http://timesofindia.indiatimes.com/articleshow.asp?artid=18900043
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
http://timesofindia.indiatimes.com/articleshow.asp?artid=18891466
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 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
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,
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 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 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 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 Tendulkar’s final tally. India still has the number on
math.
HALlo!