This article explains how the abstract concept of “number” in math differs from the concrete numbers we use in everyday life. It also covers the different ways numbers are represented and their historical and cultural meanings, focusing on the decimal system, and discusses the impact of mathematical thinking on other disciplines and human thought processes.
Number is an extremely abstract concept. The numbers we use in everyday life refer to concrete objects, but their nature is far from concrete. For example, when we say “five apples,” the number “5” refers to the number of apples, but it doesn’t include any of their other characteristics, such as color, shape, or taste. From this perspective, numbers are simply a tool for representing quantity, independent of any specific object. Nevertheless, numbers have a universality that can be applied to many things. This is why we use numbers to make sense of the world, to bring order, and to simplify complex situations. The numbers we use take on meaning in some way through their connection to an object, but ultimately remain very abstract concepts on their own.
However, the concept of a number can also change depending on the object it is used for and the person who gives it meaning. In this sense, the concept of “number” as used in mathematics does not refer to a concrete object that we use in everyday life, but is merely a symbol that expresses the number of objects, and no longer has the characteristics of the object, but only the characteristics of the number. This is because math is a discipline that explores the abstract world beyond our everyday experience. The “number” in math is just a symbol that represents a quantity and has no meaning or emotion in itself. The concept of mathematical numbers is universal, abstract, and completely detached from physical reality.
In the end, the representation of numbers appears to be a means of representing all things, but in reality, mathematical numbers represent nothing more than abstractions, nothing more and nothing less. Nevertheless, we use these representations of mathematical “numbers” to generalize different concepts of numbers, to identify common properties, and to facilitate computations. Without the concept of mathematical numbers, we would not be able to perform even everyday calculations. Furthermore, mathematical number representation is not only a tool for understanding numbers in everyday life, but also for expanding the world of infinite numbers beyond our perception. In fact, the concept of infinity in mathematics is something we cannot experience, but it is logically defined and handled through numbers.
If you remember the first time you encountered a number, it was probably a natural number. As the name suggests, natural numbers are the most basic numbers that can be found in nature. For example, when we hold an apple in one hand and two apples in the other, we naturally recognize the concepts of “1” and “2”. These natural numbers become very familiar to us through everyday experience, and we recognize the basic laws of arithmetic without having to learn them in school or have someone teach them to us. Numbers are an important tool for organizing human thought, and the concept of numbers is intertwined with every phenomenon in the world we experience. As such, the natural numbers are not just the beginning of mathematics; they have a very important place in the human thought process.
These fundamental laws of arithmetic are proved at a basic level with real, concrete objects, such as figures. However, in order to make the proofs more general and complete, it is necessary to generalize the numbers, and to do so, the natural numbers are represented by common letters. The different symbols we use in math class are also a way to represent these generalized concepts precisely. They are designed to make the application of mathematical laws more efficient in certain situations and play an important role in simplifying and solving complex problems.
There are many different ways to represent numbers. In ancient Babylonia, the hexadecimal system was also used, and as a result of its influence, the current unit of time or angle is represented by 60. This shows that mathematical representation is not just an academic discipline, but is also deeply influenced by cultural and historical factors. The most common representation we use today is the decimal system. The decimal system is very useful because it allows us to represent an infinite number of numbers with just 10 digits. But why decimal, and not octal or hexadecimal? It has a lot to do with human physics. The tools we usually use to count are our fingers. When you see young children counting on their fingers, it’s easy to understand where the decimal system came from.
The decimal system has had a huge impact not only on math, but also on cultural and economic activities. For example, in the Indus civilization of ancient India, the decimal system was the basis of metrology, which allowed them to create an efficient system for architecture, trade, agriculture, and more. By using the decimal system, humans were able to easily handle more complex calculations, which was one of the major contributing factors to the development of civilization.
The concept of number and the ability to express numbers in a simple way led to further developments in mathematics, such as the discovery of rules for numbers, such as the sequence of equivalences and the sequence of proportions, and the discovery of ways to prove numbers through mathematical induction. This allowed us to experience an expansion of mathematical thinking. Of course, these mathematical expressions are not perfect. Math is always changing and evolving, and new theories and discoveries are constantly being made. However, these developments have helped us understand the wider world through mathematical thinking and have had a major impact on the development of other disciplines.
After all, the discoveries of math and the concept of number have not just satisfied academic curiosity, but have also played an important role in the development of science, economics, philosophy, art, and many other fields. In the future, math will continue to play a central role in humanity’s intellectual pursuits, offering countless possibilities and challenges that we don’t even know about.
