All publications of Irfan Ali . Bādāh , پاکستان
The Riemann hypothesis and It's Equivalent Shapes
It been 160 years passed but the mathematics demanded more and more work from the mathematicians to unlock the some of the unsolved problems in mathematics.The one of them is the Riemann's hypothesis,the unsolved millennium problem which is ultimately connected with distributions of prime numbers.Prime numbers are like atoms in physics ,Namely they are basic buildings of the Numbers. All numbers are product of primes or itself prime.The only thing which is not obvious about primes is their distribution,that is how they are placed among the integers.Integers the probably the first things I thing mathematicians stared about.Further Study led the discovery of primes(the numbers unbreakable as product of two or more primes).Finding their pattern is very hard upto date.Another branch of mathematics Complex analysis takes the secret of primes.The German mathematician Bernhard Riemann recognized this fact and studied the complex function,Namely zeta function,this function itself is mystery.It turns out that this function has regular study of his because in the whole complex plane.This function has zeros and one simple pole mathematically,one finds these properties interesting because some how this function is related with distributions of primes.It all comes definitely from the equations and relations connecting the primes with zeta function.In the entire complex plane this function is regular and has zeros at all negative even integers,they are obvious and some other zeros which are complex and lie in the vertical strip with 0<Re(s)<1. Where s is complex argument of zeta function.But no one knows exactly where all they doing there business.The Riemann studied them and conjectured all must be on a single line Re(s)=1/2 and this is known Riemann hypothesis.Mathematically this is not proved rigorously,and it has been passed 160 years.
Another important concept in mathematics is the Equivalents of problem.The Riemann hypothesis has more than 100 problems coming out from different mathematicians ,many at itself mystery and many are beautiful and interesting,Equivalent problems are the original problems like in case of Riemann hypothesis they weight like Riemann hypothesis itself.The only thing frustrating is that,they are not proved as well.Proof of any one equivalent problem will be the proof of Riemann hypothesis.But mathematics also has no answer of these questions.
The only thing remains is the may be one day another kind of mathematics may be discovered and that might be Solve this problem.This actually shows how hard are the primes. Gaining inside of these is very difficult upto date.
Finally the hope is still there that one day may be some mathematician(s) come through to unleash the truth and ultimately the truth of primes.Like great Mathematian David Hilbert said:
We must know.we will know.
