This article was automatically translated from the original Turkish version.
Undoubtedly, mathematics is one of the oldest and most important branches of human science. The origin of mathematical knowledge stems from the needs of early humans for measurement, counting, and calculation in their daily lives. Indeed, the earliest mathematical concepts arose from fundamental requirements such as counting hunted animals, tracking exchanged goods, and recording the passage of days.
The earliest traces of mathematics appear in archaeological finds dating back approximately 20,000 years, such as the Ishango Bones. The markings on these bones indicate the conscious use of numbers. Mathematics became more systematic in Mesopotamia (Sumerians), Egypt, and Ancient Greece.
The Sumerians developed a sexagesimal number system, which is still used today in measuring time and angles. In Ancient Egypt, mathematics played a crucial role in land surveying and pyramid construction. The knowledge gained from these practices later inspired Greek mathematicians. Figures such as Pythagoras, Euclid, and Archimedes transformed mathematics into an abstract system of thought.
Thus, mathematics not only served practical needs but also became one of the key tools for understanding nature and the universe. The foundations of modern advanced mathematical theories rest upon these earliest steps.
Boyer, C.B. "A History of Mathematics" links the origin of mathematics to human practical needs. According to Boyer, mathematics developed to solve problems arising in essential areas of life such as trade, agriculture, construction, and astronomy. From ancient times, humans developed primitive mathematical methods to:
• Count objects,
• Measure land,
• Calculate exchanges of goods,
• Track the movements of celestial bodies.
Boyer particularly notes that Mesopotamia and Ancient Egypt were the sites of the first major developments in mathematics. “The Mesopotamians developed a base-60 number system, while the Egyptians applied geometry to land surveying and pyramid construction.”
Boyer also states that early mathematicians were not only motivated by daily needs but gradually turned to mathematics due to intellectual curiosity and aesthetic considerations.
In his work “The Universal History of Numbers,” Ifrah presents the origin of mathematics primarily through the evolution of the concept of number. According to Ifrah:
• The discovery and use of numbers is one of humanity’s greatest intellectual achievements.
• The first concept of number emerged from the need to group and distinguish objects. Basic needs such as knowing how many animals one owned or how many days had passed drove the development of numbers.
• Early humans began keeping count using notches, sequences of stones, or marks on bones. The Ishango Bones (approximately 20,000 years old) are a significant archaeological evidence in this regard.
• Ifrah also emphasizes that numbers were not only used for practical purposes but, over time, also for more abstract aims such as religious rituals, astrology, and calendar creation.
According to Georges Ifrah, the first organized number systems were developed by the Sumerians in Mesopotamia. Around 3000 BCE, the Sumerians created a sexagesimal (base-60) number system. This system was recorded on clay tablets using cuneiform script. Ifrah highlights that the Sumerians elevated the concept of number to a highly advanced level and developed both oral and written systems.
During the same period, Ancient Egypt developed its own distinct number system. The Egyptians used hieroglyphs for numerical notation, with each decimal place represented by a different symbol. However, this system made calculations with very large numbers cumbersome.
Roman numerals (I, V, X, L, C, D, M) were developed during the Roman Empire. While practical for everyday use, this system hindered mathematical progress due to its difficulty in performing operations such as addition and multiplication. The greatest leap in the history of mathematics occurred with the emergence of the Hindu-Arabic numeral system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Developed in India and introduced to the West by Arab scholars, this system is decimal and positional. Its most important innovation was the inclusion of the concept of “zero.” Zero served both as a digit and as a placeholder, greatly simplifying complex calculations. Ifrah further explains why the Hindu-Arabic system was so revolutionary:
• Numbers could be expressed using a small set of symbols.
• Even simple operations could be performed easily with very large or very small numbers.
• The concept of zero enabled mathematics to advance to abstract levels.
In conclusion, according to Ifrah’s analysis, the evolution of number systems did not merely facilitate daily life but also laid the foundations for science, engineering, and the modern world.
The origin of mathematics through the eyes of famous scientists