The development of mathematical notation is a fascinating journey that reflects humanity's growing understanding of abstract concepts and problem-solving approaches. In ancient times, early mathematicians relied heavily on visual symbols that held both specific and contextual meanings. These symbols were often derived directly from real-world scenarios, particularly practical problems involving measurement and calculation. For example, the roots of geometry trace back to early efforts to measure land, calculate areas, and determine distances, playing a crucial role in civilizations like Egypt and Mesopotamia.

Ancient Egyptian scribes used a set of distinct symbols to perform basic arithmetic operations. For instance, a symbol representing a leg extended forward could signify addition, whereas a backward-lying leg indicated subtraction. Similarly, Mesopotamian civilizations developed a sophisticated numerical system that included symbols for each power of ten. Their numerical notation is strikingly similar to modern conventions, with symbols explicitly representing units, tens, hundreds, and so on. Remarkably, they also devised symbols for zero as a placeholder by around 800 BC, a groundbreaking concept that laid the foundation for the development of zero as a number.

Moving forward, during the classical Greek period, mathematics evolved into a more formal and deductive science. The works of Plato and other Greek philosophers established a philosophical foundation that distinguished between pure mathematics—the study of abstract structures—and applied mathematics, which focused on practical applications. Greek mathematicians introduced deductive reasoning, axioms, and proofs, transforming mathematics into an intellectual discipline based on logical certainty.

The Greek numeration system borrowed heavily from earlier Egyptian practices but adapted them into a distinct framework. They used symbols to represent specific quantities, such as four vertical lines for the number four. The symbol for five, represented as π (pi), was a significant evolution, and ten was depicted with a triangle. The term "decimal" itself derives from the Latin "decem," meaning ten, highlighting the importance of ten-based systems in Greek numeration. These numerical conventions were later adopted and modified by the Romans and other civilizations, influencing the development of mathematics across cultures.

Throughout history, the evolution of mathematical notation has been driven by the need for efficiency, clarity, and universal comprehension. From simple tally marks to complex algebraic symbols, each development reflects advances in human thought and communication. Today, the symbols we use—such as plus (+), minus (-), multiplication (×), and division (÷)—are universally recognized and form the backbone of modern mathematics and sciences. Their origins trace back millennia and symbolize humanity’s enduring quest to understand and quantify the universe.