Science has many unsolved problems. Solving them can open up new opportunities and horizons for humanity. Seems like the Reimann problem has been solved by Nigerian. Read on to learn more.
Mathematics is a hard science. There are still many issues, which haven't been solved. Riemann problem is one of them. However, according to the recent information, one of the professors in Nigeria – Dr. Enoch has manager to finally solve it.
This issue was first published by Bernard Riemann in 1859.
Riemann hypothesis
One of problems of mathematics first appeared in 1859. Riemann was studying distribution of prime numbers. Then, he tried to extend Euler's zeta function and noticed the trivial zeros at a line -2, -4, -6, etc., while nontrivial zeros were completely symmetric about line Re(s) = ½.
According to Riemann hypothesis, all nontrivial zeros are situated on critical line. And this very fact has not been proved until today.
Brief history
The first computations were made by the Riemann himself even before his work publication. They created basis of the whole issue.
You should know, he was not even a number theorist, and this work was the only one in this field.
However, it has managed to become one of the most important in algebra. Besides, it appeared to be applicable in both math and physics, and not only in theory of numbers.
This work was predicated by L. Euler. He started to study Z(s) function. But after this, it remained useless until Riemann came. Finally new function was formed, known as ζ. The result was that for any s for which Z(s) does not blow up, ζ(s) = Z(s). In fact, such thing actually reflected Z(s). Nevertheless, there existed a single drawback – ζ(1) was undefined.
The mathematician’s question was: if we ignore negative integers and if ζ(s) = 0, does that mean that s is ½ plus a multiple of i?
This question was so confusing and difficult to answer that there was even a prize of $1,000,000 promised to a person, who would finally deal with Riemann problem.
Attempts to solve the Riemann problem
There were several attempts to solve it in the history. Among them, there are:
- Hardy and Littlewood. They actually proved the first results about infinitude of zeroes on critical line.
- Then comes Selberg. He had a stronger statement that a positive proportion of zeroes lies on critical line (it was also greatly developed by B. Conrey not long time ago).
- Montgomery. He noticed some kind of relationships between zeroes and random matrices distribution. It was very significant.
156-year-old problem solved
You'll be surprised to know the hypothesis, which has been considered one of the hardest in math, is finally solved. Opeyemi Enoch – a teacher from FUOYE (Federal University Oye-Ekiti) is now thought to be the best math solver. He has explained that the greatest breakthrough was made in 2010. It allowed him to deal with one of the Millennium Problems in Mathematics.
Now, as it has been promised, professor must receive $1,000,000 reward. However, it must be first confirmed. According to Clay Mathematical Institute, there has been no official confirmation about solving the problem yet. They say they do not comment on solutions to any Millennium Problem.
After this, critics have started to say it is just a fiction. BBC news agency has decided to talk to the professor personally. He tells them that the main thing, which has inspired him to try, is his students trust.
They have believed that he can do it. Thus, the reward was the second factor. It has been also claimed that Dr. Enoch has been working hard and has corrected many works of mathematicians of previous generations.
The proof was showed on the 11th of November, 2015. It happened in Vienna during the International Conference on Mathematics and Computer Science. Professor has uncovered the way he has come to the solution. Moreover, he’s revealed how it is applicable in quantum computers, cryptography, and quantum information science.
However, some people are very critical about him. They may probably be jealous though.
Riemann hypothesis for dummies
Not everyone is good at mathematics, so we offer a simple and short explanation of the issue:
- Complex numbers.
i is the square root of minus one. It is multiplied by i equals -1. While real numbers are in horizontal line, the others like …-3i, -2i, -i, 0, i, 2i, 3i… are in the vertical one. Taken together, it is known as complex plane. It is presented as a+bi.
Functions. -
It is presented by f. look at the example: f(x). There exist complex functions (you can put any complex number a+bi in it and get any complex number out).
- Riemann Zeta Function.
It is a kind of complex function. Unlike in any other ones, Zeta function divides zeros into two types: trivial ones, which occur at all negative even integers, and nontrivial, which are all the rest. All nontrivial zeros appear at ½ + bi for b.
The Riemann Hypothesis suggests they are all like that.
It is amazing how people can once change the world. A Nigerian finally solves the problem that has been existed for long time. It gives great opportunities to this country. Besides, we may expect much more surprises from modern people.
Congrats prof.