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Some people believe that mathematics exists inherently in nature, waiting to be discovered; while others believe that mathematics is entirely the creation of the human brain. And to this day, there is still no definitive answer to this question.
For most people, solving math problems and memorizing long lists of mathematical formulas can be quite challenging. However, have you ever wondered whether mathematics itself exists in the universe, waiting to be discovered or not? Or is mathematics just something that some people intentionally invent? The answers to these questions are as complex as mathematical calculations.
Whether you believe it or not, mathematics has become the centerpiece of our world today. Smartphones, automobiles, building constructions, and even our weather forecasts all rely on mathematics. From ancient times to the present, philosophers studying mathematics have always debated an important question: Is mathematics discovered or invented?
Some people believe that mathematics exists within us and the objects studied in mathematics are created by us. There are also philosophers who believe that mathematics exists independently of our thoughts and has nothing to do with the existence of human beings. But what is the truth? To know the truth, first, let's understand the history of mathematics.
The story of mathematics has existed for as long as humanity, and it has evolved from simple arithmetic related to the number of livestock to abstract concepts in the study of complex objects. It wasn't until 600 BCE, when human civilization stabilized and various professions began to emerge, that mathematics began to develop initially. Mathematics was used to measure land, calculate personal taxes, and so on. Then, in 500 BCE, Roman numerals appeared and they have been used to represent quantities ever since.
Scientists believe that fundamental mathematical functions such as addition and subtraction may have emerged thousands of years ago in places like India, Egypt, and Mesopotamia. Advanced mathematics may have originated from Greece 2,500 years ago, when mathematician Pythagoras proposed 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—existed worldwide a thousand years before Pythagoras used it.
Since then, more and more mathematicians have been striving to expand their understanding of mathematics. However, no one has a definitive answer to the question 'Is mathematics an invention or a discovery?'.
At certain points in history, humans have discovered that something existed before they did mathematics; at other times, humans have claimed to have invented various equations and methods to record what they think in their heads.
Some people believe that unlike objects like light bulbs and televisions, mathematics is not an invention but a discovery. The idea behind this view is that mathematics exists in the primordial world of humanity and all humans do is discover it - a viewpoint called Platonism. Ancient Greek philosopher and mathematician Plato believed that mathematical entities are abstract and exist independently in their world, outside of space and time.
Some basic mathematical ideas are so ingrained that even if you don't discover them, others will. Mathematics is the language of science and its structure is inherent and innate. Even if the universe disappears tomorrow, eternal mathematical truths will still exist. Our responsibility is to explore it, understand its function, and build our knowledge to find solutions to control physical events.
Many mathematicians support this view. They have discovered many eternal truths unrelated to the mind that discovered them - such as there is no largest prime number, the decimal form of pi extends infinitely...
Mathematics itself manifests in nature and holds answers to many universal questions. In nature, we often find an example related to mathematics - the golden ratio.
The golden ratio describes the most predictable patterns in the universe. It describes everything from atoms, storms, faces, human bodies, to galaxies. The golden ratio is the ratio of two parts a and b is (a + b) divided by the value of the larger part a, approximately 1.618, represented by the Greek letter φ. It is also called the Divine Proportion.
The golden ratio originates from the Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci. The Fibonacci sequence has fascinated mathematicians, scientists, and artists for hundreds of years. In this sequence, each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...
We can see the Fibonacci sequence in everything around us, such as seashells, animals, pyramids, and unexpected places. Flower petals also follow the Fibonacci sequence. Upon careful observation, you will notice a flower may have a total number of petals: 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 that mathematics is discovered, such as Anti-Platonists, who believe that mathematics is invented. In other words, mathematics is a human invention designed to fully describe the material world. To satisfy our needs, and consequently, the human mind continues to create various mathematical concepts.
If the universe disappeared tomorrow, then everything like football, chess, or any activities we invented would also disappear, and so would mathematics.
Humans can understand the workings of the universe by observing patterns appearing in nature. By abstracting shapes, lines, groups... from the surrounding world, we create mathematical concepts and connect them to serve a purpose or simply for entertainment.
Geometry and arithmetic stem from the ability to perceive and differentiate shapes like circles, triangles... We also use geometry to distinguish between straight and curved lines.
Initially, we used natural numbers 1, 2, 3... to count the quantity of 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.
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. Through the process of creating new concepts based on what we see around us, we can truly say that mathematics is born from our perception and mental assumptions.
Some believe mathematics is a discovery, others believe it's an invention, and the debate between these two views may linger indefinitely. Considering this question has existed for over two thousand years, it's unlikely we'll find a perfect answer soon. However, what's clear is that mathematics doesn't care whether we think it's invented or discovered or what role it plays in its existence. Regardless of our perspective on this issue, mathematics will play its role objectively and continue to benefit humanity.
