Aryabhata : The Father of Mathematics and Astronomy

You know what, when they used to say that the earth was flat and then suddenly in the history we find explorers like Christopher Columbus coming up with the idea of earth being round in shape, a sphere to be precise.

But there was an astronomer cum mathematician who actually gave birth to this idea back in the 5th century.

This intelligent man was born in the country of India and has delivered some of the concepts of mathematics which gave the robust foundation to the modern day’s Physics and Mathematics as well as Astronomy.

This man is better known as ‘Aryabhata’ who is the father of mathematics. In this blog, you will know all about Aryabhata the mathematician. I have packed this blog with a ton of Aryabhata's information.

By the end of this blog, you will get to know completely Aryabhata, the mathematician and the astronomer.

Mathematics flew in the veins of Aryabhata. Not only he studied Mathematical concepts but gave the world new ones.

With no tool and equipment in the 5th century, it was next to impossible to mark such an achievement in progressions, algebra, trigonometry, quadratic equations etc.

But, Arybhata Mathematician did it. When you are talking about Aryabhata, you can separate the word mathematician from his name.

Who was Aryabhata?

Aryabhata was a genius human being, a rarest of the rare mind this earth has seen.

Some historians believe that he was born in the southern state of Kerala, whereas, others believe his birthplace to be in Kusumapura , Bihar. There has always been an uncertainty about his birthplace.

However, it has been proved by historical facts that Aryabhata spent most of his life in Kusumapura. The exact date of birth of Aryabhata is not known but it is certain that Aryabhata was born in 476 AD.

Kusumapura

I was doubtful about the location of Kusumapura but when I googled Kusumapura I got Pataliputra (current day Patna) in the answer.

When I dug more on the Internet, I found that many historians and archeologists also point Kusumapura to be located near Patna in the ancient times.

One important thing that is known about Aryabhata's education is that he went to Nalanda University in the city of Patliputra. Aryabhata completed his studies from the Nalanda university. He was so good at studies in the university that Budhhagupta (a gupta emperor, died 480 AD) made him the university head.

A great university is the one which nurtures the talent of its alumni. Aryabhatta's education in Nalanda University played a vital role in tapping the genius in him.

Back in those days, Nalanda University was no ordinary university; it was a school and a home to some of the greatest scholars of India as well as those from the neighboring countries of India like Sri Lanka, China, Malaysia, Arab countries etc. A person has to be a prodigy and must have proposed some innovative concepts to the world in order to be made the university head of the world's most ancient college by the then Gupta emperor.

What was Aryabhata famous for?

Aryabhata’s works in the fields of Mathematics & Astronomy have been unparalleled. In fact, he was the first mathematician who presented the concepts of algebra, trigonometry, sine tables and pi to the world.

His work ‘Arbhatiya’ is the only surviving recorded wisdom and intelligence of this great genius in today’s world. His other works have been either been destroyed or couldn’t be passed down to the younger generations.

Now, imagine that you are in an era where the people around you consider the earth to be flat.

The sailors dread to go farther in the sea as they may fall, tripping over the perpendicularly turning surface, down with the currents of the waterfall, they believe which is somewhere at the horizon.

In that era, there appears a genius who at the age of just 23 writes his first compilation of the revolutionary concepts of Mathematics and Astronomy. Compiling a text like Aryabhatiya at the age of 23 is a matter of pride not only for Aryabhata but the entire India. Aryabhatiya laid the foundation stone based on which subsequent mathematicians and astronomers developed many advanced concepts. Based on these concepts, the world has seen big discoveries and inventions. This makes him the father of mathematics in World.

He gives the naive world the concepts of Algebra, Arithmetic, plane and spherical trigonometry along with the sine tables and the concepts of Quadratic equations which we read today which is why, Aryabhata is the father of mathematics.

Astronomical Works

He cleared the concepts behind day and night by bringing upfront the revolutionary fact that the earth rotates around its axis.

Earlier astronomers and mathematicians used to predict time as well as various astronomical events through motion of the planets and the sun.

Aryabhata through his superb knowledge and impeccable genius studied the motion of the planets and the sun. He established the truth behind the solar and lunar eclipses, means how they are formed, what’s the reason behind them.

Doesn't it intrigue you that he found out radius of the orbits of planets of our solar system without any telescope or any equipment just by studying the stars & probably the motion of planets? Even being a science student I couldn't imagine how he would've done that.

Being a kid, when I would watch shining full moon in the night and would enchant by the light emitted by it then my father would tell me -"you know what son, this is not the light of the moon, it is the light of the Sun which the moon emits". I got this information from my father but you know who gave this information to the world first, the father of mathematics & astronomy - Aryabhata. I am sure he never knew that not only India's first satellite but a lunar crator will be named after him.

His achievements also include determining the circumference of the earth and other planets with relation to the earth. We can be proud of ourselves that an Indian who lives in the 5th century determines the circumference of the earth without any tools, advanced technical equipment to be 24835 miles.

If you google the circumference of the earth then you will find the figure to be 24901 miles. Now imagine, how close to the accurate figure was Aryabhata in the 5th century.

Arybhata knew the real shape of the earth

The real shape of the earth is ellipsoid. An ellipsoid is a three-dimensional figure symmetrical to each of the three axes.

Few of the plane sections of an ellipsoid are ellipses while the plane sections normal to one axis are circles.

But, this is very scientific and specific. In layman's terms, the shape of earth is round or spherical. The ellipsoid is a deformed sphere.

But have you ever wondered who discovered the shape of earth?

Well, there is a big debate around it.

My teachers told me in school that the shape of earth was discovered by Christopher Columbus.

I believed it until I read about the father of mathematics - Aryabhata.

In Aryabhatiyam, the mention of the word ‘Gola’ that specifies that he knew about the real shape of earth back in the 5th century.

Eratosthenes, a librarian in the library of Alexandria, is believed to have come with the idea first. He lived in 240 BC.

Research says that Aristotle from 4 BC and Plato from 5 BC also discovered the shape of earth as round.

The information didn’t run fast as it runs now.

The point is that a mathematician who compiled his first excellent work at the age of 23, couldn’t have known about the shape of earth beforehand.

The 4th section of Aryabhatiyam is Golapada which contains 50 verses.

In it, he has thrown light on the shape of earth along with a discussion on causes of day and night.

His commentary on the size and shape of the earth is unparalleled. The best part is that it is so close to the figures and concepts discovered later.

Aryabhata may not be the first person to discover the real shape of earth but he sure discovered it on his own. It was an independent discovery by the father of mathematics in India like ‘0’.

The Vedas are the oldest text on the planet earth. Rigveda dates back to around 1500 BC. This is centuries before Eratosthenes was born.

In Vedas, the shape of the earth has been given as round. The first avatar of Vishnu ( Varaha ) saved the earth by placing it on his teeth. You see the earth resting on his teeth is round in shape.

Arbhatiyam

Any account of the life and work of Aryabhata will be incomplete if it doesn’t mention Aryabhatiyam in detail.

Aryabhatiyam or Aryabhatiya holds a special place in Aryabhata’s biography.

Aryabhata compiled Aryabhatiyam at the age of 23 like I already mentioned before. Aryabhata has written the entire Aryabhatiya in Sanskrit. It contains 121 verses in total.

The Aryabhatiyam led to the invention of so many things that we enjoy today.

It was such a landmark that the later mathematicians like Brahmagupta and Bhaskara I wrote commentaries on it.

In fact, Aryabhatiya information served as the base of many theories which they worked on. Till today, 12 recognized commentaries have been written on Arybhatiyam.

The 121 verses in Aryabhatiyam are divided across 4 sections -

1. Gitikapada - The first section contains 13 verses. Aryabhata pays tribute to Brahman first. Then he gives an account of the numeric system used in the treatise. He also gives a sine table in this chapter.

This sine table is not a conventional sine table of rows and columns. It is not that we study in the chapter of trigonometry. Rather, it consists of the first differences of the values of trigonometric sines in arc minutes. This was the first-ever such table in the history of mathematics.

Aryabhata then highlights astronomical definitions and parameters which he used in the treatise.

One important intriguing topic in the first chapter of Gitikapada is the length of the yuga. Aryabhata calculated it as 4.32 million years. It states the duration of the rotations of the earth and the other celestial bodies such as the sun and the moon.

2. Ganitapada - This chapter contains 33 verses. Ganitapada (Ganit - Maths in Hindi) is a chapter dedicated to mathematics.

The chapter contains no ordinary math concepts. It gives an account of advanced mathematics topics. They include arithmetic, geometric progressions, mensuration, roots, quadratic equations, and the indeterminate equations.

3. Kalakriyapada - This chapter contains 25 verses. In this chapter, Aryabhata puts in concepts of Astronomy.

Aryabhata determined the positions of planets in a day in this chapter. He briefed on the days, weeks, and months as per the movement of the earth, the sun, and the moon.

He based his findings on the geocentric model. While some astronomers believe it to be a partial heliocentric model. He provided the concept of seven days in a week with their proper names.

Epicycle is a geometric model that tells the motion of the sun, the moon, and the planets as well as their speed and their variations.

Many historians attribute the epicycle to the days of Copernicus. But it was Aryabhata who computed the longitudes of the planets using eccentricity and epicycles. This helped him to find the positions of the planets.

4. Golapada - The final chapter Golapada contains 50 verses.

It focuses on the shape of the earth and its rotation around its axis.

In this chapter, Aryabhata explains the solar and the lunar eclipses. He throws light on the relation of the earth with the celestial bodies.

One intriguing finding is that he stated the Kaliyuga began on 18th Feb 3102 BC.

It is on this day the sun, the moon, and the earth aligned in conjunction at zero longitudes in Lanka. This point is at the intersection of the equator and the median of the Ujjain.

He proved that this alignment is periodic and returns after exactly 4.32 million years. He then stated 4.32 million years as the length of a Yuga.

I happen to get my hands on the work of Aryabhata, and I prefer to share the link with you as well,

aryabhatiya book in hindi pdf download

I will share a few of the interesting topics from Aryabhatiya with you, which will make you read it with more interest. For the complete book, you can access the below link.

• Dasagitika or the 10 Giti Stanzas
• Divisions of circle; Circumference of the sky & orbits of planets in Yojanas
• Length of Yojana; Diameters of Earth, Sun,Moon, Meru and Planets; Numbers of years in yuga
• Table of Sine Differences

• Ganitapada or Mathematics
• Square root, Cube root,
• Names and Values of Classes of numbers increasing by powers of Ten
• Calculation of Samapatarasas; when two circles intersect

• Kalakriya or the reckoning of Time
• Number of Revolutions of Epicycles of Planets; Years of Jupiter.
• Divisions of Time; Divisions of circles correspond
• Calculation of true places of Planets from mean places

• Gola or The Sphere
• Sun, Nodes of Moon and Planets, and Earth’s shadow move along Ecliptic
• Distance from Sun at which Moon and planets become visible.
• Lanka(on equator) 90 degree from poles; Ujjain 22.5 degrees North of Lanka.

Aryabhata’s work was later used as reference by many Greek and Arab mathematicians and astronomers. It is widely believed that Aryabhata's concepts of Astronomy formed the basis of the Jalali calendar. The Jalali calendar was used in Persia(modern day Iran) and the modern adaptations of this solar calendar are still used in Iran and Afghanistan

His last treatise known as Aryabhatta Siddhanta contains astronomical calculations done by him and believe it or not, but those are still used by the modern day priests to prepare the astrological charts, to find auspicious moments for ceremonies. You must have heard people discussing in the later half of the year -'When is Diwali this year?'. You must have noticed, it doesn't fall on the same day every year, it's a new date year.

Why? Because it is calculated by a holy Hindu calendar known as 'Panchang'. This holy calendar would not have been there had there been no Aryabhatta Siddhanta. The astronomical calculations by Aryabhata gave birth to 'Panchang' which is still used by the Hindu Priests.

Aryabhata Book

The Aryabhata book which he himself compiled is Aryabhatiya. We are lucky that it survived generations and descended down to us.

But, many other authors couldn't resist writing about this genius. Although, I have provided all the information about Aryabhata in this article. But, if you are intrigued already by reading this article and want to read more then here are a few Aryabhata books which you can buy to read.

The Invention of Zero

There are how many zeroes in 1 lakh? I bet you will say 5 which is true.

Suppose it is your monthly salary. Now, if I remove 1 zero from your salary, what will be your reaction. You will be shell-shocked at the sight of your salary slip.

You will sweat, and get anxious.

Now, suppose if I increase 1 zero, how will you react? I am sure that you will jump with joy.

Such is the importance of zero in the salary slip.

But, its importance is not limited to salary slips but it is of high importance in almost every field.

The credit of the discovery of zero is attributed to India.

A few shreds of evidence suggests that India did have a major role in ‘zero invention’.

Yet, the history of the discovery of the zero number is blurry.

History suggests that the invention of zero happened in different civilizations.

Zero means ‘Nothing’

Zero suggests nothing, we all know that. It means vacant or void or null.

The concept of ‘nothing’ was first used in Sumeria.

Sumeria - present-day southern Iraq - needed a system to help their trade system. They needed to count the goods which came in the city and which went out.

Sumerians developed numbers as well as the counting system. Besides, Sumerians also developed basic arithmetic operations to perform addition and subtraction.

The counting system developed by Sumerians descended down to the Akkadian speaking Babylonians. The period was approx 300 BC.

In the mathematical works of the Babylonians, the concept of ‘nothing’ appeared for the first time.

The Babylonians first left the space empty instead of denoting ‘nothing’ by a symbol.

As the system became more mature, they started using double angled wedges to denote the ‘void’. But, no historical evidence suggests that ‘0’ appeared in their works.

Discovery of ‘Zero’ by Aryabhata

The concept behind zero is believed to be developed by Sumerians and Babylonians. But the pieces of evidence suggest that Indians developed ‘0’ number.

No direct evidence suggests that Aryabhata discovered 0. While ‘0’ first appeared in the works of a 7th-century mathematician Brahmagupta.

Brahmagupta discovered that when a number is subtracted from itself then the result is 0.

He also gave the world the application of zero in the accountancy system.

There is no evidence of the invention of zero by Aryabhata.

But, how could he give the concepts of algebra, trigonometry, quadratic equations without the use of zero?

In Arybhatiyam, Aryabhata has mentioned zero by a different word - ‘Kha’.

Bhakshali Manuscript

In the year 1881 near the current-day Peshawar(Pakistan), Bakhshali manuscript was discovered.

Scientists conducted carbon-dating experiments on Bakhshali manuscript in the year 2017.

The results of the carbon-14 technique revealed something big. It revealed that they belong to a period between the 3rd and the 4th century.

The Bakhshali manuscript is the oldest mathematical text available at present.

In it, zero appeared as a dot. This corroborates that the use of the number 0 goes back as far as the 3rd century.

It is now logical for us to think that Aryabhata used zero.

He used the concept of zero while he invented quadratic equations and Algebra.

Another piece of evidence is the discovery of zero on a temple wall in the city of Gwalior, India. The inscriptions on the wall of this temple go back to the 9th century.

So after all this piece of information, the big question is who discovered zero?

As per the historians and the research done by the top institutions of the world, the symbol ‘0’ first appeared in the works of Brahmagupta.

Thus, Brahmagupta is the one who invented ‘0’.

The Satellite Aryabhata

Aryabhata was a genius mathematician and an astronomer. You can't explain his capability in words.

I am trying so hard to do justice to his brilliance through words in this article. Only your comments will tell me how successful I got.

His brilliance continued for ages. This is relative to the fact that Indira Gandhi named India’s first satellite - Aryabhata.

This blog would be incomplete if I didn’t provide information about the Aryabhata satellite.

Under the leadership of Vikram Sarabhai, ISRO started building indigenous satellites in the early 70s.

The team indeed built a satellite of weight 100 kgs. This satellite was in talks to be launched by the USA using the Scout launch vehicle.

The USSR offered its affordable help to launch the satellite. ISRO scientists held meetings in New Delhi and Moscow.

An agreement was about to fixed but the sudden demise of Vikram Sarabhai led to a halt in the project.

The leadership of the project vanished for a significant amount of time.

Sometime later, the interim chairperson M.G.K Menon held the command.

Dr U.R. Rao - who also worked with Vikram Sarabhai - finalized the deal with the Soviets in 1972. The construction of India’s first unmanned satellite thus resumed.

So, ISRO created India’s first satellite which was a polygon of 26 sides. It had a diameter of 4.6 feet.

The satellite weighed 360 kilograms.

Indira Gandhi, the then Prime minister of India had the opportunity to name the satellite.

She had the choices - Aryabhata, Mitra, and Jawahar, to which she chose Aryabhata.

If someone asks you that India’s first satellite Aryabhata was launched from which country then you must know it was not India.

Aryabhata satellite launch happened from a Russian 'rocket launch and development site'. They call it Kapustin Yar.

So, the country from which ISRO launched the Aryabhata satellite was Russia.

By now, I am sure that you know who developed India’s first satellite Aryabhata? It was the Indian Space Research Organization (ISRO).

On 19 April 1975, ISRO's Aryabhata satellite launch using a KOSMOS-3M launch vehicle was successful.

So, below are the crucial aspects of the Aryabhata Satellite information -

1. When was Aryabhata launched

2. The country of launch

3. Which country launched it

Purpose of the Aryabhata Satellite

The Sun is the natural model of the nuclear fusion process from which gamma rays get produced.

They get emitted out in the space because of internal absorption and thermalization.

The Sun is also the producer of infrared rays, X-rays, ultraviolet, and even radio waves.

To understand these rays emitted by the Sun gave birth to the purpose behind the launch of the Aryabhata satellite.

The purpose of the Aryabhata satellite launch was to explore the field of X-ray astronomy.

A satellite’s main purpose is to examine the earth’s atmosphere. This found a place in the list of the satellite Aryabhata’s list of goals.

Aryabhata was also designed to send helpful data related to gamma rays to the curious scientists of the ISRO.

The successful launch of the Aryabhata satellite also opened further opportunities for ISRO.

Above is the picture of the Aryabhata Satellite. Source -> ISRO

Aryabhata - a success or a partial success

India launched its first satellite on April 19th, 1975. For the first four days, everything went well.

Scientists were able to collect the required data.

But on the 5th day, the satellite’s electrical power system detected a fatal failure.

As a result, ISRO lost all the communication with the satellite.

ISRO reported that the mainframe of Aryabhata was active till 1981. In the year 1992 the satellite entered the Earth’s atmosphere again as a result of the orbital decay.

After reading this information about Aryabhata satellite, a question comes to mind.

Was Aryabhata satellite successful?

I say, yes it was.

It was India’s first indigenous satellite whose launch was successful.

The satellite went into its orbit with no trouble and went on for four days.

After 17 years of its launch - when there was no communication with the satellite - something happened.

The satellite re-entered the Earth’s atmosphere. It wasn't converted into shattered debris.

To me, it is something more than successful.

The world started giving respect to the scientists of ISRO because of Aryabhata.

India's space program emerged as a jewel in the eyes of the world for the first time.

Celebration of the Aryabhata Satellite

Indian and Russian governments celebrated the collaboration behind the launch of Aryabhata Satellite.

They released the stamps which featured Bhaskara-I, Bhaskara-II, and Aryabhata. Below is the image

The satellite found its place on currency

If you were born in ’90s or ’80s then you must be familiar with this 2 rupee note.

The satellite image on the back of this note is that of Aryabhata satellite.

The Indian government released these 2 rupee notes between 1976 and 1997.

Ancient mathematicians and their contributions

The mathematics today is sending people to Space. It has indeed sent our satellites to as far as Mars.

A lot of credit for the current state of mathematics goes to ancient mathematicians of India.

When I talk about Aryabhata I also feel the need to pay tribute to a few Indian mathematicians as well.

Ancient mathematicians and their contributions set the foundation stone of advanced mathematics.

Ancient mathematicians have given to us - with blessings - the algebra we enjoy, the arithmetic we adore, and the trigonometry we play with.

The number 0 has a strong significance in the world of mathematics.

You and I know well that when you subtract a number from itself it gives the result as ‘0’.

You and I would not know it if Brahmagupta hadn't discovered it. He told the world that adding two negative numbers also results in a negative number.

In astronomy, he contributed by discovering that the earth is closer to the moon than the sun.

Brahmagupta discovered the solution of the linear equation ax2 + bx + c =0.

Another ancient mathematician, worth mentioning, is Bhaskara I.

The work of Bhaskara I is the 99% accurate sine approximation formula.

Bhaskaracharya wrote the Siddhanta-Siromani when he was 36 years old. He is referred to as Bhaskara II to avoid confusion with Bhaskara I.

This notable work includes proof of the Pythagorean theorem.

It also provides the solution of indeterminate quadratic equations (ax2 + b2 = y2) and Pell’s equation.

Pell equation is the solution of the problem x2 - ny2 = 1, and notable contributions to calculus.

One of the genius mathematicians that India ever produced is Srinivasa Ramanujam. Ramanujam was never a trained mathematician.

In the early 20th century, he discovered the complex concepts of mathematics himself.

His significant contribution is the discovery of properties of the partition function. He discovered that you can express a positive integer as a sum of other positive integers.

For example, you can express 5 as 4+1, 3+2, 1+1+1+1+1, 3+1+1 and so on.

Ramanujam mastered the complex concepts of mathematics. He also gave a theory on divergent series.

NCERT mathematics textbooks must mention the Ancient mathematicians of India and their contributions.

As a child, I never knew that Brahmagupta discovered the formula of linear equations.

Mathematics books must pay tribute to the ancient mathematicians and their contributions. Doing so will instill a sense of motivation among students.

The students would now realize that the individual people invented all the complex concepts that they study.

Aryabhata Knowledge University

The name of the influential people serves as motivation.

In the honor of Aryabhata, the Bihar government established the Aryabhata knowledge university.

The Aryabhata knowledge University is affiliated with AICTE. The full form of AICTE is All India Council For Technical Education.

The central office of AKU is in Mithapur, Bihar. It was established in the year 2010 to improve the education infrastructure.

Since then the technical and the medical field have noticed significant growth.

The AKU has under its purview 56 engineering colleges, and 12 medical colleges.

Its spectrum doesn’t stop here. AKU has brought under its belt 36 nursing colleges and 11 vocational colleges as well.

I can say that the educational infrastructure has upgraded with the opening of AKU.

All this has happened in the name of Aryabhata education.

The Bihar CM inaugurated 4 centers of excellence within the premise of the AKU in 2020.

The 4 centers are listed below

1. The Patliputra school of economics,

2. Centre for river studies,

3. center for geographical studies,

4. center for journalism and mass communication.

He also unraveled the statue of the father of mathematics - Aryabhata.

Aryabhata Ganit Challenge

CBSE started the Aryabhata Ganit challenge in the year 2019 for the students of class 8 to class 10.

Starting the Ganit challenge in the name of Aryabhata, who is known as the father of mathematics, will make his name greater with every passing year.

Ganit challenge has 2 stages exam.

In the 1st stage, students from various schools take part. The registration is free.

The CBSE chooses an online portal to conduct the examination. You can register on it and access various modules.

On the portal, you can also access the practice set. CBSE selects the top three students from every school for the second stage.

A fee of Rs 900 needs to be paid to appear in the second stage of the Aryabhata Ganit challenge.

The CBSE awards merit certificates to the top 100 students from each CBSE region who clear the second stage.

The Aryabhata Ganit challenge quiz is of 1-hour duration and 60 marks.

I am listing the areas of math which the Ganit challenge focuses on -

1. practical applications of mathematics,

2. puzzles, history of math,

3. current affairs in mathematics,

4. reasoning,

5. numerical ability,

6. space and shape etc.

Bask in the intellect of the Genius

We all must have heard about Aryabhata some or the other time, but I bet that not many of us have tried to know more about his life’s works.

There is a dearth of good material on the lives of legends like Aryabhata. When I studied in school, I firmly remember that there was no chapter in our history books as well as science books on the works of Aryabhata. The only thing which prevails is a comment “he was a great mathematician”, but if we go dive deep into his achievements and the concepts he left for the world, then we will surely encounter his real value. To us he will always be the father of mathematics in India as well as the father of mathematics in world.

I hope that this articles has done its job of arousing a little curiosity in your mind to know more about Aryabhata. I hope that after reading this you will surely google Aryabhata, or will search for a video about him on the Youtube.

But before doing that do let me know how this article was?

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