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Vedic Mathematics

- An article by Vinay Nair, as appeared in 'Tapovan Prasad' in September 2010. -

Bharat has been the motherland of many great souls whose contributions have helped the whole of mankind. One among them was Swami Bharati Krishna Tirthaji who recreated a system of Mathematics that is popularly known today, as 'Vedic Mathematics'.

Born to highly learned and pious parents in 1884 at Tirunelveli in Madras Presidency, Venkatraman was an exceptionally brilliant boy. He always stood first in his class for all the subjects. At the age of sixteen, he was awarded the title 'Saraswati' for his proficiency in Sanskrit. He was deeply influenced by his Sanskrit Guru Sri Vedam Venkatrai Shastri whom he remembered with deepest love, reverence and gratitude. When he was twenty, he passed M.A. of American College of Sciences, New York (from Bombay Centre) in seven different subjects (His subjects included Sanskrit, Philosophy, English, Mathematics, History and Science) simultaneously securing the highest honours in all. He was proficient in fourteen languages.

Prof. Venkatraman served as Principal of National College, Rajmahendri for a short period until his thirst for spiritual knowledge pulled him to Swami Satchidananda Sivabhinava Nrisimha Bharati at Sringeri. After eight years of extensive study of the scriptures, Prof. Venkatraman was initiated into the Holy order of Sanyasa as Swami Bharati Krishna Tirthaji. After few years, JagadGuru Shankaracharya Sri Madhusudan Tirtha's (of Govardhan Math) health took a severe turn and Swami Bharati Krishna Tirthaji had to take up his position at Puri Govardhan Peeth.

During his life, Swamiji travelled throughout India. He was a spiritual dynamo. Vedic Mathematics was one of his epoch-making contributions to the world. During his Vedic studies at Sringeri (1911-1918), as a result of his intense tapas in the forests of Sringeri, Swamiji unraveled the hidden meanings of certain Sutras (aphorisms or word formulae).

Vedic Mathematics is based on Sixteen Sutras and Thirteen upaSutras; which Swamiji says, he 're-discovered' from the Vedas. One may not find these Sutras as it is in the Vedas, but the essence or the root is from the Vedas. Such was the greatness of Swamiji. He could have easily claimed the ownership of the New System of Mathematics, and nobody could have doubted it. But, like any other great saint of India; he gave the credit to the Vedas.

Swamiji had written sixteen volumes on Vedic Mathematics (one volume on each sutra). But before it could be printed, it was irretrievably lost. Everyone grieved over the great loss except Swamiji, for he said he could rewrite them all recollecting from his memory. In one and a half month's time, he wrote one introductory volume. However, the toll that had taken on his failing health, on account of his rigorous work for almost four decades (and losing eye-sight due to cataract), did not allow him write more. And in February 1960, the Mahatma left his mortal frame.

About Vedic Mathematics

Swamiji's introductory Volume of Vedic Mathematics itself covers Subtraction, Multiplication, Division, Squares, Square Roots, Cubes, Cube Roots, Factorisation, Simple & Quadratic Equations, Polynomial Multiplication and Division, Compound Multiplication, Divisibility and much more. The remaining fifteen volumes had higher levels of Mathematics based on the same sixteen Sutras and thirteen upa-Sutras. Never in the past has anyone made such a discovery by encapsulating such a vast subject like Mathematics in just a few Word Formulae.

When one hears the word 'Sutras' in a language like Sanskrit, one need not think that he should have knowledge in Sanskrit to understand the subject. It is so lucid that children of any caliber can learn it with ease. Unlike the Mathematics that is taught in school which has only 'one way' to do a particular calculation, Vedic Mathematics teaches different ways to solve the same problem. Perhaps, this was Swamiji's way to connect Mathematics to God – Different ways to attain the same 'Truth'!

Using Vedic Mathematics, even a ten year old can calculate 999 x 991 in less than five seconds, and that too in a method of his own choice. This may look like an exaggeration but it is the Truth. More than 'Techniques' this subject facilitates 'Thinking', which today's educational system in India unfortunately does not allow. Another sad thing is that such a great text has not been introduced in Indian Universities. But it has been accepted as a part of syllabus in some schools of England. Today, there are many books available on Vedic Mathematics (based on the introductory volume of Vedic Mathematics), many of them written by Western Mathematicians.

Many school students are afraid of Mathematics and they have no option but to learn it. Using Vedic Mathematics we can enjoy the subject and experiment & discover different methods. Imagine how much time we could save doing calculations if we learn Vedic Mathematics!

Difference between Teaching & Learning

- an article by Vinay Nair

A toddler saw an ant coming towards him. He goes, picks it up and gets bitten. Immediately he starts crying. He had a painful experience. Next time he won't go and touch an ant; for, he had a Learning.

Learning is an experience. By the time a child is of 5 years of age, he has learnt a great deal of things without anybody teaching him. He Observes. He Experiments. He gets an Experience. He Learns. He will never forget such Learnings in his entire life because he learnt it through an Experience.

Teaching is more like a process. We are taught different subjects in schools. However, there are some things that can't be taught, but only Learnt… such as mannerism, discipline, etc. We see parents shouting at small children when he becomes cranky, adamant or demanding. The intention of the parents is to convey the message that 'demanding is not good'. But the way it is conveyed itself is demanding. Now the question is – from where does the child learn to demand or be adamant?

Many a times, parents wonder from where their child has learnt to behave like this. Only if they would observe (like the child did) their own ways of talking & behaving, will they realize that they themselves were an 'object' for the child's learning. Not realizing this fact, parents try to correct the child by scolding, punishing, ordering and expecting the child to change instead of the parents becoming a better role model for the child.

Another important aspect in parenting is, to facilitate Learning. We need to give enough opportunities to kids to explore things and improve their imaginations. For this, we should bring ourselves down to the child's level and try to see what he is thinking. Often parents and teachers correct on some creation the child has done – like when they draw a cow and colour it green, or when they fix square wheels to a car using their building set.

First of all, the question is - is correction required here? Is the child never going to realize what is correct if we don't correct him? What's wrong if the child imagines something which elders can't imagine? The damage done by correction, according to psychologists, is that, it conveys a wrong message to the child. And the message is – "I'm not correct". With repeated corrections, his interest and confidence decreases. His imaginations reduce. And one day, his creativity gets killed.

The above could be basically summarized into two points:

  • 1. Change yourself to a better role model with traits like patience, tolerance, empathy, etc instead of demanding the child to change.
  • 2. Avoid corrective steps so that a child can expand his imagination.

Let not a child's Learning be killed by Teaching.

Learning – The Other Way

- an article by Vinay Nair -

Once I happened to meet somebody with whom I was having a conversation on Mathematics. He was telling me his story as to how haunting the subject was for him during his school and college days. He would top in every other subject but Maths…would take his percentage down. Somehow, with the help of his friends (before and during the exams) he used to pass in Maths. When he was in his twelfth standard, he confessed to his father that he won't be able to clear the exam without having tuition. So his father arranged a Tuition Master for him. This Sir had a stammering problem due to which he didn't get a good job in schools and made his living by taking private tuitions. Before he started going for the tuition, he had scored 4/200. But after four months coaching, he scored 168/200 in his final exams. Of all the people in the world, he (the student) had received the greatest shock. After he thanked his Sir he asked, "Sir, how come I got so many marks in Maths? I never used to understand this subject no matter how hard my professors & I tried. How did I understand from you?" His Sir replied (stammering), "My boy…the pause taken due to my stammering, gave you time to Think!"

Today, what usually happens in schools & colleges is Teaching; and not Learning. The teachers teach, write something on the blackboard and the students copy them down and study. As a result, they just become photocopying machines, with no Actual Knowledge happening inside them. Maths is one subject, which just cannot be learnt like that. And if someone tries teaching this way, he may succeed in teaching a very few and creating nightmares for the remaining students. Maths cannot be taught. It has to be discovered within us. It's like music. Every student who learns Classical music, has to discover the correct musical notes within him.

Look at the world around. Don't we see Maths everywhere? Who taught the birds speed, time & distance? Who taught the honey bee to make every cell in a hive in the shape of a hexagon? Who taught the spider to create a web in a particular model? Innumerable are the examples in the case of animals and birds to prove this fact. In case of humans also, it's not different. Let us take a common example that we have seen many a times. Imagine a fielder on a cricket pitch. When he runs towards the boundary line to catch a ball flying through the air, all he does is keeping his focus on the ball. But unknowingly, he calculates the speed of the wind, the way in which his palms should come together to catch the ball, how fast should he run, what is the shape of the arc that he has to take to catch the ball, at which spot is the ball going to land, etc. How does this happen?

Our brain has an inbuilt capacity to do Mathematical calculations even without our knowledge. Since it is done so fast, we don't realize such a happening. Maths is in our blood. We just have to bring it out. And this can be done when we get time to think. Children can do a lot better if they are given time to think. This is what our Maths teacher, Sir P.P.Raman, taught us. He used to give us a particular problem in geometry and go out of the class for a break. By the time he comes back to the class, most of us would have got the solution to the problem, and that too not just one but different solutions. This was how he taught some great things in life – Any problem can be solved in different ways. The clue to the solution lies in the problem itself. Keep meditating and the solution will appear.

I tried experimenting this in my classes of Vedic Mathematics for secondary school students. I stopped teaching the usual way. I started writing down problems and the answer without showing how I derived it. Then all I had to do was, challenge the children to find out the method. Within no time, they started finding out the methods, without being taught. The joy that I saw in their eyes was something that cannot be explained. They started feeling as if they have become Scientists or Mathematicians doing their own discoveries. They never forget these methods of calculating because – it is 'their discovery'. Not just that, after a few days, some children (who were just average in Maths) came up with new methods of doing some particular calculations which I didn't know.

This was the beginning of a whole set of students crying out as Maths as their favourite subject. How much confidence they must have gained in themselves after deriving such methods? What a change will it bring in their lives? The effort taken was just a shift in the way of teaching.

Let's try something different. Let's give them time & opportunity to Think. And the children will come up with better ideas. Let LEARNING happen, the OTHER WAY!

Learning is Discovering

- an article by Vinay Nair

Maths is one of the oldest subjects that we have today. Oldest because, even the caveman used it. But who taught him? When birds fly, they calculate speed, time & distance. A cheetah, while chasing its prey, runs in such a way that it covers the minimum distance to catch. Who taught them Maths? The only possible answer is – they discovered it on their own. Every living organism has a Maths program in it. They use it knowingly or unknowingly as per their requirements. In the subject of Vedic Maths, we see how Maths can be discovered from our 'within'.

Vedic Maths is about observation. All we need to do to learn a particular technique in Vedic Maths is – To keep looking at it. After some time, we see a pattern that keeps repeating.


  • a) 35 x 35
  • b) 42 x 48
  • c) 77 x 73
  • d) 84 x 86

Do you see any pattern repeating in the questions?

Ans a) 1225   Ans b) 2016    Ans c) 5621    Ans d) 7224

Now keep looking at the first two digits & last two digits of every answer, you will see a pattern.

Scientists say, left side of our brain receives data & information, analyses it and gives the result. The right side of the brain observes patterns, designs, etc. Creativity & Intuition can be developed only if the right side of our brain is used more. When any subject is 'taught', only the left brain is developed. But when it is 'discovered', our right brain develops. As a result, we just don't become good at Maths but also improve on other Creative areas.

With repeated observation of patters in calculations, our brain automatically starts performing them without us even realizing of such an event happening inside our brain. It's like how we see in cricket. When the bowler releases the ball, how much time does the batsman get to decide how to hit it? Just a fraction of a second. And within that time he calculates the speed, spin / swing of the ball, his footwork, gap between fielders, force and angle at which he should hit the ball, and much more. Such is the capacity of our brain.

We can make our brains sharp by learning this wonderful subject – Vedic Maths; where Learning is Discovering!

DID YOU KNOW | Evolution of Algebra and Geometry

DID YOU KNOW that Greek and Romans were idol worshippers and Geometry developed to a great extent in their country? Arabs were not idol worshippers and Algebra developed in their country. India was a combination of both philosophies where some people follow idol worship and some didn't. Could that be one of the reasons why both Algebra and Geometry developed in India?

The ancient texts of Mathematics, Sulba Sutras, contain geometrical constructions pertaining to religious sacrificial rituals. When there was a need, the branch of geometry developed. Temples & rituals can be seen in Greek & Roman history which might have forced them to develop geometry in their country.

Be it a coincidence or a fact, it is surely a good point to think upon. Do religious faiths factor the development of mathematics in a culture?