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PROF. BALASUBRAMANIAN on the "TWIN PRIME CONJECTURE".

posted Jul 8, 2014, 6:01 PM by RMS Administrator   [ updated Jul 8, 2014, 6:05 PM ]
Dear Friends,

​Last Sunday (July 6th 2014), I heard a wonderful lecture by Prof. Balasubramanian, the well-known number-theorist from Chennai, on the "Twin Prime Conjecture".

As you may know, the original conjecture is easily stated; there are infinite prime pairs of the form (n, n+2), for example, (3, 5), (5,7), (11, 13), ​(29, 31) ....

​A breakthrough in 2013 by Yitang Zhang, was: Let p_n denote the n-th prime. There exists a constant N (approx 7 x 10^7) such that for  infinitely many n,  we have p_{n+1}
 ​ - p_n is less than N.

Then there was a feverish activity during the last year to reduce N, carried out on the internet 
by several mathematicians, and the present value of N is 246. It is believed that the present technique may reduce N = 6.​

​Prof. Balasubramanian gave a wonderful survey, essentially starting from the definition of a prime! He pointed out well the differences between the sophisticated analytic techniques involving the Riemann's zeta-function,  and the elementary combinatorial techniques, the "sieve method"
​​
 ​.

The lecture was full of mathematical, philosophical, and sociological insights, starting from Euclid, and   Eratoshthenes, through
​ ​
 Euler, Gauss, Riemann, Hardy, Brun, ...., Zitang.

By the way, Zhang, an immigrant from China,  in 2013, was  a 58-year old,   undergraduate teacher in a small college in  the US.

Prof. Balasubramanian  talked about the power of the internet, which transmitted the information about 
any advance, with 
a fantastic speed to the mathematical community all over the world. So many mathematicians could make
 ​ ​
a contribution.
​ 

So probably, no single person may get the "whole" credit! 
 
But what does it matter? The mathematics has made advance any way!!

This does raise many issues about individual originality issues, priority issues, "patent" issues (which are mostly absent in the mathematical community, but are prevalent in other areas of science like Chemistry)

We are living in very interesting times.

Ravi Kulkarni

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