*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 32, 000 BC. The recently found Lord Krishna's city is dated 32, 000 BC. The vedah were there before that as he references them.). 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-

Meaning:
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 |

Famous Jain Mathematician Mahaviracharya has said the following-

Meaning:
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 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-

Meaning: 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 KarmaIsht 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). Please find below a few examples.

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 following 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*.

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