How Vedic mathematics adds up so well
I hated maths all my life. My hate affair with numbers started from Class II and continued till I squeaked through the nationwide Class X exam. During those 10 torturous years I went through frustration, anger and depression. Two expensive daily tuitions, one at 7am and another at 1pm, desperate prayers to Lord Shiva, and offerings at the Hanuman temple helped me pass that wretched subject. Maths wasn’t my only worry. India’s school curriculum is several orders of magnitude tougher than most countries. At the age of 14, I had to joust with 11 different subjects, including two mathematics papers.
So imagine my surprise when last month I found myself enjoying maths, with the exuberance of a child who has been given a new toy. After years of estrangement with numbers, I was doing long calculations in a jiffy and handling huge sums with a big grin. No, I wasn’t on mind-altering drugs. I had discovered the ancient Indian system of mathematics called Vedic maths.
As the name suggests, Vedic maths is as old as the Vedas, the four ancient Hindu books on religion, science, mathematics, logic, philosophy and a whole lot more. In terms of date, it’s safe to assume they are at least 7,000 years old.
Vedic maths was rediscovered from the ancient Indian scriptures between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960), a scholar of Sanskrit, mathematics, history and philosophy. He studied these ancient texts for years, and after careful investigation was able to reconstruct a series of mathematical formulae called sutras.
Tirthaji, who was also the Shankaracharya (Pontiff) of the holy eastern Indian city of Puri, delved into the ancient Vedic texts and established the techniques of this system in his pioneering work - Vedic Mathematics (Motilal Banarasidas, 1965). The Shankaracharya has acknowledged the contributions of the Vedas as the source Vedic math, especially the Atharva Veda - the last of the four Vedas that deal with the existential issues of architecture, mathematics, engineering and medicine.
In his seminal book, the Shankaracharya says: “Even as regards complex problems involving a good number of mathematical operations, the time taken by the Vedic method will be a third, a fourth, a tenth, or even a much smaller fraction of the time required according to modern methods.
“And in some very important and striking cases, sums requiring 30, 50, 100 or even more numerous and cumbrous ‘steps’ of working can be answered in a single and simple step of work by the Vedic method! And little children (of only 10 or 12 years of age) merely look at the sums written on the blackboard and immediately shout out and dictate the answers. And this is because, as a matter of fact, each digit automatically yields its predecessor and its successor! And the children have merely to go on tossing off (or reeling off) the digits one after another (forwards or backwards) by mere mental arithmetic (without needing pen or pencil, paper, slate etc.).
“On seeing this kind of work actually being performed by the little children, the doctors, professors and other ‘big-guns’ of mathematics are wonder-struck and exclaim: ‘Is this mathematics or magic’? And we invariably answer and say: ‘It is both. It is magic until you understand it; and it is mathematics thereafter’. And then we proceed to substantiate and prove the correctness of this reply of ours!”
I bumped into Vedic maths quite by accident after reading about the Indian learning portal e-Gurukul.net’s live webcast on the subject. Wanting to show my son, who incidentally is good at the subject, the beauty of Vedic maths, I got hooked myself. To be sure, I was more enthusiastic than knowledgeable about the subject; I knew Vedic maths was interesting but little else.
My expectations were exceeded and a month later, my post-webcast elation hasn’t ebbed. Vedic maths is totally amazing. It’s like a book you stopped reading after a couple of pages many years ago, chanced upon it a decade later while cleaning the attic, and found it hard to put down. You can do calculations such as 5989 x 1111 in about five seconds – a lot faster than it takes you to punch out those numbers on a calculator.
It’s not about shortcuts though. Vedic maths demystifies numbers and lifts the veil of secrecy from the world of maths. James T. Glover, a Welshman, who has written the three-volume Vedic Mathematics for Schools, illustrates the brilliant simplicity of Vedic maths:
Can you find out how many matches are played during the Wimbledon men's singles tennis championship, based on the information that the first round has 64 games, the next 32 until you reach the quarter-finals, semi-finals and the final?
The conventional approach is to add the number of games: 64+ 32+16+8+4+2+1 to get to the answer, 127.
Try the Vedic approach: Since there are 128 players (2 x 64) and only one person wins the competition, there must be 127 losers and for each loser there is a match, so there are 127 matches.
It’s so uncannily simple that you can’t help wondering how many decades or centuries of toil and thought the ancient Hindu mathematicians must have put in before discovering these steps that make maths such a pleasure.
Such simplicity means calculations can be carried out mentally too. Also, the Vedic system distills all maths problems to the everyday numbers zero to 9, so students treat even the largest sums as friends, rather than as cumbersome chores. This creates a lifelong love for maths, opening up more career streams. Also, students get an edge over the rest in competitive exams where speed matters as much as skill.
Predictably, Vedic maths has its fair share of detractors. While an increasing number of people outside India are discovering the joy of numbers, in its home country Vedic maths has lost traction.
e-Gurukul deserves a massive congratulation for taking maths to numerophobic people like me. Sure, it’s too late in the day for me but for schoolchildren it could well be a game changer. If systematically introduced, Vedic maths has the potential to create an even larger number of students pre-disposed towards maths.
Remember that India has produced one of the greatest mathematicians of the ancient as well as medieval world. Aryabhata, Brahmagupta, Bhaskara, Varahamira, Madhava and Nilakantha, to name just a few, belong to a long and impressive line of mathematicians, who gave the world the zero, the numbers 1-9, the decimal system, algebra, trigonometry, calculus (before Newton), in fact too numerous to list here.
However, in the modern era, our record has been pathetic. In the last 100 years we have produced perhaps one mathematician of repute – S. Ramanujan. If India wants to reclaim its position as the world's leading scientific nation, we must follow Swami Vivekananda’s advice: “Back to the Vedas.”
(Rakesh Krishnan is a features writer at Fairfax New Zealand. He has previously worked with Businessworld, India Today and Hindustan Times, and was news editor with the Financial Express.)
I hated maths all my life. My hate affair with numbers started from Class II and continued till I squeaked through the nationwide Class X exam. During those 10 torturous years I went through frustration, anger and depression. Two expensive daily tuitions, one at 7am and another at 1pm, desperate...
I hated maths all my life. My hate affair with numbers started from Class II and continued till I squeaked through the nationwide Class X exam. During those 10 torturous years I went through frustration, anger and depression. Two expensive daily tuitions, one at 7am and another at 1pm, desperate prayers to Lord Shiva, and offerings at the Hanuman temple helped me pass that wretched subject. Maths wasn’t my only worry. India’s school curriculum is several orders of magnitude tougher than most countries. At the age of 14, I had to joust with 11 different subjects, including two mathematics papers.
So imagine my surprise when last month I found myself enjoying maths, with the exuberance of a child who has been given a new toy. After years of estrangement with numbers, I was doing long calculations in a jiffy and handling huge sums with a big grin. No, I wasn’t on mind-altering drugs. I had discovered the ancient Indian system of mathematics called Vedic maths.
As the name suggests, Vedic maths is as old as the Vedas, the four ancient Hindu books on religion, science, mathematics, logic, philosophy and a whole lot more. In terms of date, it’s safe to assume they are at least 7,000 years old.
Vedic maths was rediscovered from the ancient Indian scriptures between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960), a scholar of Sanskrit, mathematics, history and philosophy. He studied these ancient texts for years, and after careful investigation was able to reconstruct a series of mathematical formulae called sutras.
Tirthaji, who was also the Shankaracharya (Pontiff) of the holy eastern Indian city of Puri, delved into the ancient Vedic texts and established the techniques of this system in his pioneering work - Vedic Mathematics (Motilal Banarasidas, 1965). The Shankaracharya has acknowledged the contributions of the Vedas as the source Vedic math, especially the Atharva Veda - the last of the four Vedas that deal with the existential issues of architecture, mathematics, engineering and medicine.
In his seminal book, the Shankaracharya says: “Even as regards complex problems involving a good number of mathematical operations, the time taken by the Vedic method will be a third, a fourth, a tenth, or even a much smaller fraction of the time required according to modern methods.
“And in some very important and striking cases, sums requiring 30, 50, 100 or even more numerous and cumbrous ‘steps’ of working can be answered in a single and simple step of work by the Vedic method! And little children (of only 10 or 12 years of age) merely look at the sums written on the blackboard and immediately shout out and dictate the answers. And this is because, as a matter of fact, each digit automatically yields its predecessor and its successor! And the children have merely to go on tossing off (or reeling off) the digits one after another (forwards or backwards) by mere mental arithmetic (without needing pen or pencil, paper, slate etc.).
“On seeing this kind of work actually being performed by the little children, the doctors, professors and other ‘big-guns’ of mathematics are wonder-struck and exclaim: ‘Is this mathematics or magic’? And we invariably answer and say: ‘It is both. It is magic until you understand it; and it is mathematics thereafter’. And then we proceed to substantiate and prove the correctness of this reply of ours!”
I bumped into Vedic maths quite by accident after reading about the Indian learning portal e-Gurukul.net’s live webcast on the subject. Wanting to show my son, who incidentally is good at the subject, the beauty of Vedic maths, I got hooked myself. To be sure, I was more enthusiastic than knowledgeable about the subject; I knew Vedic maths was interesting but little else.
My expectations were exceeded and a month later, my post-webcast elation hasn’t ebbed. Vedic maths is totally amazing. It’s like a book you stopped reading after a couple of pages many years ago, chanced upon it a decade later while cleaning the attic, and found it hard to put down. You can do calculations such as 5989 x 1111 in about five seconds – a lot faster than it takes you to punch out those numbers on a calculator.
It’s not about shortcuts though. Vedic maths demystifies numbers and lifts the veil of secrecy from the world of maths. James T. Glover, a Welshman, who has written the three-volume Vedic Mathematics for Schools, illustrates the brilliant simplicity of Vedic maths:
Can you find out how many matches are played during the Wimbledon men's singles tennis championship, based on the information that the first round has 64 games, the next 32 until you reach the quarter-finals, semi-finals and the final?
The conventional approach is to add the number of games: 64+ 32+16+8+4+2+1 to get to the answer, 127.
Try the Vedic approach: Since there are 128 players (2 x 64) and only one person wins the competition, there must be 127 losers and for each loser there is a match, so there are 127 matches.
It’s so uncannily simple that you can’t help wondering how many decades or centuries of toil and thought the ancient Hindu mathematicians must have put in before discovering these steps that make maths such a pleasure.
Such simplicity means calculations can be carried out mentally too. Also, the Vedic system distills all maths problems to the everyday numbers zero to 9, so students treat even the largest sums as friends, rather than as cumbersome chores. This creates a lifelong love for maths, opening up more career streams. Also, students get an edge over the rest in competitive exams where speed matters as much as skill.
Predictably, Vedic maths has its fair share of detractors. While an increasing number of people outside India are discovering the joy of numbers, in its home country Vedic maths has lost traction.
e-Gurukul deserves a massive congratulation for taking maths to numerophobic people like me. Sure, it’s too late in the day for me but for schoolchildren it could well be a game changer. If systematically introduced, Vedic maths has the potential to create an even larger number of students pre-disposed towards maths.
Remember that India has produced one of the greatest mathematicians of the ancient as well as medieval world. Aryabhata, Brahmagupta, Bhaskara, Varahamira, Madhava and Nilakantha, to name just a few, belong to a long and impressive line of mathematicians, who gave the world the zero, the numbers 1-9, the decimal system, algebra, trigonometry, calculus (before Newton), in fact too numerous to list here.
However, in the modern era, our record has been pathetic. In the last 100 years we have produced perhaps one mathematician of repute – S. Ramanujan. If India wants to reclaim its position as the world's leading scientific nation, we must follow Swami Vivekananda’s advice: “Back to the Vedas.”
(Rakesh Krishnan is a features writer at Fairfax New Zealand. He has previously worked with Businessworld, India Today and Hindustan Times, and was news editor with the Financial Express.)
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