Math Yoga
Ancient Hindu sutras offer intriguing shortcut to solving complex 
modern math problems


http://consciouschoice.com/2006/01/img/vedicmath1.jpg
Nikhil Reghunath (left), 11, and P.V.
Sarath Nath, 12, race through a set of practice problems in Vivek 
Astunkar's
Vedic math course. Photo: John Myers
----------------------------------------------------------------------

A taste of Vedic math 

The "Nikhilam" (by one more
than the one before) sutra 

One fun technique derived from this sutra instantly gives squares to 
any number ending with 5. So, to find the square of 75: 

1) Simply put 25 on the "right-hand side" of your answer. 

2) Take the number that precedes five (7, in this case) and add one, 
giving you 8. (This is where "by one more than the one before" takes 
flight.) 

3) Next, multiply 8 by 7 to get 56. This is the "left-hand side" of 
your answer. 

4) Put the results together, 56 and 25, to form 5,625. Check it! 

By John Myers
BOMBAY, INDIA - Math instructor Vivek Astunkar barely caps his pen 
before 12-year-old Janhavi Shah calls out "one, three, two, one, six, 
double zero!" She has, in mere seconds, correctly answered Astunkar's 
whiteboard challenge — multiply 1,120 by 1,180. 

Unlike Dustin Hoffman in the film "Rain Man," Janhavi cannot 
instantly count toothpicks dropped to the floor. In fact, her nine 
classmates — all normal, middle-class Indian youngsters — confirm her 
results just seconds later. 

They've used a shortcut from Vedic math, an alternative approach to 
calculation that Indian ascetics may have devised more than 3,500 
years ago. These yogic math techniques are mental exercises that can 
waylay the fear of numbers, build confidence and enhance creativity, 
says Astunkar. 

Vedic math is largely unknown in India, let alone the West. But 
that's changing. A local newspaper recently counted more than 40 
Bombay schools using it. Astunkar, alone, has tutored thousands of 
students, and also supplies newspapers with weekly Vedic problems. 
And a few organizations such as Mathvedics, which has franchises in 
California and Colorado, are pioneering the approach in America. 

"School is just studies. This is fun," says Janhavi, who sits at the 
end of a couch, sandwiched by peers, in Astunkar's small apartment, 
four floors up in one of New Bombay's mid-rise buildings. It's Sunday 
morning and the students are happy, even giggling, as they speed 
through multiplication problems that would make the average adult 
sweat. 

Astunkar, an aeronautical engineer who left his software firm five 
years ago to teach Vedic math, excels at making it fun. Using a small 
whiteboard, he writes out problems for the kids to race through, 
afterwards explaining the Vedic techniques in a flash of scribbling. 

He says the methods, derived from devotional Sanskrit verses called 
sutras, should not replace classic math practices. But, he adds, they 
offer students fresh, and ultimately faster, ways to calculate. 

A Hindu holy man, steeped deeply in Sanskrit and math scholarship, 
marshaled Vedic math into the modern era. Followers of Bharati 
Krishna Tirthaji believe he discovered 16 sutras in a long-lost 
appendix to the Vedas, Hinduism's most sacred religious texts. Using 
these verses, Tirthaji spent eight years (1911-18) reconstructing 
formulas that span math's various realms, from basic arithmetic to 
advanced calculus. 

Indeed, Tirthaji enthusiasts claim the 16 sutras encompass all 
possible mathematical knowledge. But they're left with precious 
little guidance from their guru. He supposedly wrote one book for 
each sutra and entrusted them to a disciple. Near the end of his 
life, however, the works mysteriously disappeared. Tirthaji obliged 
frantic devotees and rewrote the works from memory into one 
compressed volume, published posthumously in 1965 under the title 
Vedic Mathematics. 

Average readers will find the book virtually impenetrable. The 
sutras, simple phrases loaded with meaning, like "All from nine and 
last from 10," and "By one more than the one before," are spelled out 
but hardly illuminated. And the resulting math procedures are 
recorded but left largely unexplained, notes Astunkar. 

"I have read a little last night and not understood a word," says his 
student Janhavi. (Her mother, a college professor of commerce, bought 
a copy out of curiosity.) 

But, for most Indians, the appeal of Vedic math has less to do with 
its spiritual and cultural roots and more to do with the intense 
competition facing students on college entrance exams, says Atul 
Gupta, author of The Power of Vedic Maths. 

Gupta's book skims over the underlying sutras, instead featuring more 
than 1,000 practice problems with detailed explanations of the math 
techniques themselves. In a workshop Gupta offered in November, all 
but one of the students were preparing for technical examinations in 
the spring. 

Still, Gupta waxes poetically about the spiritual nature of Vedic 
math. "The simplicity and the brilliance of the techniques will make 
you feel humble," he says. 

Of course, Vedic math is not without controversy. Many scholars say 
it's neither "Vedic" nor "mathematics." 

Joining 15 math and Sanskrit scholars, Madhav Deshpande, a Sanskrit 
professor at the University of Michigan, argued as much in a signed 
letter sent to India's national council on school curriculum. 
Advocates hope to add Vedic math to the national curriculum, which 
these critics characterize as arithmetic "tricks." 

"I believe as a Sanskrit scholar that whatever its intrinsic merits 
or lack thereof, the contents of `Vedic Mathematics' have no 
historical connection with the Vedas," says Deshpande. 

Regardless what Sanskrit scholars make of the Vedic connection, it is 
full steam ahead for Astunkar, Gupta and other Vedic math teachers 
who hope to spread the practice. The goal is not to get students 
mired in Sanskrit, but to get them excited about math, says Astunkar. 

Recalling a student who found a way to expand a method for squaring 
numbers that end in 5 (see sidebar), Astunkar notes, "With Vedic 
math, their hidden creativity just pops up." 

Thanks to Vedic math, Chicago-based writer John Myers can instantly 
convert any price in rupees to dollars, astounding both chaiwallas 
and fellow travelers throughout India. 
http://consciouschoice.com/2006/01/vedicmath.html