HAL asked to speed up the delivery schedule.
profrv at nex.net.au
Sat May 1 22:12:54 PDT 1999
Designed for hot and high conditions Mmm."...third- generation
anti-tank missile Nag My wifes got that already.
Speaking of hot and high.Oregen burning,Smog cloud threw monsoon off course
and driest July in 100 years.Is there a runaway green indahouse?
Thank all the gods for
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 subscribe to Bill Clintons 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
algorithm , 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,
its 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. Thats 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. Thats 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
What Messrs Manindra Agrawal, Neeraj Kayal and Nitin Saxena of the IIT
Kanpur did was to arrive at a algorithm that helped determine the primality
of a number accurately and quickly. But more of that later.
Prof Alladi is one of the legatees of Indias 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 Alladis 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 dont have to be in
America to hit the bulls eye. Having devised their primality test, the
three Indians put their algorithm 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 algorithm , 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
algorithm . 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 algorithm 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
algorithm . 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 Tendulkars final tally. India still has the number on math.
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