Some people believe that mathematics exists in nature, waiting to be discovered, while others argue that mathematics is entirely a creation of the human brain. To this day, there is still no definitive answer to this question.
For most people, solving equations and memorizing long lists of mathematical formulas can be quite challenging. However, have you ever wondered if mathematics itself exists in the universe, waiting to be uncovered? Or is mathematics just something a few people have deliberately invented? The answers to these questions are as complex as the calculations themselves.
Pythagorean Theorem. (Illustrative image).
Whether you believe it or not, mathematics has become the center of our world today. Smartphones, cars, the construction of buildings, and even our weather forecasts all rely on mathematics. Throughout history, philosophers studying mathematics have always debated a crucial question: Is mathematics discovered or invented?
Some believe that mathematics exists within us and that the objects studied in mathematics are created by us. There are also philosophers who argue that mathematics exists independently of our thoughts and has no relation to human existence. But what is the truth? To uncover the truth, we must first understand the history of mathematics.
Plato was a famous philosopher and mathematician of ancient Greece, believing that mathematical entities are abstract and exist independently in their world, outside of space and time.
The story of mathematics has been around as long as humanity, evolving from simple arithmetic related to counting livestock to abstract concepts studied in complex objects. It wasn’t until 600 BCE, when human civilization stabilized and various professions began to emerge, that mathematics took its initial developmental steps. Mathematics was used to measure land, calculate personal taxes, and more. Then, in 500 BCE, Roman numerals appeared and have been used to represent quantities ever since.
Scientists believe that basic mathematical functions like addition and subtraction may have emerged thousands of years ago in places such as India, Egypt, and Mesopotamia. Advanced mathematics may have originated in Greece around 2,500 years ago when the mathematician Pythagoras presented a famous equation – the Pythagorean Theorem. However, historians believe that this theorem – the sum of the squares of the lengths of the two sides of a right triangle in a plane equals the square of the hypotenuse – had already existed worldwide a thousand years before Pythagoras utilized it.
Since then, more and more mathematicians have endeavored to expand their understanding of mathematics. Yet, no one has a definitive answer to the question “Is mathematics an invention or a discovery?”
We can see the Fibonacci sequence in everything around us. (Illustrative image).
At various points in history, humans have discovered that there is something that exists before they do mathematics; at other times, people have considered themselves the inventors of various equations and methods to record what they think in their minds.
Some believe that unlike objects like light bulbs and televisions, mathematics is not an invention but a discovery. The idea behind this viewpoint is that mathematics exists in the original world of humanity, and all humans do is uncover it – a perspective known as Platonism. The ancient Greek thinker and mathematician Plato believed that mathematical entities are abstract and exist independently in their world, beyond space and time.
Some fundamental mathematical ideas are so basic that even if you do not discover them, others will. Mathematics is the language of science, and its structure is natural and intrinsic. Even if the universe were to disappear tomorrow, eternal mathematical truths would still exist. Our responsibility is to explore it, understand its function, and build our knowledge to find solutions that can govern physical events.
Many mathematicians support this view. They have discovered numerous eternal truths that have nothing to do with the minds that uncovered them – such as there being no largest prime number, the decimal representation of pi being infinite…
Mathematics itself manifests in nature and contains answers to many universal questions. In nature, we often find examples related to mathematics – the golden ratio.
The golden ratio describes everything from atoms, storms, faces, to the human body… (Illustrative image).
The golden ratio describes the most predictable patterns in the universe. It describes everything from atoms, storms, faces, the human body, and galaxies. The golden ratio is the ratio of two parts, a and b, equal to (a + b) divided by the value of the larger part a, approximately 1.618, represented by the Greek letter φ. It is also known as the divine ratio.
The golden ratio originates from the Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci. This sequence has fascinated mathematicians, scientists, and artists for centuries. In this sequence, each number is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…
We can observe the Fibonacci sequence in everything around us, such as seashells, animals, pyramids, and other unexpected places. Petals also follow the Fibonacci sequence. If you look closely, you will see that a flower can have a total number of petals such as: 3, 5, 8, 13, 21, 34, or 55. These phenomena support the argument that mathematical functions always exist in nature, and all we do is discover them.
Some people oppose the idea of mathematics being a discovery, such as those who adhere to Anti-Platonism, who believe that mathematics is invented. In other words, mathematics is a human invention designed in a way that can fully describe the physical world. To satisfy our needs, the human mind continues to create various mathematical concepts.
If the universe were to disappear tomorrow, everything like soccer, chess, or any activity we invented would also vanish, and so would mathematics.
Humans can learn about the workings of the universe by observing patterns that emerge in nature. By abstracting shapes, lines, groups, etc., from the surrounding world, we create mathematical concepts and connect them for a purpose or simply for entertainment.
Geometry and arithmetic developed from the ability to see and differentiate shapes like circles and triangles… We also use geometry to distinguish between straight and curved lines.
At first, we used natural numbers 1, 2, 3… to count the objects around us. Later, we invented many more concepts, such as negative numbers, rational numbers, irrational numbers, complex numbers… These extensions of mathematical concepts are designed to serve our various purposes.
If the universe disappears, everything will also disappear, including mathematics. (Illustrative image).
For example, if the temperature of a mercury thermometer drops below 0 degrees. Then, to describe a number less than 0, we will introduce the concept of negative numbers and write -10oC or -25oC. Thanks to the process of creating new concepts based on what we observe around us, we can truly say that mathematics was born from our perception and mental assumptions.
Some argue that mathematics is a discovery, while others claim it is an invention, and the debate between these two viewpoints may last forever. Given that this question has existed for over two thousand years, it is unlikely we will soon find a perfect answer. However, it is clear that mathematics does not care whether we think it is an invention or a discovery or what role it plays in its existence. No matter our perspective on this issue, mathematics will fulfill its role objectively and continue to benefit humanity.
