It is the 150th anniversary of this problem. It, after not been solved in 150 years, has still not been deemed unsolvable. The easiest way to explain the theory would be PI(x). This theory is about prime numbers. PI(x) means that there are a certain number of prime number that are under x which would be a positive number.For example, PI(10) would be 4 because the prime numbers 2,3,5, and 7 are under 10. This is the simplest way to explain it. It also has to do with complex numbers. The idea of complex numbers is that is -3,-2,-1,0,1,2,3 is the horizontal axis then the complex numbers -2i,-1i,0i,1i,2i would be the vertical axis. the whole plane is called a complex plane. This is a two-dimensional plane of numbers. All complex numbers can be represented in the form of a+bi, for real numbers we take b=0. “A function is a little black box that is u put a number into it spits a different number out.” If x is put into the box then what it spits out would look like f(x). To explain a function is rather simple. f(x)=x^2 is a rather simple function, it means that what ever you put in x, you get x^2 out. So f(3)=9, or f(6)=36. An example of a complex function would be f(i)=-1 because the square root of -1 is i. The zeta function in the equation is one such complex function.(ζ is the zeta function) I really don’t understand the actual zeta function so im not going to explain it.
“Now, a zero of a function is a point a+bi where f(a+bi)=0. If f(x)=x2 then the only zero is obviously at 0, where f(0)=0. For the Riemann Zeta Function this is really confusing. It basically has two types of zeros: the trivial zeroes that occur at all negative even integers that is, -2, -4, -6, -8… and the nontrivial zeroes, which are all the OTHER ones. As far as we know, all the nontrivial zeroes occur at 1/2 + bi for some b. No others have been found in a lot of looking… but are they ALL like that? The Riemann Hypothesis suggests that they are. But as I said earlier nobody has been able to prove it.”
In 2000 it was announced that clay institute would give $1 million to whoever solved it. Riemann Hypothesis is in fact one of the seven millenia problems. It would revolutionize the world because of the fact that most encryption’s are based on the fact that there is no simple way to find/count prime numbers. He discovered was a way of using the properties of a relatively simple function to count the primes.
Karl Friedrich Gauss discovered that prime numbers are sparser the father you go out. They follow a simple logarithmic law and he didn’t know why. Riemann was a student of Gauss and took up the prime number distribution in his only number theory paper. Einstein based his theory of graviton on this. I just think that all of the world would greatly change if this was proven.
many thanks to the website http://qntm.org/?riemann for providing the formulas previously mentioned.