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     Gamingfan Side Hero Username: Gamingfan Post Number: 7483 Registered: 08-2012 Posted From: 59.93.106.88 Rating: N/A |
http://www.thehindu.com/sci-tech/number-theory-can-popularis e-mathematics/article4290657.ece About your work... My work does not relate to Fermat’s last theorem. Some of the work that I’ve done recently and spoke about at the conference on Ramanujan in Delhi last week, has to do with new techniques that emanated from the solution of Fermat’s last theorem to another problem called the Sato-Tate conjecture. That conjecture more or less made predictions beyond that of Ramanujan. Ramanujan made some predictions on the Tau function and Sato and Tate conjecture made further predictions beyond that. Ramanujan’s three conjectures on the Tau function have been settled. (as of 1976) ...What I have done is to use the Sato-Tate conjecture, now that it is a theorem, to go further and see what are it’s applications and consequences. Kumar (Kumar Murty) and I have just finished a book called the Mathematical Legacy of Srinivasa Ramanujan. The purpose of writing this book was to introduce to undergraduate students of mathematics some of Ramanujan’s work and the developments that came after that. That might be useful for an undergraduate level course or a graduate level seminar. Can Number Theory be used to popularise mathematics? The answer to that question is a resounding “Yes” because Number theory is a very beautiful topic in that the unsolved problems are easy to state in ways that a high school student can understand them. Here is an example of an unsolved problem. Everyone knows that there are infinitely many prime numbers. Prime numbers are like 2,3,5,7,,11, 13 and so forth, numbers which do not have any proper divisors. We know that there are infinitely many primes, p. The question arises whether p+2 is also a prime for infinitely many p. Such primes are called twin primes. For example, 3 is a prime and 5 is also a prime; similarly 5 is a prime and 7 is also a prime. But 7 and 9 are not both primes. 11 and 13 are twin primes. 17 and 19 are twin primes. So you have these pairs of primes that differ by two. The question arises whether there are infinitely many such primes. The interesting thing is that the question whether there are infinitely many such twin primes, is an open question. That’s a question I can explain to a high school student. That’s an unsolved problem. We do not know the answer. We do know however that if p is a prime number, p+2 is either a prime or a number that is divisible by at most two prime numbers. You see, now I have been able to explain a major achievement of twentieth century mathematics to a high school student. If students want to know how this comes about, then I will have to tell them that either they will have to take a course in number theory, or, (laughs) if you are Ramanujan, you go to a local library and teach yourself all of undergraduate mathematics. So certainly number theory can be used ... to attract students to take up higher mathematics. I see that in Chennai the Pie Mathematics Association is using number theory and Ramanujan's life to popularise mathematics. Applied math can be understood and appreciated by many people while pure math is considered very elitist. Your comments. There are lots of examples where the purest of pure mathematics can be applied in a profound way. When Einstein came up with the theory of relativity, he needed something called Tensor Calculus and differential geometry. Now these were developed in the 18 and 19 centuries purely for their own sake. These were mathematical theories and were beautiful, coherent and consistent. Of course they had some applications, but not as dramatic as its use in theory of relativity. But the theory wouldn’t have been in place had someone worked it out with an application in mind. I don't like to waste time making a point on someone that ain't going to understand the point in the first place. If you want a boy to love you for a lifetime, love his heart, not his money.If you want a girl to love you for a lifetime, love her soul, not her body. |
