Mathematics: Was it discovered or invented?

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Mathematics, often simply referred to as math, needs no introduction in our world. From our early school days to higher education, it’s a subject we all encounter. Math encompasses a vast domain of knowledge, involving numbers, formulas, geometry, shapes, intricate calculations, and more.

While some may question its relevance in their future careers, it’s crucial to recognise the myriad applications of mathematics in our daily lives. The study of mathematics has played a pivotal role in human evolution, sparking a profound question: Was mathematics discovered or invented? In this article, we will delve into this intriguing question.

Historical background

Before we explore whether mathematics was discovered or invented, let’s journey through its captivating history. The roots of mathematics can be traced back to around 3000 BC in West Asia and ancient Egypt. In its nascent stage, it encompassed basic arithmetic calculations, algebraic principles, and geometric concepts. These mathematical foundations found practical applications in taxation, commerce, trade, astronomy, timekeeping, and calendar creation.

The earliest hints of discovering mathematical principles emerge from the annals of Mesopotamia, a historical region in West Asia, and ancient Egypt. These texts suggest the application of fundamental mathematical ideas, including what we now recognise as the Pythagorean theorem. This implies that Pythagoras’ theorem, a cornerstone of mathematics, is among the most ancient and universally acknowledged mathematical techniques, following basic arithmetic and geometry.

As mathematics evolved, it took on diverse forms in various parts of the world, each contributing unique perspectives and methodologies to its development. Before the advent of Greek mathematics, problem-solving often relied on inductive reasoning based on specific observations. In contrast, Greek mathematicians adopted deductive logic to derive conclusions from definitions and axioms. Roman mathematics leaned towards practical applications, whereas Chinese mathematics stood out with its revolutionary decimal positional notation system, known as “rod numerals,” an advanced system for its time.

Mathematics continued to develop independently worldwide, crafting a multifaceted history characterized by diverse approaches.


The debate over whether mathematics was discovered or invented has raged for centuries. Both sides present compelling arguments, but definitive answers remain yet to be found. We are left with a plethora of questions. Would mathematics even exist in its current form if humanity never existed? Did we create mathematics to comprehend the world around us, or was it an inherent aspect of nature awaiting our discovery? Are all mathematical theorems and equations universally real? These questions have fueled intense debate.

Some proponents argue that mathematics, unlike the smart devices we use today, was not invented; it was discovered. They contend that the fundamental principles of math existed in nature, and we drew inspiration from them to unveil various theorems and formulas. A pivotal argument supporting this perspective is the universality of mathematics. Mathematical logic, concepts, formulas, and theories apply universally across the globe, transcending cultural and belief boundaries. This universality suggests that, rather than being an invention, mathematics is a discovery from the fundamental fabric of the world.

Plato, the ancient Greek philosopher, was a believer in this view. He believed that mathematical objects existed in a separate realm of reality. Platonism, a philosophical perspective, posits the existence of abstract mathematical entities independent of human thought. According to this view, mathematicians discover these mathematical truths rather than invent them.

Others argue that mathematics is discovered through the observation of natural phenomena. By scrutinizing the natural world and its complicated patterns, mathematicians unearth various relationships and principles. For instance, the Fibonacci sequence in plant growth patterns or the geometric properties of crystals exemplify how mathematics is uncovered through our exploration of nature.

Moreover, some maintain that mathematics is discovered because of its applicability in the real world. Mathematics permeates numerous fields, from engineering and science to economics and computer science. Its efficiency and effectiveness in solving everyday problems constitute a compelling argument for the discovery of mathematics.


Despite the prevailing belief that mathematics was discovered, there are compelling arguments suggesting that it was, in fact, invented. Mathematical structures, concepts, and systems are human creations, devised by mathematicians to comprehend the world around them. They proposed theorems, equations, and both theoretical and practical proofs. Without these mathematical pioneers, the complex mathematics we study today would not exist.

The history of mathematics attests to its invention. Great mathematicians introduced theorems, axioms, and other proofs to meet the needs of their time. For example, Newton and Leibniz independently developed calculus to facilitate their study and analysis of physics, demonstrating that mathematics can be a tool invented for specific purposes.

Additionally, paradoxes such as Russell’s paradox and Gödel’s incompleteness theorems arise from within mathematics itself, implying that mathematics is a human invention. Furthermore, mathematical concepts and theorems have evolved and adapted over time. New mathematical tools and theorems have emerged in various fields, indicating the malleable nature of mathematics and reinforcing the argument that it is an invention.

The question of whether mathematics was discovered or invented remains a formidable and enduring debate. Philosophers, mathematicians, and scholars continue to explore this intricate question from various angles.

In conclusion, the answer may be both. Mathematics, in its purest form, exists in the natural world, awaiting discovery. However, the process of uncovering, comprehending, and applying these mathematical principles is a human invention in itself; a testament to human curiosity, ingenuity, and the profound relationship between mathematics and the world around us.

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