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Vedic Mathematics – Introduction

Vedic mathematics is the natural home of mathematics as we know it today. Mathematics as a subject is the one invented by humans, for our own convenience to represent things and to do calculations, unlike other sciences whose basic laws are found in nature. In Mathematics, it is the humans who have devised the computational methods.

And we all know that the roots of modern mathematics go back to ancient India. To quote Albert Einstein

We should be thankful to the Indians who taught us how to count, without which no worthwhile scientific discovery would have been possible.

Those who have studied the Roman Number System readily understand the difficulty in it. Every single number has its own unique symbol in Roman System and after a few numbers the system runs out of symbols! L gets introduced to represent 50, C gets introduced to represent 100, D at 500, M at 1000 and so on. And so, no reasonable mathematics beyond simplest of additions is possible in this system.

Ancient Indians took a completely scientific approach to mathematics. Mathematics was not about symbols, it was more about the actual numbers. So Indians decided about using a given set of symbols to represent any and every number, so that we don’t have to search for new symbols as we climb towards larger numbers.

The result was a place value based system, where a base was taken first, which simply meant the number of symbols used to represent numbers. And the same symbols would be used everywhere, and as we ran out of symbols, we simply push the symbols to left to represent the new number, and reintroduce other symbols on the right side.

I feel that the world’s best innovation was this place value based mathematical system which forced Indians to invent zero too. As a saying goes, the greatest contribution of Indians to world is Nothing! Nothing meaning Zero

Please note that zero was only a byproduct of this place value based system. The most important concept here is the place value system itself, not Zero.

Let me explain how.

First let us consider a base. Say 1 2 3 4 5 6 7 8 9. So these are our nine symbols for base 10.

Now ancient Indians devised a system where any number however big or small could be represented using only the nine symbols mentioned above.

The nine symbols used today are 1,2,3,4,5,6,7,8,9

Why 9, why not 10 symbols? The actual idea was a base 10 system because humans have 10 fingers, so base 10 looks more natural. But one symbol was left out to make room for symbol promotion, a symbol increases its value 10 times when it shifts one place to the left! This amazing place value based system then can be used to represent any large number however big, without having to add any new symbols to the list!

So what next? well, just repeat the cycle by pushing the first number again one place left (called the ten’s place), and then create a new number by repeating the symbols in the original place (called the unit’s place).

Why was zero invented OR why should there be nothing? To understand this, consider 101. If 1 is in hundred’s place and 1 is in unit’s place, how do we represent it symbolically showing there is nothing between the two one’s in the tenth place?

This is when ancient Indians invented Zero. Zero is called Shunya in Sanskrit, meaning nothing. So zero as a place holder was used to represent an empty space, with no value stored there. Zero is not a number, in fact it was invented to say, there is no numeric value here. 100 means there is no value here(0) and here(0) at the end, but only here(1)

So we had 10 after 9, where the symbol 1 in 10 meant the value of 1 is ten times more than its value in 1, and this was visually indicated by having 0 in the unit place. An amazing system this was, where the value of a symbol is decided depending upon where it is placed! so 1 in 212 is different from 1 in 199! You never run out of symbols here, unlike the roman system!

Vedic Mathematics was again a continuation of this basic mathematical principles, where methods were devised by ancient Indians to make mathematics easy. So easy that, what we call to be difficult problems in modern mathematics, can be done mentally without using a pen and paper in the vedic mathematics! Why? Because vedic mathematics was the math devised by the very same people, the ancient Indians, who had created the basics of the mathematics. They clearly knew how to play with the numbers!

Why then did the vedic mathematics did not enter west along with place value and zero? Well, because most of the modern mathematics was popularized in the west by the arab merchants who borrowed the simple ancient Indian math, which was very helpful for their trade, and popularized this system in the west when they went there to trade the Indian spices, diamonds and other goods. Which is why the base 10 symbols (1 to 9) are called Hindu-Arabic numerals, invented by Hindus i.e ancient Indians and popularized in the west by Arab merchants.

Ancient India was the world’s largest exporter of goods! Entire europe panicked, when ottoman turks captured constantinople by blocking the land route to India in 1453, the turks demanded that the european/arab traders pay a heavy tax to pass to India through Constantinople which was the connecting land route from Europe to India!

Panicked by this european countries started a series of naval adventures to find a sea route to India. Note that it was not the Indians who were desperate to find a sea route to Europe, it was the other way round! Just imagine how dependent the rest of the world was on India then! What is America today was discovered and known to the rest of world because of this quest to search a sea route to India! Columbus who had set out to discover a sea route to India, thought he had reached India when he touched the west indies island and the american continent, which is why west indies is called so, and the native americans were called Red Indians by him!! America was discovered, thanks to India!

Which is what I keep stressing to the Indian youth that we need to bring back those golden days to make India a great power!

Coming back to the vedic mathematics, the ancient greeks learnt mathematics from the Indians. The famous historian Albert Burk, says that Pythagoras visited Arakonam, India, and learnt the so called Pythagorean theorem there! The very fact that Pythagoras never gave a proof to his theorem, proves that he did not discover it.

Baudhayana, a mathematician who lived in ancient India, centuries before Pythargos, has written a list of Pythagorean triplets discovered algebraically, has stated the so called Pythagorean theorem, and also has given a geometrical proof of the Pythagorean theorem for an isosceles right angled triangle!

Another great aspect of vedic mathematics is there is no single fixed way of solving a problem. Students can devise their own better ways also! And this gives scope for ample creativity and fun. Students will ENJOY this form of mathematics, because they UNDERSTAND it, unlike the methods taught in the schools and colleges today where for ex, many students who solve differential equations, really have absolutely no idea of what they are solving or what a limit means!

The beauty of vedic mathematics is the way in which the entire system is inter related, where when you know something is a reverse of an existing thing, all you have to do is to reverse the method to calculate that something! For ex, the multiplication method when reversed becomes the division method, because division is the opposite of multiplication!! The method of finding squares when reversed becomes the method of finding square roots!!

In vedic mathematics, maths becomes , not something that is difficult/cryptic to understand, but like reading a novel or like watching a movie, full of fun and entertainment

Dr David Gray says . .the role played by India in the development (of the scientific revolution in Europe) is no mere footnote, easily and inconsequentially swept under the rug of Eurocentric bias. To do so is to distort history, and to deny India one of its greatest contributions to world civilization .

He also says, The Yajurveda Samhitaa, one of the Vedic texts predating Euclid and the Greek mathematicians by at least a millennium, lists names for each of the units of ten up to 10 to the twelfth power (paraardha). Later Buddhist and Jain authors extended this list as high as the fifty-third power, far exceeding their Greek contemporaries, who lacking a system of enumeration were unable to develop abstract mathematical concepts.

The place value system of enumeration is in fact built into the Sanskrit language, where each power of ten is given a distinct name. Not only are the units ten, hundred and thousand (dasha, shatha, sahasra) named as in English, but also ten thousand, hundred thousand, ten million, hundred million (ayuta, laksha, koti, vyarbuda), and so forth up to the fifty-third power, providing distinct names where English makes use of auxillary bases such as thousand, million, etc.

George Ifrah, the professor of mathematics who traveled around the world in search of origin of numbers has said that By giving each power of ten an individual name, the Sanskrit system gave no special importance to any number. Thus the Sanskrit system is obviously superior to that of the Arabs (for whom the thousand was the limit), or the Greeks and Chinese (whose limit was ten thousand) and even to our own system (where the names thousand, million etc. continue to act as auxillary bases). Instead of naming the numbers in groups of three, four or eight orders of units, the Indians, from a very early date, expressed them taking the powers of ten and the names of the first nine units individually. In other words, to express a given number, one only had to place the name indicating the order of units between the name of the order of units immediately immediately below it and the one immediately above it. That is exactly what is required in order to gain a precise idea of the place-value system, the rule being presented in a natural way and thus appearing self-explanatory. To put it plainly, the Sanskrit numeral system contained the very key to the discovery of the place-value system.

Irfah concluded that place-value numeral system developed in India and this system is embedded in the Sanskrit language

Before we start the actual Vedic mathematic lessons, I strongly recommend that you read this article on the Origin of Mathematics by Dr David Gray.

Recommended Reading

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Gurudev is the developer of Gurunudi AI Platform. This is his official website where he pens his thoughts on a wide range of topics, answers queries, shares resources and tools developed by him.

4 COMMENTS

  1. Kind regards,
    I request you to give me the exact wordings of Albert Burk, the famouse historian and also the name and page no. of the book inwhich he has written as ‘Pythagorus came to Arakkonam and copied the the theorem’, please. What is the proof he has given in support of his statement on Pythagorus? – Dr.M.L.Raja

    • The Apastamba Sulba Sutra composed by Apastamba at around 600 BCE contains1. The method of squaring the circle
      2. Considers the problem of dividing a segment into 7 equal parts
      3. Calculates the square root of 2 correct to five decimal places
      4. Solves the general linear equation
      5. Contains a numerical proof of the Pythagorean theorem, using an area computation. 

      Albert Burk claims this was the original proof of the theorem which Pythagoras copied on his visit to India.Reference: Das Apastamba Sulba S?tra by Albert Burk (published in 1901)See http://www.vedah.com/essays-on-veda-upanishad-etc/advanced-topics/85-mathematics-in-veda/493-mathematics-in-veda

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