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| India still has the number on maths |
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| jaihoon |
| 08/12/02 at 16:16:27 |
| India still has the number on maths CHIDANAND RAJGHATTA TIMES NEWS NETWORK [ MONDAY, AUGUST 12, 2002 10:06:25 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 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 thajks 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. |
| Re: India still has the number on maths |
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| imaazh |
| 08/13/02 at 04:08:00 |
[color=Green]odd exceptions notwithstanding. [/color] That was definitely aimed at me!!! When i first went out on prac and all the prac students were being assigned to individual teachers, one of the older maths teachers took one look at me and said, "goody you look like you're a maths person", with a glint in my eye, i was so sorry to have to tell him that i was absolutely clueless when it came to maths, and that appearances could often be decieving. Moral of the story? Not all indians are good at maths and stereotypes don't always ring true. |
| 08/13/02 at 10:00:53 |
| imaazh |
| Re: India still has the number on maths |
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| jaihoon |
| 08/13/02 at 05:45:52 |
| same's the case here as well ;) (maths persons have always been my enviable competitors. ) |
| Re: India still has the number on maths |
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| mwishka |
| 08/13/02 at 08:33:45 |
| brother jaihoon, this was one of the funniest articles i have read in a long time --- it made me laugh out loud a lot! this is my [i]favorite[/i] line: [i]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.[/i] :-/ :-/ :-/ but, was this a misprint, or just a very silly joke?? (ok, it's a JOKE mouse, don't be so serious.....::) ) [i]For instance, is 4958372640287988786544 a prime number?[/i] though i know the the point of this article was not just to be funny, thanks for the great laughs! and no, though math desn't frighten me, i'm nott one of those automatic numbers crunchers either. but not a total crunchee, either, i guess --- i'm stranded on a floating point ;) somewhere in between, probably drifted far far to the side of language..... this was really entertaining! (i hope you had a chance to be equally entertained by that "science is hard" theorem i put up a while back in bebzi, in which scientists made fun of how ridiculously hard science seems for people outside it, as this article shows for people outside the world of math.....) mwishka (who'd much prefer to dream the solutions to her molecules' mysteries than to have to go in there and measure they little bond lengths...) |
| Re: India still has the number on maths |
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| safa |
| 08/13/02 at 17:29:06 |
| [quote][/quote] For instance, is 4958372640287988786544 a prime number? It obviously isnt, coz its an even number. |
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