Josef Oosthuizen & Emily Sacke Explore the Beauty and Relevance of Mathematics in Our World. From Simplicity to Complexity, Mathematics Shapes Our Lives and Minds.

Mathematics is in everything around us, woven into the very fabric of our society and daily lives. It affects us in a variety of ways that many might not even be aware of, from the simple calculations we perform when we make purchases at our local Spar to the sophisticated algorithms that drive our digital gadgets and financial systems. It enables us to move around the world more confidently and precisely, making defensible judgments and logically resolving issues. Without mathematics, we would be unable to make sense of the intricate systems and processes that define our world and would be trapped in a sea of ambiguity.

Learning mathematics cultivates critical thinking, creativity, and problem-solving abilities, all of which are fundamental life skills. It encourages students to approach problems logically, reason abstractly, and communicate their ideas effectively. These skills enable students to think more creatively and critically, preparing them to handle the intricacies of the outside world.

We believe that everyone should appreciate the wonders of mathematics. If more people were aware of its beauty and importance, they would be more eager to learn about it.

For millennia, mathematicians have been captivated by the concept of infinity, both in theory and practical applications. The infinite series used to determine pi and the Hilbert space with unlimited dimensions are just a couple of examples. The idea of infinity continues to inspire new mathematical discoveries and insights.

Fractals are geometric shapes that exhibit self-similarity at different scales, this concept is another fascinating aspect of mathematics.They can be found in nature, such as in the branching patterns of trees and the forms of snowflakes, as well as in computer graphics and art.

Mathematicians have been fascinated by the concept of prime numbers for ages. They are numbers that can only be divided by itself and one. One would think that the qualities of prime numbers aren’t that interesting, but extensive studies about the distribution primes have proven otherwise. They have important applications in many fields such as cryptography and number theory.

Symmetry is a beautiful mathematical concept which can be applied in various ways, especially when applying geometry not only to equations, but also to art. The fact that mathematics is an integral part of how art is created and how our mind interprets and decides what is aesthetically pleasing is quite special.

Chaos theory is a subfield of mathematics that studies the behaviour of nonlinear dynamical systems, including weather, the stock market, economics, meteorology and planetary motion. These applications have prompted the creation of new mathematical methods and tools for the purpose of predicting the future.

An intriguing mathematical concept that is strongly related to chaos theory and fractal geometry is the Mandelbrot set. It is named after Benoit Mandelbrot, a French mathematician who initially discovered the set in the 1970s while researching on problems connected to complex numbers. The collection of complex integers known as the Mandelbrot set are those for which an iterative mathematical formula does not diverge to infinity. The Mandelbrot set’s distinctive and complicated patterns are produced by this formula, which yields a collection of values that may be displayed on a two-dimensional plane. Both mathematicians and artists have been captivated by the set, and the beauty and intricacy of the set continue to spur new mathematical ideas and discoveries.

Game theory is another subfield of mathematics that examines how actors interact strategically in fields like economics, politics, and biology. Game theory enables and assists our understanding of market behavior, the development of social norms, and the dynamics of conflict and cooperation.

Everything in the universe can be boiled down to basic mathematics. Mathematics is, after all, the language of the universe, and it is through mathematical principles that we can gain insights into the workings of the physical world around us.

Another marvel is that mathematics is the “be all end all” of music. It enables the comprehension and control of the numerous sound waves that produce musical tones. The mathematical principles of frequency, pitch, and amplitude of these waves are all essential to the production of music. The link between mathematical ideas and musical tones has been extensively investigated in the scientific community, and research suggests that using these concepts can result in novel and creative methods to music composition.

When we examine the physical laws that govern the behavior of objects and particles, we find that they all have the ability to be expressed mathematically. For instance, the Schrödinger equation provides a description of the wave functions that govern the motion of small particles. Similarly, the laws of thermodynamics are based on mathematical concepts like energy and entropy and can be expressed using equations that describe the behavior of systems in terms of energy transfer and transformation.

Mathematical methods can be used to analyze seemingly non-mathematical concepts such as emotions and psychology. Models have been used by researchers to better understand the dynamics of social networks and the spread of ideas and information. These models have also been used to study crowd behavior and the emergence of collective behavior in groups. Some aspects of the world may be difficult to simulate using mathematical techniques. Technology and our understanding of mathematical principles are constantly evolving and with that, we will hopefully find new ways to use mathematical language to describe and predict the complex behaviors of the universe.

Individuals can grow a deeper appreciation for the beauty and power of mathematics by investigating the previously mentioned and many other topics. Although many marvel at the beauty of mathematics, it can unfortunately be intimidating to certain people. This is a frequent occurrence due to a combination of internal and environmental factors. Women and minorities have historically been underrepresented in many scientific fields and have suffered systematic prejudices that prevent them from pursuing jobs in the area. Others may lack confidence in their abilities to think mathematically as a result of previous unpleasant experiences or a lack of support and encouragement.

Conventional teaching techniques frequently emphasize memorization and rote learning, which can be challenging and uninteresting. This method might be especially difficult for individuals who study differently or have learning impairments. For example, students with dyscalculia may struggle and believe they are unable to think numerically, not knowing that there are techniques that can help them. Many students also fail to recognize the relevance of mathematics in their lives and may not grasp how the principles they are learning apply to real-world situations.

We believe that everyone is capable of mathematical thinking. It is critical to emphasize that mathematical ability is not innate and can be developed through practice and hard work. We can help students develop a more positive attitude and improve their performance by fostering a growth mindset, which stresses the importance of effort and perseverance in learning. Mathematics is utilized in several practical ways, from calculating a tip at a restaurant to managing personal finances and comprehending fractions and ratios for following cooking recipes. Individuals who grasp concepts like inflation, and compound growth may make more educated judgments about saving for retirement or investing in the stock market.

Mathematics can be made more accessible and enjoyable for all students by changing teaching approaches to better fit diverse learning styles. Instructors may help to create a more inclusive atmosphere by fostering collaboration and debate. In mathematics, there are, more often than not, numerous ways of coming to the same conclusion. Therefore, it is important to stress the diversity of mathematical approaches and viewpoints. Pupils who are having difficulty may benefit from focused assistance such as tutoring, peer mentorship, or more resources. We can help students overcome learning barriers and achieve success by providing support that is tailored to their specific needs.

In conclusion, it is clear that mathematics is a fundamental part of human existence and that it is the language of the cosmos. Math is used to make sense of the world around us, from the simplest computations to the most intricate algorithms. It develops critical thinking, creativity, and problem-solving abilities, all of which are necessary in everyday life. Despite the challenges faced by individuals in learning mathematics, we believe that everyone is capable of thinking mathematically. With the right support and tailored teaching approaches to different learning styles, mathematics can be made more accessible and enjoyable for all.

As technology continues to evolve and our understanding of mathematical principles broadens, we can only expect to find new or improved ways to use mathematical language to describe and predict the complex behaviors of the universe. The beauty and importance of mathematics cannot be underestimated, and everyone should get to experience and appreciate its wonders.

### Josef Emile Oosthuizen

2nd Year Student at Stellenbosch University

### Emily Athalie Sacke

2nd year student at Stellenbosch University