Mathematics is the foundation of all sciences and has come a long way since humans started counting. But when did humans start doing math?
The answer is complicated because abstract mathematics is thought to be different from counting, even though counting is fundamental to mathematics, and because many advanced types of mathematics, such as calculus, have only been developed in the last few hundred years.
The Origin of Counting
Humans could not have mastered complex and abstract mathematics without first learning to count. Researchers have found evidence that humans learned to count tens of thousands of years ago.
In 1950, they discovered Ishango bone fragments in Congo, Africa, which showed that Homo erectus had been practicing some form of counting for about 20,000 years.
Each bone fragment is about 10 centimeters long, possibly from a baboon or a wildcat. Dozens of parallel notches on the surface of these bones are believed by scientists to be a form of counting of some kind of object.
And in 1970, archaeologist Alexander Marshack argued that this was a form of lunar calendar with six months per year.
In addition, researchers also found Lebombo bones in southern Africa dating back about 43,000 years. These bones also had cut marks and possibly a calculation representing the 29 lunar days of a lunar month or a woman's menstrual cycle.
Danish historian of mathematics Jens Hoyrup says we cannot be sure of the very ancient origins of counting but it most likely stems from observations of changes in the night sky before humans left Africa.
“There was no artificial light, just fires lit in the caves. And with no light pollution, the Moon and stars were magical things to look at,” said Jens Hoyrup.
Sumerian progress
A major step forward in the history of mathematics was the invention of the ancient Sumerians, who are credited with inventing cuneiform, the earliest known form of writing.
The Sumerians were one of the first masters of Mesopotamia. Their city-states flourished in what is now southern Iraq from about 4500 to 1900 BC.
One of their most important achievements was the invention of numerals that could be written on clay tablets in the form of cuneiform characters, along with the decimal number system and the traditional base-60 system still used today in trigonometry, navigation, and timekeeping.
In contrast to simple counting, mathematics is the study of patterns and relationships through logical reasoning and the use of abstract concepts. The ancient Sumerians developed concepts of arithmetic, including multiplication and division tables, in algebra, in which unknown quantities are represented by symbols.
They also developed formulas for calculating the areas of triangles, rectangles, and irregular shapes. They applied these calculations to survey land and design irrigation systems.
Mathematician Duncan Melville of St. Lawrence University in the US says that the development of accounting systems, along with the need to keep track of things, stimulated the development of calculations. Supervisors needed to know what was coming into or leaving the warehouse, and in what quantities.
Different mathematical symbols were used depending on what was being measured, and the Sumerians switched back and forth between these recording systems to perform tasks such as finding the area of a field.
By this reasoning we see the beginnings of arithmetic and computational geometry.
Modern Mathematics
Besides the advances in the culture of Sumer and its successors in Mesopotamia, especially the Babylonians, mathematical innovations came from ancient Egypt, Greece, India, and China, and later from Islamic civilization.
Mathematics flourished in early modern Europe, where two scientists both claimed to have invented differential calculus, a way to determine the geometric area enclosed by any curve and a major advance in mathematics that is the foundation for many modern sciences and engineering.
One was Isaac Newton, who invented differential calculus as mentioned in his book "Principia Mathematica" published in 1687. The second was the polymath Gottfried Wilhelm Leibniz, who published a system of differential and integral calculus a few years before Newton's book appeared.
These two scientists and their supporters have been involved in a fierce dispute over who deserves credit for the invention, but historians believe that Newton and Leibniz developed the calculations in two separate, independent ways.
Source: https://dantri.com.vn/khoa-hoc/toan-hoc-duoc-phat-minh-khi-nao-20250513235311483.htm
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