In this article, Italo and Caeden discuss how mathematics should be accessible to everyone. They describe how mathematics can be used in the different aspects of life.

The official International Day of Mathematics theme, “Mathematics is for everyone,” is a call to action to challenge the notion that mathematics is only for the “really intelligent.” Mathematics is a fundamental subject that underpins many areas of life, from science and technology, finance and medicine, to art and music. In this article, we will discuss the accessibility of mathematics to everyone as well as its value in all areas of life by drawing links to topics covered in the Foundations of Abstract Mathematics (FAM) 278 course, headed by Prof. Zurab Janelidze at Stellenbosch University.

Set theory is a fundamental discipline in mathematics that can be applied in various branches of the field. The study of sets is essential to many areas of mathematics, including topology, number theory, and algebra. However, the beauty of set theory is that it is not limited to the realm of mathematics; it can be understood and applied in everyday life (Stanford, 2023).

We all possess a natural intuition for the concept of a set, even if we do not use mathematical language to express it. The idea of a set is intuitive and can be applied in various contexts. For instance, we may discuss the set of books we own, which can be used to organize our reading materials. We may also discuss the set of individuals we know, which can be used to classify and categorize our social relationships (Stanford, 2023).

Moreover, set theory can be used to describe abstract concepts that may be difficult to understand without the use of mathematical language. For example, the concept of infinity can be difficult to comprehend, but it can be described using set theory. The set of natural numbers is an infinite set, and we can use set theory to describe the properties of this set.

Subsequently, the study of axiomatic incidence geometry, which focuses on geometric objects and their relations, including the properties of objects such as points, lines, and planes, is also an essential topic that demonstrates the universal nature of mathematics. The field of incidence geometry helps individuals understand and describe their innate sense of space and geometry more precisely. The practical applications of incidence geometry make it a useful tool for everyone. Whether you are an architect designing a building, a surveyor mapping a plot of land, or a physicist studying the behavior of light, the principles of incidence geometry can be applied to solve problems and develop new ideas (Stanford, 2021).

The usefulness of incidence geometry extends beyond the technical applications mentioned above. Understanding the principles of incidence geometry can aid us in better understanding the universe we live in. For example, by understanding the concept of intersecting lines, we can better understand the relationships between different objects in space. By studying the nature of space and the relationships between objects within it, we can gain a deeper appreciation for the beauty and complexity of the universe (Stanford, 2021).

Axiomatic arithmetic, another critical area of mathematics, examines the properties of natural numbers and their relationships, including the basic operations of addition, subtraction, multiplication, and division. Individuals employ arithmetic in various daily activities, such as computing the total cost of groceries or calculating the tip at a restaurant. Axiomatic arithmetic offers a better understanding and definition of these operations, enabling individuals to view the underlying relationships between them (Stanford, n.d.).

Furthermore, the accessibility of arithmetic can help break down barriers between people from different cultures and backgrounds. Mathematics is a universal language that transcends cultural and linguistic boundaries. By understanding the principles of arithmetic, individuals can communicate and collaborate more effectively with people from diverse backgrounds.

Consequently, it is essential to recognize that mathematics can be enjoyable. Mathematics is not just a dry and abstract discipline solely applicable to academics and professionals. There are various ways to make mathematics engaging and entertaining, such as art and music. By making mathematics enjoyable, we can incentivise more individuals to engage with the subject and recognize its relevance in their daily lives.

The significance of these topics is that they all provide individuals with tools to comprehend and describe the world around them. By studying sets, incidence geometry, and arithmetic, individuals can acquire a deeper understanding of the world and the relationships between different objects and concepts. Furthermore, mathematics is not only essential for understanding the world but also for problem-solving and making new discoveries. Mathematics is used in a wide range of fields, including music, literature, and philosophy. By studying mathematics, individuals bridge the gap between abstraction and reality. Pyotr Ilyich Tchaikovsky was one of the greatest composers of the Romantic era. Tchaikovsky had a deep interest in mathematics, so much so that he would frequently discuss mathematical concepts with his friends and colleagues.

Tchaikovsky was particularly interested in the mathematics of music theory, specifically the application of mathematical principles to his composition. He was fascinated by the mathematical relationships that exist between musical intervals, chords, and scales, and he believed that understanding these relationships was essential to composing music that was both structurally sound and aesthetically pleasing.

One of Tchaikovsky’s most famous compositions, the “1812 Overture,” is an example of his interest in Mathematical symmetry. The overture is structured symmetrically, with a central theme that is repeated in a modified form at various points throughout the composition. This use of symmetry creates a sense of balance and unity that is integral to the work’s grandiosity (Britannica, 2021).

Another notable example is French troubadours. During the Middle Ages, French troubadours are said to have invented the common ABAB rhyming scheme that we have all come to love today. The ABAB rhyme scheme is another way in which mathematics can be used in seemingly unrelated fields such as poetry. Due to the cyclic and arithmetic nature of this rhyming scheme, this gives rise to the auditory pleasure that a listener experiences.

Another noteworthy individual was Plato. He was a philosopher who recognized the importance of mathematics in understanding the world. He believed that mathematics was not just a tool for measuring quantities but a way of grasping the nature of reality itself. In Plato’s view, mathematical concepts were not just abstract ideas but were rooted in the real world, and the study of mathematics was a way to access the underlying forms or ideas that constituted reality. Plato also recognized the importance of mathematics in the education of the ruling class. He believed that the study of mathematics was essential for the development of the mind and for the cultivation of the virtues of wisdom and justice. In his famous work, “The Republic,” Plato argued that mathematics should be a central part of the education of the philosopher-kings who would govern the ideal city-state (Stanford, 2009).

Mathematics is a subject that should be accessible to everyone, regardless of their background or natural abilities. It is not an innate talent that some people have but rather a skill that can be developed through practice and hard work. Srinivasa Ramanujan, a self-taught mathematician from India, is a perfect example of this. Despite having no formal education in mathematics, Ramanujan made significant contributions to several areas of the field (Stewart, 2015).

Ramanujan’s early life was not easy. He grew up in poverty and had to drop out of school due to financial difficulties. However, he continued to pursue his interest in mathematics on his own, reading books and working on problems in his spare time. His work eventually caught the attention of a British mathematician named G.H. Hardy, who recognized Ramanujan’s talent and invited him to study in England (Reddy, 2021) (Stewart, 2015).

In England, Ramanujan continued to make significant contributions to mathematics, including developing new theories and formulas in areas such as number theory and analysis. His work has had a lasting impact on the field and has inspired many other mathematicians to pursue their interests and passions (Reddy, 2021) (Stewart, 2015).

Ramanujan’s story demonstrates that mathematical ability is not limited to individuals with formal education or high IQ scores. It is a skill that can be developed through dedication and hard work. By promoting the idea that mathematics is for everyone, we can encourage more people to pursue their interests in the subject and make important contributions to the field.

In conclusion, the official international day of Mathematics is celebrated under the theme “Mathematics is for everyone,” which challenges the idea that only the “really intelligent” can excel in mathematics. The text discusses how mathematics is accessible to everyone and has value in all areas of life. The study of sets, axiomatic incidence geometry, and arithmetic provides individuals with tools to comprehend and describe the world around them. Mathematics is used in a wide range of fields, including music, literature, and philosophy, bridging the gap between abstraction and reality. By making mathematics enjoyable, more individuals can engage with the subject and recognize its relevance in their daily lives.

### Italo Marini

2nd-year Student, Computer Science, Stellenbosch University

### Caeden Telfer

2nd year student, Computer Science, Stellenbosch University

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