Hindu–Arabic numeral system

The Hindu–Arabic numeral system is the way most of the world writes numbers today. It is a base ten (decimal) positional numeral system, meaning it uses ten basic symbols to represent numbers and their position affects their value.

This system was invented between the 1st and 4th centuries by Indian mathematicians. By the 9th century, Arabic mathematicians learned about it and added ways to work with parts of numbers, like fractions. Important books written in Arabic helped spread the system.

It reached Europe during the Middle Ages, especially through a famous book called Liber Abaci by Fibonacci in the 13th century. Before that, it was mostly used in Northern Italy. The system uses ten simple symbols, from zero to nine, to write any number by combining them in different orders. These symbols come from old Indian shapes and have developed into different styles used in places like Europe, the Middle East, and the Indian subcontinent.

Positional notation

Main articles: Positional notation and 0 (number)

The Hindu–Arabic numeral system uses positional notation in a decimal system. This means each digit’s position shows its value. Over time, a decimal marker was added to separate whole numbers from parts less than one. Today, we usually use a decimal point or comma for this. There is also a special symbol to show that some digits repeat forever, like in one-third, which is written with a horizontal line above the repeating part.

Even though the Arabic writing system reads right to left, numbers in this system are read left to right, with the biggest digit on the left. This helps keep things clear when we mix different writing directions.

Symbols

Many different symbols are used to show numbers in the Hindu–Arabic numeral system, and most of these come from the old Brahmi numerals.

Over time, these symbols changed and are now used in three main ways:

• The common Western "Arabic numerals" are used with the Latin, Cyrillic, and Greek alphabets. They started from the "West Arabic numerals" made in al-Andalus and the Maghreb.
• The "Arabic–Indic" or "Eastern Arabic numerals" are used with Arabic writing, mainly in what is now Iraq. A version of these is also used in Persian and Urdu.
• The Indian numerals are used with Brahmic family scripts in India and Southeast Asia. Each of India's many scripts has its own number shapes.

History

Main article: History of the Hindu–Arabic numeral system

Around 600 CE, the way people wrote dates in India and Southeast Asia changed. Instead of using different symbols for each number size, they started using a system where the position of a number showed its value. This new system used just nine symbols (1 to 9) and a dot for zero. Over time, this system replaced the older ways of writing numbers.

Indian mathematicians developed this system, and later Arab and Persian scholars helped spread it. By around the 10th century, Arab traders brought the system to Europe. European mathematicians began calling the numbers “Arabic,” even though they started in India. Today, this is the most common way people around the world write numbers.

Predecessors

Before this system, ancient Indian scripts used different symbols for numbers. These older symbols were used along with another set called Kharosthi numerals. Both were used in ancient India, often in important messages from leaders.

Early Buddhist writings from around 300 BCE show some of the symbols that later became our numbers 1, 4, and 6. Over time, more symbols were added, but they did not use a zero or a place-value system like we do today.

Development

The place-value system with zero first appears in an old Indian book called the Bakhshali manuscript, which scientists think was written between 224 and 383 CE. Indian astronomers and mathematicians, like Aryabhata around the year 500, used the word for “emptiness” to mean zero. By the 7th century, Indian books showed a deeper understanding of how zero worked in math.

The first known stone writing with a symbol for zero was found in India in a temple in Gwalior, dated to 876 CE.

Medieval Islamic world

Indian ideas about numbers were shared with scholars in the Islamic world during the 8th century. By the 10th century, Muslim mathematicians began using the system to show parts of a whole, like fractions, which Indian mathematicians had not done. This helped make the system known as “Hindu–Arabic.”

The system reached famous Muslim scholars like Khwarizmi and Al-Kindi, who wrote books about it. These books helped spread the system across the Islamic world and later to Europe.

Adoption in Europe

Main article: Arabic numerals

In Europe, the first known use of these numbers (1 to 9, but not zero) was in a book from Spain in 976 CE. A teacher named Gerbert later became Pope Sylvester II and helped teach these numbers in Europe.

A book by Leonardo Fibonacci in 1202 called Liber Abaci introduced the system to many Europeans. After that, the numbers were used more and more, replacing older Roman numerals by the 15th century. The shapes of the numbers we use today were developed in the late 1400s and early 1500s when printing began.

Adoption in East Asia

The symbol ‘〇’ is used for zero in some old Chinese number systems. The oldest Chinese book to use this symbol is from 1247. It is not sure how this symbol began. Some think it came from Indian numbers, while others think it was changed from a Chinese symbol that meant “empty space.”

China and Japan started using the Hindu–Arabic numbers in the 1800s, stopping their old rod counting systems.

Spread of the Western Arabic variant

The form of the numbers most people use today, called “Western Arabic” numbers, spread worldwide along with the Latin alphabet. Even in places that used other kinds of Hindu–Arabic numbers, or used Chinese or Japanese writing, these Western forms became common.