A brief history of numbers and counting, Part 1: Mathematics advanced with civilization (2023)

The origins of numbers are cloaked in mystery. But, I think it’s safe to say that as civilization advanced numbers advanced with it; and it is equally safe to say that civilization could not have advanced without it.

Common intuition, and recently discovered evidence, indicates that numbers and counting began with the number one. (Even though in the beginning, they likely didn’t have a name for it.) The first solid evidence of the existence of the number one, and that someone was using it to count, appears about 20,000 years ago. It was just a unified series of unified lines cut into a bone. It’s called the Ishango Bone.

The Ishango Bone (it’s a fibula of a baboon) was found in the Congo region of Africa in 1960. The lines cut into the bone are too uniform to be accidental. Archaeologists believe the lines were tally marks to keep track of something, but what that was isn’t clear.

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But numbers, and counting, didn’t truly come into being until the rise of cities. Indeed numbers and counting weren’t really needed until then. Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest civilizations. With so many people, livestock, crops and artisan goods located in the same place, cities needed a way to organize and keep track of it all, as it was used up, added to or traded.

Their method of counting began as a series of tokens. Each token a man held represented something tangible, say five chickens. If a man had five chickens he was given five tokens. When he traded or killed one of his chickens, one of his tokens was removed. This was a big step in the history of numbers and counting because with that step subtraction — and thus the invention of arithmetic — was invented.

In the beginning Sumerians kept a group of clay cones inside clay pouches. The pouches were then sealed up and secured. Then the number of cones that were inside the clay pouch was stamped on the outside of the pouch, one stamp for each cone inside. Someone soon hit upon the idea that cones weren’t needed at all. Instead of having a pouch filled with five cones with five marks written on the outside of the pouch, why not just write those five marks on a clay tablet and do away with the cones altogether? This is exactly what happened.

This development of keeping track on clay tablets had ramifications beyond arithmetic, for with it, the idea of writing was also born.

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But, if you’re keeping track of your wealth with marks made on a clay tablet what’s to stop you from making your own clay tablet and stamping in 50 marks, and trading those 50 marks on a clay tablet for grain?

To prevent this from happening, the Sumerians needed an official method of keeping track, and an official group of people who kept track. A select few were allowed to enter this group. They essentially became the world’s first accountants. So a farmer may have made his own clay tablet with 50 marks on it and claimed that this proved that he was the owner of 50 chickens, but if that tablet didn’t have an official seal from the accountants it was worthless.

It was the Egyptians who transformed the number one from a unit of counting things to a unit of measuring things. In Egypt, around 3,000 BC, the number one became used as a unit of measurement to measure length. If you’re going to build pyramids, temples, canals and obelisks you’re going to need a standard unit of measurement — and an accurate method of applying it to real objects. What they invented was the cubit, which they considered to be a sacred measurement. A cubit is the length of a man’s forearm, from elbow to fingertips, plus the width of his palm. Considered sacred as they were, they had officially ordained sticks which they kept in the temples. If copy cubits were needed they were made from one of the original cubits kept in the temple. Thanks to this very official, very guarded and very precise unit of measurement the Egyptians were able to create colossal buildings and monuments with wondrous accuracy.

The Egyptians were the first civilization to invent different symbols for different numbers. They had a symbol for one, which was just a line. The symbol for ten was a rope. The symbol for a hundred was a coil of rope. They also had numbers for a thousand and ten thousand. The Egyptians were the first to dream up the number one million, and its symbol was a prisoner begging for forgiveness, which was a person on its knees, hands upraised in the air, in a posture of humility.

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Greece made further contributions to the world of numbers and counting, much of it under the guidance of Pythagoras. He studied in Egypt and upon returning to Greece established a school of math, introducing Greece to mathematical concepts already prevalent in Egypt. Pythagoras was the first man to come up with the idea of odd and even numbers. To him, the odd numbers were male; the evens were female. He is most famous for his Pythagorean theorem, but perhaps his greatest contribution to math was laying the groundwork for Greek mathematicians who would follow him.

Pythagoras was one of the world’s first theoretical mathematicians, but it was another famous Greek mathematician, Archimedes, who took theoretical mathematics to a level no one had ever taken it to before. Archimedes is considered to the greatest mathematician of antiquity and one of the greatest of all time. Archimedes enjoyed doing experiments with numbers and playing games with numbers.

But as trivial as his math games may have seemed to outsiders they often led to results that proved practical in the real world, some of which we still benefit from today. One example: Archimedes wondered if you could turn the surface of a sphere into a cylinder, and if you did, what would be the difference in area covered? Archimedes successfully worked this problem out, and to him that was the end of it. But thanks to the formulas he left behind, later mapmakers were able to turn the surface of the globe into a flat map.

Archimedes is also famous for his Archimede’s screw, which is a circular inclined plane (a screw) inside a tube that pumps water from one level to a higher level. He is equally famous for inventing a method of determining the volume of an object with an irregular shape. The answer came to him while he was bathing. He was so excited he leapt from his tub and ran naked through the streets screaming “Eureka!,” which is Greek for “I have found it.”

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Archimedes made many, many other mathematical contributions, but they are too numerous to mention here during a brief history of numbers.

The Greek’s role in mathematics ended, quite literally, with Archimedes. He was killed by a Roman soldier during the Siege of Syracuse in 212 BC. And thus ended the golden age of mathematics in the classical world. Under the rule of Rome, mathematics entered a dark age, and for a couple different reasons.

In Part 2 we’ll look at numbers from the mathematical dark ages of the Romans to the modern digital age.

If you'd like to read Steven Law's previous science articles go to www.curiosity101.com.

(Video) 50 Centuries in 50 minutes (A Brief History of Mathematics)


What is the history of numbers and counting? ›

Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest civilizations. With so many people, livestock, crops and artisan goods located in the same place, cities needed a way to organize and keep track of it all, as it was used up, added to or traded.

What was the first civilization to use mathematics? ›

The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC.

What is the history of numbers in mathematics? ›

Several civilisations developed positional notation independently, including the Babylonians, the Chinese and the Aztecs. By the 7th Century, Indian mathematicians had perfected a decimal (or base ten) positional system, which could represent any number with only ten unique symbols.

What civilization made advancements in mathematics? ›

The civilizations that most contributed to the development of Mathematics were: Egyptian, Babylonian, Roman, Chinese, Mayan and Hindu.

Who invented numbers and counting? ›

The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets.

Who invented numbers in math? ›

The origins of numbers date back to the Egyptians and Babylonians, who had a complete system for arithmetic on the whole numbers (1,2,3,4,. . . ) and the positive rational numbers.

How was math created in civilization? ›

Ancient tax collectors used basic numeracy to fuel the growth of early civilization, navigators used clever geometrical tricks to engage in trade and connect people across vast distances, astronomers used logarithms to unlock the secrets of the heavens, and their descendants put them to use to land us on the moon.

Which civilization was most advanced in mathematics? ›

The ancient Maya had the most advanced system of mathematics of any ancient civilization in the Americas, and quite possibly in Europe and Asia. The Maya were one of the first ancient cultures to use the concept of zero, which allowed them to write and calculate large sums.

How did mathematics evolve in early civilizations? ›

It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.

What is the history of counting? ›

There is archaeological evidence suggesting that humans have been counting for at least 50,000 years. Counting was primarily used by ancient cultures to keep track of social and economic data such as the number of group members, prey animals, property, or debts (that is, accountancy).

How many types of numbers are there? ›

What does it look like?
Type of NumberExample
Prime NumberP=2,3,5,7,11,13,17,…
Composite Number4,6,8,9,10,12,...
Whole NumbersW=0,1,2,3,4,…
5 more rows
Dec 9, 2022

What are the three 3 ancient civilizations in the history of mathematics? ›

Existing specimens of mathematics represent all the major eras—the Sumerian kingdoms of the 3rd millennium bce, the Akkadian and Babylonian regimes (2nd millennium), and the empires of the Assyrians (early 1st millennium), Persians (6th through 4th century bce), and Greeks (3rd century bce to 1st century ce).

Why mathematics is the mirror of civilization? ›

The prosperity and the cultural advancement of man depend on the advancement in mathematics. That is why Hogben says, 'mathematics is the mirror of civilization'. Different laws of science and scientific instruments are based on the exact mathematical concept.

What ancient civilization contributed to the field of mathematics by developing a counting system? ›

The ancient Sumerians of Mesopotamia developed a complex system of metrology from 3000 BC. From 2600 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.

What is the oldest form of counting? ›

The Babylonian number system is the oldest in the world. It relies upon a series of cuneiform marks to denote a digit. This base-60 concept developed by the Babylonians is still in use today with the division of time into 60-second minutes and 60-minute hours.

How did people start counting? ›

This first happened in Mesopotamia around the time when cities emerged there, creating an even greater need for numbers to keep track of resources and people. Archaeological evidence suggests that by 5,500 years ago, some Mesopotamians had begun using small clay tokens as counting aids.

How counting was done before numbers existed? ›

For thousands of years, humans used various forms of tallies and stones to count things. But maintaining large piles of stones and long lists of tallies became cumbersome. So grew the need to group numbers together.

Why are numbers so important to us? ›

Numeracy in everyday life

Our confidence and ability with numbers impacts us financially, socially, and professionally. It even affects our health and wellbeing. Some examples of the ways we use maths every day include: Working out how many minutes until our train.

How do ancient people use numbers? ›

The earliest number systems were simple tally marks, probably first made on sticks and later on stone tablets or pottery. The Babylonian number system was the first known positional number system, and it was sexagesimal, meaning it used a base of sixty.

Why do numbers exist? ›

When we have numbers we can consistently discriminate them, and that allows us to find fascinating and useful patterns of nature that we would never be able to pick up on otherwise, without precision. Numbers are this really simple invention.

Did humans create math or discover it? ›

Mathematics is not discovered, it is invented.

How did ancient Chinese do math? ›

Mathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry.

How Was math invented or discovered? ›

A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them--shapes, lines, sets, groups, and so forth--either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts.

Which civilization was the most advanced and why? ›

Arguably the New World's most advanced pre-Columbian civilization, the Maya carved large stone cities into the jungles of southern Mexico and Central America, complete with elaborate plazas, palaces, pyramid-temples and ball courts.

What civilization did math signs discover? ›

The earliest evidence of written mathematics dates back to the ancient Sumerians and the system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems.

Where did advanced mathematics originate? ›

More advanced mathematics can be traced to ancient Greece over 2,500 years ago. Ancient mathematician Pythagoras had questions about the sides of a right triangle. His questioning, research, and testing led to a basic understanding of triangles we still study today, known as the Pythagorean Theorem.

Who said mathematics is the mirror of civilization? ›

The above-mentioned statement was stated by Lancet Thomas Hogben. It is true as the culture and civilization reflect the mode of living of a particular society.

When did humans first use numbers? ›

Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.

What are the 12 types of numbers? ›

The different types of numbers in maths are: Natural Numbers: Natural numbers are known as counting numbers that contain the positive integers from 1 to infinity.
Also, read:
  • Natural Numbers And Whole Numbers.
  • Sequence And Series.
  • Real Numbers.
  • Integers.
  • Prime Numbers.
  • Composite Numbers.
  • Perfect Numbers.
  • Rational Numbers.

What are the 4 types of real numbers? ›

The set of real numbers consists of different categories, such as natural and whole numbers, integers, rational and irrational numbers.

Is √ 1 a real number? ›

√ 1 is a real number.

Why were numbers invented? ›

Keeping track of small numbers of items with tally marks was sufficient for individuals and small groups. As societies began to form and grow, however, trade became more complex, requiring the development of numbers to perform simple mathematical calculations.

Who invented 1 to 10 numbers? ›

Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.

What are 5 uses of numbers? ›

We use numbers in school and work, counting money, measurements, phone numbers, password on our phone , locks, reading, page numbers, and TV channels.

What is basic number theory? ›

Number theory is a branch of mathematics which helps to study the set of positive whole numbers, say 1, 2, 3, 4, 5, 6,. . . , which are also called the set of natural numbers and sometimes called “higher arithmetic”. Number theory helps to study the relationships between different sorts of numbers.

Is zero a number or not? ›

0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usually by 10.

What are the 4 main ancient civilizations? ›

The four oldest civilizations are Mesopotamia, Egypt, the Indus valley, and China as they provided the basis for continuous cultural development in the same geographic location.

What 3 things did all the civilizations have in common? ›

All civilizations have certain characteristics. These include: large population centers; monumental architecture and unique art styles; shared communication strategies; systems for administering territories; a complex division of labor; and the division of people into social and economic classes.

What is the most important contribution of mathematics in human civilization? ›

Math helps us have better problem-solving skills

With math, we can think analytically and have better reasoning abilities. Analytical thinking means the ability to think critically. Reasoning is the ability to think logically. Analytical and reasoning skills are essential as they help us solve problems.

What impact does mathematics have on human civilization? ›

Mathematics is a significant part of human logic and thoughts. It gives an effective way to create mental discipline and increases logical reasoning. Moreover, mathematical knowledge plays an essential role in understanding the concept of other subjects like science, social studies, and even music and art.

Why mathematics is important in the development of our society? ›

Mathematics has significantly helped the development of science and technology for thousands of years and will continue to do so now. It has uses in commerce, business, culture, government, athletics, medicine, farming, architecture, and the natural and social sciences, among other things.

Which civilization invented the number system? ›

The Sumerian number system

The city of Sumer in Mesopotamia developed its number system well before its script, which it invented around 3000 BC. Its number system used the main base 60 and the auxiliary base 10.

What civilization developed the first method of counting and modern concepts in mathematics? ›

Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest civilizations.

What is the history of real numbers? ›

In the 16th century, Simon Stevin created the basis for modern decimal notation, and insisted that there is no difference between rational and irrational numbers in this regard. In the 17th century, Descartes introduced the term "real" to describe roots of a polynomial, distinguishing them from "imaginary" ones.

What was the first number in history? ›

Common sense and ancient evidence points to the idea that numbers and counting began with the number one. Although they probably didn't call it "one," prehistoric people likely counted by ones and kept track by carving lines on a bone.

How was the number 1 created? ›

As a digit

The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Brahmic script of ancient India, where it was a simple vertical line.

How did numbers get their names? ›

The English words for numbers can be traced back to the original Indo-European language, but during the early Middle English period, English speakers began to borrow related number words from Greek, Latin and French.

What is the first real number? ›

Set of Real Numbers

Contain all counting numbers which start from 1. All numbers such as 1, 2, 3, 4, 5, 6,…..…

What is the importance of real numbers in real life? ›

Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting. The word real distinguishes them from the imaginary numbers, involving the symbol i, or Square root of√−1.

Why real number is important? ›

Real numbers are all the numbers on the number line, and there are infinitely many of them. Their types and categories are important because they can give you more information about the problem you are looking at.

Where did humans begin using numbers? ›

This first happened in Mesopotamia around the time when cities emerged there, creating an even greater need for numbers to keep track of resources and people. Archaeological evidence suggests that by 5,500 years ago, some Mesopotamians had begun using small clay tokens as counting aids.

What is the biggest number known in history? ›

A "googol" is the number 1 followed by 100 zeroes. The biggest number with a name is a "googolplex," which is the number 1 followed by a googol zeroes. The story goes that mathematician Edward Kasner asked his 9-year-old nephew to come up with a name for a very large number.

When did civilizations start counting? ›

The Egyptians were the earliest known civilization to start counting years in 4241 BCE, so if we used their calendar it would 6257. The earliest known writing system is believed to have emerged circa 5500 BCE, so if we went by that it would be 7516.

What is the oldest counting device? ›

abacus, plural abaci or abacuses, calculating device, probably of Babylonian origin, that was long important in commerce. It is the ancestor of the modern calculating machine and computer.

When did humans start counting time? ›

ACCORDING TO archaeological evidence, the Babylonians and Egyptians began to measure time at least 5,000 years ago, introducing calendars to organize and coordinate communal activities and public events, to schedule the shipment of goods and, in particular, to regulate cycles of planting and harvesting.


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