Saturday, August 14, 2004

Vedic Mathematics?

I didn't even know there was such a thing. Ambition can push people to do strange things.

MUMBAI, India -- What is the square of 85? In an instant, a 17-year-old boy said without blinking, "7,225."

Kamlesh Shetty had used a trick from a quaint concept called Vedic math, a compilation of arithmetic shortcuts believed to have been written by ancient Indians who lived centuries before Christ, during a glorious period in Indian history called the Vedic Age. Its math has now crawled into the 21st century to further Shetty's dream of cracking a nasty engineering entrance exam.

For most Indian students, engineering is a calling decided in the cradle by their parents. It is engineering that is most likely to take them away from Third World realities to the shores of America's good life. So the tussle to get into engineering colleges is often cruel. In top entrance exams, only one out of 100 candidates makes the cut.

Quick problem-solving ability becomes the most crucial link between aspiration and fortune. Coaching for these exams is a multimillion-dollar industry in India, but with almost every student equipped with such preparatory courses, the applicants search for something more. That's why several Indian students are beginning to get help from an ancient source -- Vedic math. It has 16 brief formulas in Sanskrit that have been translated and interpreted into astonishing arithmetic shortcuts.

Shetty did not know the original Sanskrit verses, but he did know how to crack the square of 85 in less than a second. "To find the square of any number ending with 5, just put 25 on the right-hand side," he said. "Take the number that precedes five. In this case it is 8. Add 1 to it. So in this case it becomes 9. Multiply 8 and 9. You get 72. 7,225 is the square of 85. It's easy."

Shetty is preparing for the prestigious Joint Entrance Exam. Over 150,000 candidates take this entrance exam every year to compete for only about 3,500 seats in the Indian Institute of Technology. Two-thirds of IIT's graduates leave for America, augmenting the thousands already there who contribute to the institute's reputation. American colleges and industry greatly favor students from IIT, a situation that has only increased competition to enter the institute.

Pradeep Kumar, who teaches Vedic math in Delhi, said, "There is an increasing interest among IIT aspirants to take the help of Vedic math." Kumar charges such students about $120 for 40 hours of lessons. He teaches more than 200 students in the classroom and guides over 600 through long-distance courses.

Not all of his students dream of attending IIT. Several, mostly engineering pupils, are preparing for MBA entrance exams as tough as IIT's. One of Kumar's students, Kartik Arora, said, "Obviously Vedic math cannot teach you how to solve a problem. But it greatly reduces the computing time. I can vouch for the fact that in a two-hour exam, I can save about 10 minutes using Vedic math."

Vedic mathematics was ushered into the modern age by a Hindu seer called Tirthaji Maharaja, after his book on the subject was published posthumously in 1965. He culled 16 formulas from ancient scriptures. Whether the formulas were indeed written centuries ago or were largely partisan interpretations of obscure Sanskrit text is a matter of academic debate.

T.A. Ramasubban, who has penned a book on Vedic math, said, "The controversy arises because some people question how a cryptic Sanskrit verse that means several things can be safely interpreted as an arithmetic shortcut. For example, there is a verse in the Vedas (scriptures) that praises Lord Krishna in the Vedas. If the Sanskrit words are interpreted, the verse gives the value of pi to 30 decimal points.

"My point is that a verse may extol a god, but ... if it also gives the value of pi to 30 decimals, it cannot be a coincidence or desperate translation."
To be honest, this story doesn't really make any sense to me. First of all, one doesn't need any "Vedic mathematics" to be able to mentally multiply 2 or even 3 digit numbers in one's head: I've been able to do that for years, relying on plain old algebraic formulas like
(a+b)2 = a2 + 2ab + b2

(a+b)(a-b) = a2 - b2
After a bit of practice, familiarity starts to set in, and one no longer even needs to consciously think to know what the products of numbers will be; anyone can acquire this level of proficiency with just a little effort. As a matter of fact, the "shortcut" outlined in the story for finding the square of 85 takes longer to work with than simply adding up the sums of 6400, 800 and 25.

Now, putting aside for the moment the question of whether or not "Vedic mathematics" has anything to offer that good old elementary algebra doesn't, I also have to question the notion that mere mental arithmetic either does or should play a major role in any selection examinations to enter into prestigious academic institutions. The odd individual like Leonhard Euler aside, most mathematicians I'm aware of haven't been calculating prodigies, and it's actually rather surprising to the unitiated how insignificant a role numerical calculations play in the daily affairs of mathematical researchers. Being able to think carefully about abstract ideas and being able to regorgitate memorized tables of products are not at all the same thing, and God help the firm that hires an MBA who got his degree primarily because of his skill in the latter.

"Vedic mathematics" looks and smells like a confidence trick to me, a mere packaging of a few elementary tricks in a mysteriously antique guise designed to part desperate students from their money. As these things go, it seems like a nice little racket though, I must say.

UPDATE: Here's a monograph that confirms my suspicions that this is just a scam.