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*Ganit* (Mathematics) has been considered a very important subject
since ancient times. We find very elaborate proof of this in Vedah
(which were compiled around 6000 BC). The concept of division, addition
et-cetera was used even that time. Concepts of zero and infinite were there. We
also find roots of algebra in Vedah. When Indian Beez Ganit reached Arab, they
called it Algebra. Algebra was name of the Arabic book that described Indian
concepts. This knowledge reached to Europe from there. And thus ancient Indian
Beez Ganit is currently referred to as Algebra.

The book *Vedang jyotish* (written 1000 BC) has mentioned the
importance of Ganit as follows-

Just as branches of a peacock and jewel-stone of a snake are
placed at the highest place of body (forehead), similarly position of Ganit is highest in all the branches of |

has said the following-

What is the use of much speaking. Whatever object exists in
this moving and nonmoving world, can not be understood without the base
of |

This fact was well known to intellectuals of India that is why they gave special importance to the development of Mathematics, right from the beginning. When this knowledge was negligible in Arab and Europe, India had acquired great achievements.

People from Arab and other countries used to travel to India for commerce. While doing commerce, side by side, they also learnt easy to use calculation methods of India. Through them this knowledge reached to Europe. From time to time many inquisitive foreigners visited India and they delivered this matchless knowledge to their countries. This will not be exaggeration to say that till 12th century India was the World Guru in the area of Mathematics.

The auspicious beginning on Indian Mathematics is in *Aadi Granth *(ancient/eternal
book) Rigved. The history of Indian Mathematics can be divided into 5 parts, as
following.

1) Ancient Time (Before 500 BC)

a)Vedic Time (1000 BC-At least 6000 BC)

a)Later Vedic Time (1000 BC-500BC)

2) Pre Middle Time (500 BC- 400 AD)

3) Middle Time or Golden Age (400 AD - 1200 AD)

4) Later Middle Time (1200 AD - 1800 AD)

5) Current Time (After 1800 AD)

Ancient time is very important in the history of Indian Mathematics. In this time different branches of Mathematics, such as Numerical Mathematics; Algebra; Geometrical Mathematics, were properly and strongly established.

There are two main divisions in Ancient Time. Numerical Mathematics developed
in Vedic Time and Geometrical Mathematics developed in Later Vedic Time.

Numerals and decimals are cleanly mentioned in Vedah (Compiled at lease 6000
BC). There is a *Richa* in Veda, which says the following-

In the above mentioned Richa , |

In this age the discovery of ZERO and "10th place value method"(writing number based on 10) is great contribution to world by India in the arena of Mathematics.

If "zero" and "10 based numbers" were not discovered, it would not have been possible today to write big numbers.

The great scholar of America Dr. G. B. Halsteed has also praised this. Shlegal has also accepted that this is the second greatest achievement of human race after the discovery of Alphabets.

This is not known for certain that who invented "zero" and when. But it has been in use right from the "vedic" time. The importance of "zero" and "10th place value method" is manifested by their wide spread use in today's world. This discovery is the one that has helped science to reach its current status.

In the second section of earlier portion of *Narad Vishnu Puran (written
by Ved Vyas)* describes "mathematics" in the context of *Triskandh
Jyotish*. In that numbers have been described which are ten times of each
other, in a sequence (10 to the power n). Not only that in this book, different
methods of "mathematics" like Addition, Subtraction, Multiplication,
Addition, Fraction, Square, Square root, Cube root et-cetera have been
elaborately discussed. Problems based on these have also been solved.

This proves at that time various mathematical methods were not in concept stage, rather those were getting used in a methodical and expanded manner.

"10th place value method"
dispersed from India to Arab. From there it got transferred to Western
countries. This is the reason that digits from 1-9 are called "hindsa"
by the people of Arab. In western countries 0,1,2,3,4,5,6,7,8,9 are called
Hindu-Arabic Numerals.

*Vedi* was very important while performing rituals. On the top of
"Vedi" different type of *geomit*(geometry: as you notice this
word is derived from a Sanskrit word)) were made. To measure those geometry
properly, "geometrical mathematics" was developed. That knowledge was
available in form of *Shulv Sutras* (Shulv Formulae). *Shulv*
means rope. This rope was used in measuring geometry while making *vedis*.

In that time we had three great formulators-*Baudhayan*, *Aapstamb*
and *Pratyayan*. Apart from them *Manav*, *Matrayan*, *Varah*
and *Bandhul* are also famous mathematician of that time.

The following excerpt from "Baudhayan Sulv Sutra (1000 BC)" is today known as Paithogorus Theorem (amazing, isn't it ?)

In the above formula , the following has been said. In a |

In the same book Baudhayan has discussed the method of making a square equal to difference of two squares. He has also described method of making a square shape equal to addition of two squares. He has also mentioned the formula to find the value (upto five decimal places) of a root (square root, cube root ...) a number, according to that the square root of 2 can be found as below-

While Geometric Mathematics was developed for making *Vedi* in *Yagya
*, in parallel there was a need to find appropriate timing for *Yagya*.
This need led to development of *Geotish Shastra *(Astrology) In *Geotish
Shastra *(Astrology) they calculated time, position and motion of stars. By
reading the book *Vedanga Jyotish* (At least 1000 BC) we find that
astrologers knew about addition, multiplication, subtraction et-cetera. For
example please read below-

Multiply the date by 11, then add to it the "Bhansh" of "Parv" and then divide it by "Nakshatra" number. In this way the "Nakshtra" of date should be told. |

We find elaborated description of Mathematics in the *Jain *literature.
In fact the clarity and elaboration by which Mathematics is described in Jain
literature, indicates the tendency of Jain philosophy to convey the knowledge to
the language and level of common people (This is in deviation to the style of
Veda which told the facts indirectly).

*Surya Pragyapti* and *Chandra Pragyapti *(At least 500 BC) are
two famous scriptures of Jain branch of Ancient India. These describe the use of
Mathematics.

*Deergha Vritt *(ellipse) is clearly described in
the book titled *Surya Pragyapti*. *"Deergha Vritt" *means
the outer circle *(Vritta)* on a rectangle*(Deergha)*, that was
also known as *Parimandal*.

This is clear that Indians had discovered this at least 150 years before Minmax
(150 BC). As this history was not known to the West so they consider Minmax as
the first time founder of ellipse.

This is worth mentioning that in the book *Bhagvati Sutra *(Before 300
BC) the word *Parimandal* has been used for *Deergha Vritt *(ellipse).
It has been described to have two types 1) *Pratarparimandal* and 2)*Ghanpratarparimandal*.

Jain *Aacharyas *contributed a lot in the development of Mathematics.
These gurus have described different branches of mathematics in a very through
and interesting manner. They are examples too.

They have described fractions, algebraic equations, series, set theory,
logarithm, and exponents .... Under the set theory they have described with
examples- finite, infinite, single sets. For logarithm they have used terms like
*Ardh Aached , Trik Aached, Chatur Aached*. These terms mean log base 2,
log base 3 and log base 4 respectively. Well before Joan
Napier (1550-1617 AD), logarithm had been invented and used in India which is a
universal truth.

Buddha literature has also given due importance to Mathematics. They have
divided Mathematics under two categories- 1)* Garna *(Simple Mathematics)
and 2)*Sankhyan *(Higher Mathematics). They have described numbers under
three categories-1)*Sankheya*(countable),2)*Asankheya*(uncountable)
and 3)*Anant*(infinite). Which clearly indicates that Indian
Intellectuals knew "infinite number" very well.

This is unfortunate that except for the few pages of the books *Vaychali
Ganit, Surya Siddhanta and Ganita Anoyog *of this time, rest of the writings
of this time are lost. From the remainder pages of this time and the literature
of Aryabhatt, Brahamgupt et-cetera of Middle Time, we can conclude that in this
time too Mathematics underwent sufficient development.

*Sathanang Sutra, Bhagvati Sutra and Anoyogdwar Sutra* are famous
books of this time. Apart from these the book titled *Tatvarthaadigyam Sutra
Bhashya *of Jain philosopher Omaswati (135 BC) and the book titled *Tiloyapannati
*of *Aacharya *(Guru) Yativrisham (176 BC) are famous writings of
this time.

The book titled *Vaychali Ganit* discusses in
detail the following -the basic calculations of mathematics, the numbers based
on 10, fraction, square, cube, rule of false position, interest methods,
questions on purchase and sale... The book has given the answers of the problems
and also described testing methods. *Vachali Ganit* is a proof of the
fact that even at that time (300 BC) India was using various methods of the
current Numerical Mathematics. This is noticeable that this book is the only
written Hindu Ganit book of this time that was found as a few survived pages in
village Vaychat Gram (Peshawar) in 1000 AD.

*Sathanang Sutra* has mentioned five types of infinite and *Anoyogdwar
Sutra* has mentioned four types of *Pramaan *(Measure). This *Granth*(book)
has also described permutations and combinations which
are termed as *Bhang and Vikalp *.

This is worth mentioning that in the book *Bhagvati
Sutra *describes the following. From n types taking 1-1,2-2 types together
the combinations such made are termed as *Akak, Dwik Sanyog* and the
value of such combinations is mentioned as n(n-1)/2 which is used even today.

Roots of the Modern Trignometry lie in the book titled *Surya
Siddhanta *. It mentions *Zya*(Sine),
*Otkram Zya*(Versesine), and *Kotizya*(Cosine).
Please remember that the same word (Zia) changed to "Jaib" in Arab.
The translation of Jaib in Latin was done as "Sinus". And this
"Sinus" became "Sine" later on.

This is worth mentioning that *Trikonmiti *word is
pure Indian and with the time it changed to Trignometry. Indians used
Trignometry in deciding the position , motion et-cetera of the spatial planets.

In this time the expansion of *Beezganit*
(When this knowledge reached Arab from India it became Algebra)was
revolutionary. The roots of Modern Algebra lie in the book *Vaychali
Ganit*. In this book while describing *Isht Karma
Isht Karm* "Rule of False" as the origin of expansion of Algebra.
Thus Algebra is also gifted to world by Indians

Although almost all ancient countries used quantities of unknown values and
using them found the result of Numerical Mathematics. However the the expansion
of *Beez Ganit* (Now known as Alzebra) became possible when right
denotion method was developed. The glory for this goes to
Indians who for the first time used Sanskrit Alphabet to denote unknown
quantities. Infact expansion of *Beez Ganit* (Now known as Alzebra)
became possible when Indians realized that all the calculations of Numerical
Mathematics could be done by notations. And that +, - these signs can be used
with those notations.

Indians developed rules of addition, subtraction, multiplication with these
signs (+,-,x). In this context we can not forget the contribution of great
mathematician *Brahmgupt *(628 AD). He said-

The multiplication of a positive number with a negative
number comes out to be a negative number and multiplication of a positive number
with a positive number comes out to be a positive number.

He further told:

When a positive number is divided by a positive number the
result is a positive number and when a positive number is divided by a negative
number or a negative number is divided by a positive number the result is a
negative number.

Indians used notations for squares, cube and other exponents of numbers.
Those notations are used even today in the mathematics. They gave shape to *Beezganit
Samikaran*(Algebraic Equations). They made rules for transferring the
quantities from left to right or right to left in an equation. Right from the
5th century AD, Indians majorly used aforementioned rules.

In the book titled *Anoyogdwar Sutra* has described some rules of
exponents in *Beez Ganit *(Later the name Algebra became more popular).

Thus it proves that Beez Ganit (Later the name Algebra became more popular) was well expanded by the mathematicians of Pre-middle Time. This was more expanded in the Middle Time.

It is without doubt that like *Aank Ganit *(Numerical
Mathematics) *Beez Ganit *(Later the name Algebra became more popular)
reached Arab from India. Arab mathematician Al-Khowarizmi (780-850 AD) has
described topics based on Indian Beez Ganit in his book titled "Algebr".
And when it reached Europe it was called Algebra.

This period is called golden age of Indian Mathematics. In this time great
mathematicians like *Aryabhatt, Brahmgupt, Mahaveeracharya, Bhaskaracharya *who
gave a broad and clear shape to almost all the branches of mathematics which we
are using today. The principles and methods which are in form of *Sutra*(formulae)
in *Vedas* were brought forward with their full potential, in front of
the common masses. To respect this time India gave the name "Aryabhatt"
to its first space satellite.

The following is the description about great mathematicians and their creations.

He was a resident of Patna in India. He has described, in a very crisp and
concise manner, the important fundamental principles of Mathematics only in 332 *Shlokas*.
His book is titled *Aryabhattiya*. In the first two sections of *Aryabhattiya*,
Mathematics is described. In the last two sections of *Aryabhattiya*, *Jyotish
*(Astrology) is described. In the first section of the book, he has
described the method of denoting big decimal numbers by the alphabets.

In the second section of the book *Aryabhattiya* we find difficult
questions from topics such as Numerical Mathematics, Geometrical Mathematics,
Trignometry and Beezganit (Algebra). He also worked on indeterminate equations
of Beezganit (Later in West it was called Algebra). He was
the first to use *Vyutkram Zia *(Which was later known as Versesine in
the West) in Trignometry. He calculated the value of pi correct upto four
decimal places.

He was first to find that the sun is stationary and the earth revolves around it. 1100 years later, this fact was accepted by Coppernix of West in 16th century. Galileo was hanged for accepting this.

He did matchless work on Indeterminate equations. He expanded the work of
Aryabhatt in his books titled *Mahabhaskariya, Aryabhattiya Bhashya and Laghu
Bhaskariya *.

His famous work is his book titled *Brahm-sfut*. This book has 25
chapters. In two chapters of the book, he has elaborately described the
mathematical principles and methods. He threw light on around 20 processes and
behavior of Mathematics. He described the rules of the solving equations of
Beezganit (Algebra). He also told the solution of
indeterminate equations with two exponent. Later Ailer in 1764 AD and Langrez in
1768 described the same.

Brahmgupt told the method of calculating the volume of Prism and Cone. He also described how to sum a GP Series. He was the first to tell that when we divide any positive or negative number by zero it becomes infinite.

He wrote the book titled "Ganit Saar Sangraha". This book is on Numerical Mathematics. He has described the currently used method of calculating Least Common Multiple (LCM) of given numbers. The same method was used in Europe later in 1500 AD. He derived formulae to calculate the area of ellipse and quadrilateral inside a circle.

He wrote books titled *"Nav Shatika", "Tri Shatika",
"Pati Ganit"*. These books are on Numerical Mathematics. His books
on *Beez Ganit *(Algebra) are lost now, but his method of solving quadratic
equations is still used. This is method is also called "Shridharacharya
Niyam". The great thing is that currently we use the same formula as told
by him. His book titled "Pati Ganit" has been translated into Arabic
by the name "Hisabul Tarapt".

He wrote a book titled *Maha Siddhanta*. This book discusses Numerical
Mathematics *(Ank Ganit)* and Algebra. It describes the method
of solving algebraic indeterminate equations of first order. He was the first to
calculate the surface area of a sphere. He used the value of pi as 22/7.

He wrote the books titled *Siddhanta Shekhar *and *Ganit Tilak*.
He worked mainly on permutations and combinations.
Only first section of his book *Ganit Tilak* is available.

His famous book is titled *Gome-mat Saar*. It has two sections. The
first section is *Karma Kaand* and the second section is titled *Jeev
Kaand*. He worked on Set Theory. He described universal
sets, all types of mapping, Well Ordering Theorems et-cetera.One
to One Mapping was used by Gailileo and George Kanter(1845-1918) after many
centuries.

He has written excellent books namely *Siddhanta Shiromani*,*Leelavati
Beezganitam*,*Gola Addhaya*,*Griha Ganitam* and *Karan
Kautoohal*. He gave final touch to Numerical Mathematics,
Beez Ganit (Algebra), and Trikonmiti (Trignometry).

The concepts which were in the form of formulae in Vedah. He has also described 20 methods and 8 behaviors of Brahamgupt.

Great Hankal has praised a lot Bhaskaracharya's Chakrawaat Method of solving indeterminate equations of Beezganit (Algebra). This Bhaskaracharya's Chakrawaat Method was used by Ferment in 1667 to solve indeterminate equations.

In his book *Siddhanta Shiromani*, he has described
in length the concepts of Trignometry. He has described Sine, Cosine, Versesine,...
Infinitesimal Calculus and Integration. He wrote that earth has gravitational
force.

Not much original work was done after Bhaskaracharya Second. Comments on ancient texts are the main contribution of this period.

In his book (1500 AD), the mathematician Neel Kantha of Kerla has given the formula to calculate Sine r -

The same formula is given in the Malyalam book *Mookti
Bhaas*. These days this series is called Greygeries Series. The
following is a descriptions of the famous mathematicians of this period.

He wrote the book titled *Ganit Kaumidi*. This book
deals with Permutations and Combinations, Partition of Numbers, Magic Squares.

He wrote the book titled *Tagikani Kanti*. This book deals with *Zeotish
Ganit*(Astrological Mathematics).

He wrote a book titled *Siddhanta Tatwa Viveka*.

He wrote two books titled *Samraat Siddhanta *and *Rekha Ganit *(Line
Mathematics)

Apart from the above-mentioned mathematicians we have a few more worth
mentioning mathematicians. From Kerla we have Madhav (1350-1410 AD). Jyeshta
Deva (1500-1610 AD) wrote a book titled *Ukti Bhasha*. Shankar Paarshav
(1500-1560 AD) wrote a book titled *Kriya Kramkari*.

Please find below a list of famous mathematicians and their writings.

He wrote books on Geometrical Mathematics, Numerical Mathematics and Trignometry.

He wrote books titled *Deergha Vritta Lakshan*(which means
characteristics of ellipse), *Goleeya Rekha Ganit*(which means sphere
line mathematics),*Samikaran Meemansa*(which means analysis of equations)
and *Chalan Kalan*.

Ramanujam is a modern mathematics scholar. He followed the vedic style of writing mathematical concepts in terms of formulae and then proving it. His intellectuality is proved by the fact it took all mettle of current mathematicians to prove a few out of his total 50 theorems.

He wrote the book titled *Vedic Ganit*.