A STORY OF
3 NUMBERS
3.1 Reema’s Curiosity
One lazy afternoon, Reema was flipping through an old book when —
whoosh! — a piece of paper slipped out and floated to the floor. She
picked it up and stared at the strange symbols all over it. “What is this?”
she wondered.
She ran to her father, holding the paper as if it were a secret treasure.
He looked at it and smiled. “Around 4000 years ago, there flourished a
civilisation in a region called Mesopotamia, in the western part of Asia,
containing a major part of the present-day Iraq and a few other
neighbouring countries. This is one of the ways they wrote their
numbers!”
Reema’s eyes lit up, “Seriously? These strange symbols were numbers?”
Her curiosity was sparked, and questions started swirling in her head.
Since What was their
when have need for counting?
humans been What were they
counting? counting?
How would the
Since when Mesopotamians
have written
have people
20? 50? 100?
been writing
numbers in
the modern
form?
Reprint 2026-27
, A Story of Numbers
Sensing her curiosity, her father started telling her how the idea of
number and number representation evolved over the course of time,
across geographies, to finally reach its modern efficient form.
Get ready to travel back in time with them!
Humans had the need to count even as early as the Stone
Age. They were counting to determine the quantity of food
they had, the number of animals in their livestock, details
regarding trades of goods, the number of offerings given in
rituals, etc. They also wanted to keep track of the passing
days, e.g., to know and predict when important events such
as the new moon, full moon, or onset of a season would occur.
However, when they said or wrote down such numbers, they
didn’t make use of the numbers that we use today.
The structure of the modern oral and written numbers that we use
today had its origin thousands of years ago in India. Ancient Indian texts,
such as the Yajurveda Samhita, mentioned names of numbers based on
powers of 10, almost as we say them orally today. For example, they listed
names for the numbers one (eka), ten (dasha), hundred (shata), thousand
(sahasra), ten thousand (āyuta), etc., all the way up to 1012 and beyond.
The way we write our numbers today — using the digits 0 through 9 —
also originated and were developed in India, around 2000 years ago. The
first known instance of numbers being
written using ten digits, including the digit 0
(which was then notated as a dot), occurs in
the Bakhshali manuscript (c. 3rd century
CE). Aryabhata (c. 499 CE) was the first
mathematician to fully explain, and do
elaborate scientific computations with the Zero in the Bakhshali manuscript
Indian system of 10 symbols.
The Indian number system was transmitted to the Arab world
by around 800 CE. It was popularised in the Arab world by the great
Persian mathematician Al-Khwārizmī (after whom the word ‘algorithm’
is named) through his book On the Calculation with Hindu Numerals
(c. 825) and by the noted philosopher Al-Kindi through his work On the
Use of the Hindu Numerals (c. 830).
From the Arab world, the Hindu numerals were transmitted to Europe
and to parts of Africa by around 1100 CE. Though Al-Khwārizmī’s work
on calculation with Hindu numerals was translated into Latin, it was the
Italian mathematician Fibonacci who around the year 1200 really made
the case to Europe to adopt the Indian numerals. However, the Roman
numerals were so ingrained in European thinking and writing at the
time that the Indian numerals did not gain widespread use for several
more centuries. But eventually, during the European Renaissance and
by the 17th century, not adopting them became impossible or it would
impede scientific progress.
49
Reprint 2026-27
, Ganita Prakash | Grade 8
“The ingenious method of expressing every possible number using a set of ten
symbols (each symbol having a place value and an absolute value) emerged in
India. The idea seems so simple nowadays that its significance and profound
importance is no longer appreciated. Its simplicity lies in the way it facilitated
calculations and placed arithmetic foremost among useful inventions.”
— Pierre-Simon Laplace (1749 – 1827)
Their use then spread to every continent, and are now used in every
corner of the world.
Because European scholars learned the Indian numerals from the
Arab world, they called them ‛Arabic numerals’ to reflect their European
perspective. On the other hand, as noted above, Arab scholars, such as
Al-Khwārizmī and Al-Kindi, called them ‛Hindu numerals’. During the
period of European colonisation, the European term Arabic numbers
became widely used. However, in recent years, this mistake is being
corrected in many textbooks and documents around the world, including
in Europe. The most commonly used terminologies for the numbers we
use today are ‛Hindu numerals’, ‛Indian numerals’, and the transitional
‛Hindu-Arabic numerals’. It is worth noting that the word ‛Hindu’ here
does not refer to a religion, but rather a geography/people from whom
these numbers came.
The shape of the digits 0, 1, 2, ..., 9 used to write numbers in the Indian
number system today evolved over a period of time, as shown below:
Evolution of the digits used in the Indian number system
Prior to the global adoption of the Indian system of numerals, different
groups of people used different methods of representing numbers. We
50
Reprint 2026-27
, A Story of Numbers
shall take a glimpse of some of them. We will not be looking at different
systems in a chronological order, but rather an order that shows us the
main stages in the development of the idea of number representation.
But first, let us explore some of the foundational ideas needed to count
and to determine the number of objects in a given collection.
The Mechanism of Counting
Imagine that we are living in the Stone Age, say, around ten thousand
years ago. Suppose we have a herd of cows. Here are some natural
questions that we might ask about our herd —
Q1. How do we ensure that all cows have returned safely after
grazing?
Q2. Do we have fewer cows than our neighbour?
Math
Talk
Q3. I f there are fewer, how many more cows would we need so
that we have the same number of cows as our neighbour?
We need to tackle these questions without the use of the
number names or written numbers of the Hindu number
system. How do we do it?
Here are some possible methods.
Method 1: We could tackle the questions by using pebbles, sticks or
any object that is available in abundance. Let us choose sticks. For every
cow in the herd, we could keep a stick. The final collection of sticks tells
us the number of cows, which can be used to check if any cows have
gone missing.
51
Reprint 2026-27
3 NUMBERS
3.1 Reema’s Curiosity
One lazy afternoon, Reema was flipping through an old book when —
whoosh! — a piece of paper slipped out and floated to the floor. She
picked it up and stared at the strange symbols all over it. “What is this?”
she wondered.
She ran to her father, holding the paper as if it were a secret treasure.
He looked at it and smiled. “Around 4000 years ago, there flourished a
civilisation in a region called Mesopotamia, in the western part of Asia,
containing a major part of the present-day Iraq and a few other
neighbouring countries. This is one of the ways they wrote their
numbers!”
Reema’s eyes lit up, “Seriously? These strange symbols were numbers?”
Her curiosity was sparked, and questions started swirling in her head.
Since What was their
when have need for counting?
humans been What were they
counting? counting?
How would the
Since when Mesopotamians
have written
have people
20? 50? 100?
been writing
numbers in
the modern
form?
Reprint 2026-27
, A Story of Numbers
Sensing her curiosity, her father started telling her how the idea of
number and number representation evolved over the course of time,
across geographies, to finally reach its modern efficient form.
Get ready to travel back in time with them!
Humans had the need to count even as early as the Stone
Age. They were counting to determine the quantity of food
they had, the number of animals in their livestock, details
regarding trades of goods, the number of offerings given in
rituals, etc. They also wanted to keep track of the passing
days, e.g., to know and predict when important events such
as the new moon, full moon, or onset of a season would occur.
However, when they said or wrote down such numbers, they
didn’t make use of the numbers that we use today.
The structure of the modern oral and written numbers that we use
today had its origin thousands of years ago in India. Ancient Indian texts,
such as the Yajurveda Samhita, mentioned names of numbers based on
powers of 10, almost as we say them orally today. For example, they listed
names for the numbers one (eka), ten (dasha), hundred (shata), thousand
(sahasra), ten thousand (āyuta), etc., all the way up to 1012 and beyond.
The way we write our numbers today — using the digits 0 through 9 —
also originated and were developed in India, around 2000 years ago. The
first known instance of numbers being
written using ten digits, including the digit 0
(which was then notated as a dot), occurs in
the Bakhshali manuscript (c. 3rd century
CE). Aryabhata (c. 499 CE) was the first
mathematician to fully explain, and do
elaborate scientific computations with the Zero in the Bakhshali manuscript
Indian system of 10 symbols.
The Indian number system was transmitted to the Arab world
by around 800 CE. It was popularised in the Arab world by the great
Persian mathematician Al-Khwārizmī (after whom the word ‘algorithm’
is named) through his book On the Calculation with Hindu Numerals
(c. 825) and by the noted philosopher Al-Kindi through his work On the
Use of the Hindu Numerals (c. 830).
From the Arab world, the Hindu numerals were transmitted to Europe
and to parts of Africa by around 1100 CE. Though Al-Khwārizmī’s work
on calculation with Hindu numerals was translated into Latin, it was the
Italian mathematician Fibonacci who around the year 1200 really made
the case to Europe to adopt the Indian numerals. However, the Roman
numerals were so ingrained in European thinking and writing at the
time that the Indian numerals did not gain widespread use for several
more centuries. But eventually, during the European Renaissance and
by the 17th century, not adopting them became impossible or it would
impede scientific progress.
49
Reprint 2026-27
, Ganita Prakash | Grade 8
“The ingenious method of expressing every possible number using a set of ten
symbols (each symbol having a place value and an absolute value) emerged in
India. The idea seems so simple nowadays that its significance and profound
importance is no longer appreciated. Its simplicity lies in the way it facilitated
calculations and placed arithmetic foremost among useful inventions.”
— Pierre-Simon Laplace (1749 – 1827)
Their use then spread to every continent, and are now used in every
corner of the world.
Because European scholars learned the Indian numerals from the
Arab world, they called them ‛Arabic numerals’ to reflect their European
perspective. On the other hand, as noted above, Arab scholars, such as
Al-Khwārizmī and Al-Kindi, called them ‛Hindu numerals’. During the
period of European colonisation, the European term Arabic numbers
became widely used. However, in recent years, this mistake is being
corrected in many textbooks and documents around the world, including
in Europe. The most commonly used terminologies for the numbers we
use today are ‛Hindu numerals’, ‛Indian numerals’, and the transitional
‛Hindu-Arabic numerals’. It is worth noting that the word ‛Hindu’ here
does not refer to a religion, but rather a geography/people from whom
these numbers came.
The shape of the digits 0, 1, 2, ..., 9 used to write numbers in the Indian
number system today evolved over a period of time, as shown below:
Evolution of the digits used in the Indian number system
Prior to the global adoption of the Indian system of numerals, different
groups of people used different methods of representing numbers. We
50
Reprint 2026-27
, A Story of Numbers
shall take a glimpse of some of them. We will not be looking at different
systems in a chronological order, but rather an order that shows us the
main stages in the development of the idea of number representation.
But first, let us explore some of the foundational ideas needed to count
and to determine the number of objects in a given collection.
The Mechanism of Counting
Imagine that we are living in the Stone Age, say, around ten thousand
years ago. Suppose we have a herd of cows. Here are some natural
questions that we might ask about our herd —
Q1. How do we ensure that all cows have returned safely after
grazing?
Q2. Do we have fewer cows than our neighbour?
Math
Talk
Q3. I f there are fewer, how many more cows would we need so
that we have the same number of cows as our neighbour?
We need to tackle these questions without the use of the
number names or written numbers of the Hindu number
system. How do we do it?
Here are some possible methods.
Method 1: We could tackle the questions by using pebbles, sticks or
any object that is available in abundance. Let us choose sticks. For every
cow in the herd, we could keep a stick. The final collection of sticks tells
us the number of cows, which can be used to check if any cows have
gone missing.
51
Reprint 2026-27
