with Professor Heimbeck. As I tracked him down, I discovered that after his retirement from Unam, he was back in teaching and he was now a Professor of mathematics at NUST, where he was teaching engineering mathematics. On the 18th of August 2016, I sat down with Professor Heimbeck in his office at NUST.
Professor Heimbeck appeared to me as a humble man. He was very old but looked very good and strong at his age (By 2016, Professor Heimbeck was 70 years old. He was born in 1946). Heimbeck was able to tell me a lot about the nature of mathematics. In my interview with him, I began by asking him what his area of specialization in mathematics is. Without hesitation, he confidently responded: “Translation Planes”. There was a tone of joy and pride in his voice as he said that, and his face lighted up with joy.
I could tell that he was really proud of what he does. “What is it all about?” I asked. He tried his best to explain it, but I could see that it is a topic of pure mathematics, and pure mathematics is very difficult to explain casually because it is something that is really far removed from reality. He pointed that Translation Planes is a sub-discipline of projective geometry, born out of a geometry theorem developed by the French architect, Girard Desargues (1591 – 1661). Heimbeck says that Desargues’ work was ignored by many mathematicians for nearly 200 years and only around the year 1864, was a collection of his work published. Heimbeck has been running with this sub-discipline of translation planes for years.
Professor Heimbeck holds a PhD in Groups of Motion and a Doctor of Science (D.Sc) in geometric algebra, which he both obtained from Würzburg University in Germany. After teaching at his alma mater for a few years, he later joined Wits University in Johannesburg (1984 – 1986) and from there he came to Namibia where he taught at Unam from 1987 until his retirement in 2011.
It was during these 25 years at Unam that Professor Heimbeck developed new results on translation planes. Today, there are four objects in mathematics that carry his name: 1) The Theorem of Glauberman-Heimbeck; 2) The Heimbeck Plane; 3) The Heimbeck Planes and 4) The Axioms of Ewald-Heimbeck.
The 2012 lecture
I began to bring Professor Heimbeck back to the 2012 lecture. He said that he had actually come across a problem of projective geometry in a geometry textbook, but what he noticed about the problem is that it was half-solved. He then decided to work on the problem and solve it completely.
His 2012 public lecture at NUST was therefore an opportunity to show to Namibia the solution he had come up with. As our discussion on pure mathematics continued, Professor Heimbeck mentioned something that really surprised me. I asked him a question concerning the application of mathematical theorems. And he responded: “No mathematician ever considers where a theorem can be used. That is not relevant.” When he said this, I looked at him surprised, and for a few seconds, I didn’t say anything. He saw that I needed more explanation on that statement and he continued: “our logic [as mathematicians] is that eventually a theorem will be applied somewhere.”
When he said this, I immediately realised that my question to him in the 2012 public lecture was inappropriate. When a mother gives birth to a newborn baby, you can’t ask the mother: “what is the use of this baby? In which area of life will this child contribute?” The mother cannot tell you with absolute certainty of the future of the child. Every mother is likely to say the same thing: “It is too early to tell.”
The child might turn out to be a robber; a drug dealer or it may turn out to be a doctor or a teacher. The point is that the mother loves the child because of what it is: a child. Her motive of getting a child is not so much a function of future usefulness.
There was nothing wrong with Heimbeck’s answer back in 2012. The solution he came up with was like a “child” to him. And there I was, asking him in what areas will his “child” be useful. I was the one who completely missed the entire purpose of his lecture: to marvel and to behold the beauty and elegance of the solution he had discovered.
I was trained as a math teacher in the former BETD programme, which had a strong practical orientation in its philosophy of learning and teaching. As a result, that orientation caused me to lean very strongly towards applied mathematics for many years, and that is why I asked a question about applications.
It is about understanding
At the end of my interview, Professor Heimbeck told me an interesting story about a group of prominent mathematicians who were giving a press conference in France.
They were announcing something important in mathematics, and one of the journalists who attended the event decided to pose a question to the group. The journalist asked: “Why do people do mathematics?” According to Heimbeck, the mathematicians were surprised at this rather strange and simple question that had nothing to do with their press conference, and so there was a bit of silence.
Finally, one of the mathematicians in the group, The British mathematician, John Conway (Combinatorial Game Theory) finally responded. He said: “Because we want to understand.”
Professor Heimbeck paused for a while, and in his thick voice filled with wisdom, he emphasised firmly: “The main thing in mathematics is understanding.” He pointed out that a student of pure mathematics is interested in understanding the mathematics and not just in using the formulae and theorems, as is often the case with engineering students.
Professor Heimbeck further emphasised that a science major or a math major must do much more mathematics than an engineering student.
This was a huge paradigm shift for me as a math teacher. For years in Khomas High School, I have always told learners: “The main purpose of studying mathematics is to solve problems.”
I never really emphasised and prioritized the issue of “understanding” that Professor Heimbeck stressed now. I reflected deeply on Heimbeck’s statement about understanding. Although mathematics is all about solving real-life problems, understanding is a critical element in the process of solving all kinds of problems. For years in Khomas High School, I have been asked questions by learners such as “Sir, what is the use of this algebra stuff.
Where will we ever use these things?” As a teacher, you are then forced to demonstrate to the learners the practicality of mathematics. And once learners are not convinced or impressed by the utility of a particular concept, they can easily label that concept as useless and irrelevant to their lives.
An excessive focus on the utility of knowledge can result in a misunderstanding of the real purpose of erudition. We pursue education not only because of the economic benefits it brings and the utility of knowledge, but because we want to understand the mysteries of nature.
Conclusion
I told Professor Heimbeck about my ideas of the Maths & Science Clinic System and the Engineers-in-the-Classroom (EiC) programme. He was very impressed and said that “it is a good idea, but you will have one problem: who is going to teach? You need quality teachers to teach. The idea is good, but without good teachers, you cannot do much.”
The Maths & Science Clinic System is an educational innovation that is currently being developed at the Centre for Advanced Research on Radical Innovation and Engineering (CARRIE).
The Maths & Science Clinic System is about creating innovative learning infrastructures, alternative schooling models, programmes and systems in order to support the learning and intellectual needs of future generations. May Professor Heimbeck serve as a model of the type of scholar that we want to produce in our Maths & Science Clinics.
*Salomo S. Mushinga is a mathematics teacher at Khomas High School, Founder of CARRIE and co-inventor of the Maths & Science Clinic System (with Ephraim Tutjavi of NYS). He writes in his personal capacity as a CARRIE researcher to create awareness of the Maths & Science Clinic System.