India’s has the number on math

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India's has the number on math

 

 

CHIDANAND RAJGHATTA

 

TIMES NEWS NETWORK [ MONDAY, AUGUST 12, 2002 8:22:09 PM ]

 

Chidanand Rajghatta muses about the Indian legacy in mathematics

following the latest number crunching feat from Kanpur

 

 

On the subject of mathematics, there are two kinds of people – the

number crunchers and the number crunchees i.e., those who can crunch

numbers with great facility, and those who get crunched by numbers.

 

 

There are those of you who love to develop your quadriceps with

quadratic equations and have binomial theorem for breakfast. Then

there are those of us, who, faced with simple multiplication tables,

have to lie down with a cold wet towel on our forehead.

 

 

Where do you think you belong?

 

 

There is a widespread belief that we Indians have a yen for numbers.

It might not entirely be true. There are plenty of people even in

Bharatvarsh who will to Bill Clinton's jocular admonition

that folks across the world would have been perfectly happy if

Bhaskara and Brahmagupta had kept their works to themselves.

 

 

Still, in the same spirit that contrived the number zero and the

value pi, it turns out that Indians are still contributing

significantly to the world of numbers even now, odd exceptions

notwithstanding.

 

 

The announcement this week that three mathematicians from the Indian

Institute of Technology, Kanpur, have devised a method (or arrived

as a logarithm, in mathematese) to determine whether a number is

prime or not has created quite a flutter (or a quiet flutter) in the

world of numbers.

 

 

Prime numbers, for those of us mathematically challenged, are those

that are divisible only by itself or by one. Although it sounds

simple enough, it's quite a task to determine what mathematicians

call the "primality" of a number. For instance, is

4958372640287988786544 a prime number?

 

 

Of course, the more facetious among us can say -- does it really

matter? Apparently it does in ways that we may not immediately

comprehend, like for instance, in determining whether the bristles

on the toothbrush hurts our gums. That's a joke. But you get the

point.

 

 

Some applications are not immediately apparent to the matho-phobics.

One of the applications of prime numbers is in the world of

cryptography i.e encryption and code breaking, which may be evident

if you read the secret passage hidden in the preceding paragraph.

That's another joke. Read on.

 

 

For years then, mathematicians have wrestled with ways to determine

the primality of numbers. There are established methods, but they

pose problems. One method can determine with absolute accuracy

whether a number if prime or not, but it is a laborious process.

 

 

Another method can determine the primality of a number far more

quickly, but with a small probability of error, leading to what Prof

Krishnaswami Alladi, a leading US-based mathematician

calls, "industrial grade prime number."

 

 

What Messrs Manindra Agrawal, Neeraj Kayal and Nitin Saxena of the

IIT Kanpur did was to arrive at a logarithm that helped determine

the primality of a number accurately and quickly. But more of that

later.

 

 

Prof Alladi is one of the legatees of India's great tradition in the

field of numbers that begins with Aryabhata and Brahmagupta.

Currently Chairman of the Department of Maths at the University of

Florida in Gainesville, he is an authority on the works of

Ramanujan, and he edits a publication called The Ramanujam Journal

that deals with the areas the great man worked in and influenced.

Prof Alladi's grandfather was part of the group that gave India

another remarkable document: the Indian Constitution.

 

 

Like Prof Alladi, several other illustrious mathematicians of Indian

origin live in America, none more renowned than Prof Harish Chandra,

who had a distinguished career at Princeton before his death in

1996. The current heads of the mathematics department at the

University of Minnesota (Prof Naresh Jain) and McGill University

(Prof K.N.Gowrisankaran) are also Indians, and there are numerous

others crunching away quietly in other groves of academia.

 

 

But what the latest feat illustrates is that you don't have to be in

America to hit the bull's eye. Having devised their primality test,

the three Indians put their logarithm up on the IIT Kanpur website

and e-mailed last Sunday it to well-known mathematicians across the

world. Among the recipients of this e-mail was Prof Carl Pomerance

at Bell Labs, an authority on prime numbers.

 

 

No sooner had he seen the logarithm, Prof Pomerance discussed the

draft with colleagues over lunch, and arranged an impromptu seminar

on the subject the same afternoon. Within hours, the gathering

validated the logarithm. "We were all quite excited about it," Prof

Pomerance told this correspondent in an interview on Thursday. "They

had solved the problem quite elegantly and arrived at beautiful

result."

 

 

The remarks were typical of math aficionados, who see beauty and

elegance in numbers and equations that we number "crunchees" see in

words and phrases.

 

 

Mathematicians can also be delightfully quirky. We of course know

the famous episode how Ramanujan, receiving Prof Hardy by his

hospital bed, startled him by analysing impromptu the properties of

his taxi cab number.

 

 

Prof Pomerance is a mathematician in the same vein. One of his

papers, published in the Journal of Recreational Mathematics,

revolves around the interesting properties of the numbers 714 and

715, which was the number of home runs scored by Babe Ruth and Hank

Aaron respectively.

 

 

But to return to the story, there are two striking aspects to the

IIT-ians prime numbers saga. One is how quickly the logarithm was

shared across the world and validated by peers, thanks to the

Internet. (Ironically, the so-called primality testing plays a

crucial role in the widely used RSA algorithm, which is used to

secure transactions over the Internet).

 

 

In fact, attending Prof Pomerance seminar on Monday was Anupam

Gupta, a computer scientist at Bell Labs who happens to work just

down the corridor from the mathematician. Gupta is also from IIT-

Kanpur, but he did not know the prime numbers trio. What he did

recognise was the beauty of their logarithm. "It was so simple and

elegant that even I, more a computer scientist than a mathematician,

could understand and appreciate it," he said.

 

 

The second aspect of course is the longevity of the Indian legacy.

Whether in India or in the United States, our mathematical bequest

is alive and ticking (or clicking), and thanks to the Internet, the

boundaries are even fewer than when Ramanujan shared his genius with

the west.

 

 

So now we know and can rest assured: Some day, there will be a paper

on the properties of Tendulkar's final tally. India still has the

number on math.