Is mathematics an invention or a discovery?

Some believe that mathematics itself exists in nature, waiting to be discovered; while others believe that mathematics is entirely a 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 is quite difficult. However, have you ever wondered if mathematics itself exists in the universe, waiting to be discovered? Or is mathematics just something that some people deliberately invented? The answers to these questions are as complex as the calculations themselves.

Pythagoras's Theorem. (Illustration).

Believe it or not, mathematics is at the heart of our world today. Our smartphones, our cars, the construction of buildings, and even our weather forecasts rely on mathematics. Philosophers of mathematics have long debated an important question: Was mathematics discovered or invented?

Some people believe that mathematics exists within us and that the objects of study in mathematics are created by us. There are also philosophers who believe that mathematics exists independently of our thinking and has nothing to do with human existence. But what is the truth? To know the truth, let us first understand the history of mathematics.

Plato was a famous ancient Greek philosopher and mathematician who believed that mathematical entities were abstract and existed independently in their own world, outside of space and time.

The story of mathematics is as old as humanity, and it has evolved from simple arithmetic related to livestock numbers, to abstract concepts of complex studies of an object. It was not until 600 BC, when human civilization was stable and many professions began to appear, that mathematics had its initial development. People used mathematics to measure land, calculate personal taxes. Then, in 500 BC, Roman numerals appeared and they have been used to represent quantities ever since.

Scientists believe that basic mathematical functions such as addition and subtraction may have existed thousands of years ago in places like India, Egypt, and Mesopotamia. Advanced mathematics may have originated in Greece 2,500 years ago, when the mathematician Pythagoras came up with a famous equation— the Pythagorean theorem . However, historians believe that the theorem—the sum of the squares of the lengths of the two sides of a right triangle in the plane is equal to the square of the hypotenuse—was known around the world a thousand years before Pythagoras used it.

Since then, more and more mathematicians have tried to expand their understanding of mathematics. However, no one has a definite answer to the question "Is mathematics an invention or a discovery?".

We can see the Fibonacci sequence all around us. (Illustration).

At some point in history, people discovered that something existed before they did math; at other times, people took it upon themselves to invent different equations and methods to record what they had in mind.

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 existed in the early world of humanity and that all humans did was discover it—a view known as Platonism . The ancient Greek thinker and mathematician Plato believed that mathematical entities were abstract and existed independently in their own world, outside of space and time.

Some mathematical ideas are so fundamental that even if you don't discover them, someone else will. Mathematics is the language of science, and its structure is natural and inherent . Even if the universe disappeared tomorrow, eternal mathematical truths would still exist. It is our responsibility to explore them, understand their function, and build our knowledge to find solutions that can control physical events.

Many mathematicians support this view. They have discovered many eternal truths that have nothing to do with the mind that discovered them - such as there is no largest prime number, the decimal form of pi goes on forever.

Mathematics itself manifests itself in nature and contains answers to many universal questions. In nature, we can often find an example related to mathematics - the golden ratio.

The golden ratio describes everything from atoms, storms, faces, human bodies. (Illustration photo).

The Golden Ratio describes the most predictable patterns in the universe. It describes everything from atoms, hurricanes, 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 Proportion .

The golden ratio is derived 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 numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…

We can see the Fibonacci sequence all around us, such as seashells, animals, pyramids, and other unexpected places. Flower petals also follow the Fibonacci sequence. If you look closely, you will see that a flower can have a total of: 3, 5, 8, 13, 21, 34, or 55 petals. These phenomena support the argument that mathematical functions exist in nature and we are just left to discover them.

Some people oppose the idea that mathematics was discovered, such as the Anti-Platonists, who believe that mathematics was invented. In other words, mathematics is a human invention designed in a way that it can fully describe the physical world. To satisfy our needs, and accordingly, the human mind continues to create many different mathematical concepts.

If the universe disappeared tomorrow, everything like football, chess or any activity we invented would disappear, and so would mathematics.

Humans can learn about the workings of the universe by observing patterns that appear in nature. By abstracting shapes, lines, groups, etc. from the world around us, we create mathematical concepts and connect them to serve a purpose or just for fun.

Geometry and arithmetic develop from the ability to see and distinguish shapes such as circles, triangles, etc. We also use geometry to distinguish between straight lines and curves.

At first, we used natural numbers 1, 2, 3. to count the number of objects around us. Later, we invented more concepts, such as negative integers, rational numbers, irrational numbers, complex numbers. These extensions of mathematical concepts are designed to serve our different purposes.

If the universe disappears, everything disappears, including mathematics. (Illustration).

For example, if the temperature of a mercury meter drops below 0 degrees. Then, to describe a number less than 0, we will introduce the concept of negative integers and write -10 ^o C or -25 ^o C. Thanks to the process of creating new concepts based on what we see around us, we can truly say that mathematics is born from our mental perceptions and assumptions.

Some people think mathematics is a discovery, others think it is an invention, and the debate between the two could go on forever. Given that this question has been around for over two thousand years, it is unlikely that we will find a definitive answer anytime soon. However, what is clear is that mathematics does not care whether we think it was invented or discovered, or what role it played in its existence. Regardless of our views on the matter, mathematics will objectively play its role and continue to benefit humanity .