Mathematics is about the journey, not the destination

Join Rachel and Zea as they unravel the Journey of Mathematics, with their personal insights and perspectives.

Illustration by Sara Eskandari

What is Mathematics?

Would you believe us if we told you that Mathematics is more than memorizing formulas, proofs, and difficult integration problems? Mathematics is the study of numbers, systems, structures, and change. It can be applied to many other subjects including physical sciences, engineering and operations research. We can think of Mathematics as a logical system from which axioms, (which are the rules of math) are derived. These axioms are then used to produce the theorems and models we’ve been learning about since preprimary.

Where is Mathematics?

To many, Mathematics is this pointless concept invented for the greatly talented, but math is necessary for everybody. Mathematics is essential for navigating daily life, from the rules of currency to telling the time and even cooking and baking which has ratios of ingredients. Thus, Mathematics appears everywhere in life around us, whether we realize it or not.

The houses we live in were constructed by engineers through the use of mathematics. Our phones and computers operate on complex algorithms derived from Mathematics. Mathematics is also responsible for the pitch, tempo, and rhythm of music. Math is also present in nature’s patterns, for example, the Fibonacci sequence in flowers.

Mathematics is not a new concept, but in fact has been around for centuries. It was used to construct ships and was even used to build the pyramids in Egypt. Mathematics was also used to tell time through the use of sundials which relied on the angle of the shadow cast by the sun as it moved through the sky during the day.

Is creativity in Mathematics a myth?

Some people believe they are more “right brain” or creative and are not made to think Mathematically. They believe Math is this uniform, rigid subject that just does not “click” with them. However, they could not be more wrong. Math requires creativity in being able to visualize concepts and being able to invent innovative ways to solve them. There are also aspects of Mathematics that require “left brain” thinking, and thus Mathematics requires a combination of analytical and creative thinking.

Mathematics teaches us about logic in combination with creativity, therefore it becomes a unique experience for everybody. There is no one right way to do Mathematics. As long as the core principles are understood, they can be applied in infinitely many ways according to the limits of our creativity. Mathematics should not be a chore. Instead, it should be an entertaining way to ponder concepts that we are taught as facts in other subjects. Everybody should be able to experience the wonders, creativity, and enjoyment that should come with Math.

Illustration by Liani Malherbe

So, why do people view Math so negatively?

Most students have a negative outlook on Mathematics, with thoughts about Math being too difficult, stressful, and rigid. We believe this issue is due to both the way that concepts in Mathematics are taught, and how students deal with “failure” in Mathematics.

Most academic systems allow you to move on to the next grade if you achieved 50%. This, however, can be problematic because it means that a student continues to the next year where concepts are built on, without fully understanding the previous work. A vicious cycle of misunderstanding is created which makes it feel almost impossible to ever catch up. The focus of learning is then not on how interesting a new concept might be, but rather on trying to understand how the lecturer got there in the first place.

When a topic is taught, it is easy to memorize the given method, but it is the understanding that matters. The importance of understanding can sometimes be overlooked, with one way, the “right way”, being given instead of exploring unusual ways that could be interesting.

How can we change this?

The ultimate goal would be for academic systems to have a different assessment method or measurement based on your understanding of Mathematics. Having levels of Mathematics in school that are independent of the grade the student is in. But this will take some time and will not be in place by tomorrow. For now, we can change our mindset towards Math. Instead of thinking “How am I going to pass?” and “This has no purpose” we can try and think “Why does this method give this answer and what about a different method?” and “How can Mathematics be applied in my field of interest?” Maybe you can calculate how Mathematical principles apply to your music, gardening, or sports game?

We should realize that it is okay to struggle. Everyone struggles. The point is to try and try and try again until you eventually truly understand the problem and as a result, figure it out. Even though another person might snap a concept faster than you, it does not mean that you will not be able to get there. Once we change our attitude, we will be capable of so much more. We should remind ourselves that the aim of doing Mathematics is to make you think and not to memorize formulas and proofs.

What is the journey?

We thought about what makes Mathematics different to other subjects, and came to the conclusion that Math is not there to teach us facts or concepts, but rather to teach us how to think. Math is not about learning, but about understanding how to learn and think differently about concepts. Therefore, Mathematics is an integral (mind the pun) subject that provides the core basics for learning about everything else in life. It teaches us the methods of problem-solving and critical analysis, which is a vital skill for everyone to have. Mathematics is not about knowing the answer to an equation but understanding the journey that brought us to the results. Mathematics truly is for everyone.

Rachel Pereira

BSc Mathematical sciences, focal area Biomathematics Student, Stellenbosch University

Zea de Bruyn

BSc Bioinformatics and Computational Biology Student Stellenbosch University

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Title inspired by “Life is a journey, not a destination” by Ralph Waldo Emerson.

Russell’s Paradox

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