MILLION DOLLAR QUESTION

Yes, that’s true. If you solve this puzzle you get cool $1,000,000!! That is only the prize money, without considering the perks and fame that will come with it. You will be as famous as some Mr. Einstein or Mr. Newton. History will remember you as the person who solved a 150 year problem!!!


Yep, that’s right too!! It’s a 150 year old problem. For 150 years the best minds of the world tried to solve this problem and came up short. The great minds were convinced that a solution to this problem exists but were unable to find it. Even taking the aid of high performance computers couldn’t help the matter. Now, you must be thinking-“what the big deal about a damn puzzle!!”. Well, to answer that you have to understand the puzzle.

Let get introduced to the hardest unsolved problem in mathematics since 1859---“REIMANN HYPOTHESIS”.

And yes, I didn’t forget about the $1 million. Boston Clay Mathematics Institute declared in 2000 a list of 7 unsolved problem of mathematics. For each problem $1 million was announced as prize money. Since then 6 problems have been solved and the 7th and the most important one is still waiting.
In 1859, Bernard Reimann published his eight page article where he discussed this idea. It’s about prime numbers. So, let’s dig into the problem.
Prime numbers are type of numbers which can be divided only by 1 and itself. The series of prime numbers look like this.
1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73…and so on.
You can clearly see it. It is NOT a series. There is no sequence in the numbers. We can’t say what will be the number next to 59 without calculating individually each number. To make my point clear consider the following series, which is actually a series.
1,4,9,16,25,36,49,64,81,100,121,144,169,__.
We can see the sequence and we can also deduce the last number, it is 196. For the mathematically challenged people the series is simply the square values of natural numbers i.e. 1, 2, 3, 4, 5…and so on. We can even say what will the 500th number of the series without checking the in between numbers. By this definition the prime numbers do not constitute a series. It’s too haphazard.
But it is also mathematics. Mathematics can’t be haphazard. There must be a method in madness. People (not normal people, mathematicians I mean) tried and failed to find a formula of prime numbers. In a desperate attempt to find any resemblance of order they tried to find the occurrences of prime numbers. See for yourself.
In 1 to 10 there are 4 prime numbers, which means 40%, so there should be 40 prime numbers in between 1 to 100, but there are 25 actually i.e. 25%. In case of less than 1000 it is 168 or 16.8%.
And between 9999901 to 10000000 it is just 9. The next 100 contains just 2. This was a total chaos.
But, there are some who do not conform to the norms. They think in their own way using their own logic. We call them genius.
One such genius was Leonardo Eular. This guy found an order where seemingly everyone had failed. What he showed was not only remarkable was incredibly easy too.

1+ 1/2^2 +1/3^2 +1/4^2 +1/5^2 +⋯=2^2/(2^2-1)*3^2/(3^2-1)*5^2/(5^2-1)*7^2/(7^2-1)*…

It was really wonderful. On the left hand side was natural numbers like 1, 2, 3, 4…..and on the right side was the prime numbers 2, 3, 5, 7…..
There was an order here. It was a start, but wasn’t an end. This equation was developed further and it was proved that the power of the numbers is not only limited to 2. It can be raised further i.e. the following equation will also hold true
1+ 1/2^3 +1/3^3 +1/4^3 +1/5^3 +⋯=2^3/(2^3-1)*3^3/(3^3-1)*5^3/(5^3-1)*7^3/(7^3-1)*…

and also if the power is 4, 5, 6 anything.

Now, the stage was set for Mr. Reimann to appear and did so in style. He developed the equation one more step and proved that the power of the numbers is not only limited to natural numbers, it can be complex numbers too i.e. the equation will hold true even if the power is a complex number.

Complex numbers are numbers which are created using rational and √-1. √-1 is square root of -1 which is an imaginary number.
Now, the question that naturally arises is that WHY THE HELL DID HE USED COMPLEX NUMBER????
Well, the answer to this question is the topic we started on. Reimann kept on developing the equation and discovered this


1+ 1/2^(0.5+7√-1) +1/3^(0.5+7√-1) +1/4^(0.5+7√-1) +1/5^(0.5+7√-1) +⋯=0


The most important aspect of this equation is that the co-efficient of √-1, which is 7 here, is of NO IMPORTANCE.
Yes, you read it right. It is of no importance as long as the first rational part is 0.5. You can change the co-efficient to anything you like, positive, negative, fraction, real anything, it doesn’t matter.
So, this is also same as the above.
1+ 1/2^(0.5+3√-1) +1/3^(0.5+3√-1) +1/4^(0.5+3√-1) +1/5^(0.5+3√-1) +⋯=0


This is Reimann Hypothesis. But it is never going to be possible to physically check every number imaginable to see if the equation works. Reimann said that the equation will be equal to zero if the rational part of the power is 0.5 and the co-efficient of the irrational part is any number. That was 1859.

150 years passed. So many other problems were solved using Reimann Hypothesis. They are proved as “if Reimann Hypothesis is true, then……”. So, if those answers are right then Reimann Hypothesis must also be true. But that doesn’t solve the problem. It has to be proved using mathematical logic and the quest still eludes the man. Solve it and the glory is yours. 1 Million dollars doesn’t hurt either!!