The Riemann Hypothesis is a mathematical conjecture (question), it has got a special thing called the Riemann Zeta function. It deals with the numbers, if the answer to the question is “YES” then the mathematician knows more about the prime numbers. This hypothesis makes predictions about the distribution of prime numbers even though there is an unsolved problem in the subject. The hypothesis of Bernard Riemann upholds the real part of every non-trivial zeros of the Zeta function. He proposed the answer to a particular thorny math question.
Bernard Riemann is a German mathematician who introduced this hypothesis in the year 1859 and this is all about the prime numbers. His idea on this is to distribute the prime number as regularly as possible and this is what he had conveyed in these findings. The Riemann Hypothesis is still mysterious and this remains unsolved in mathematical units.
Riemann’s Hypothesis remained unsolved because the Riemann Zeta function is closely related to the equation of frequently used prime numbers and thus he believed that the distribution was not possible in any regular patterns. So it remained unsolved even today.
This theory was proved by three great mathematicians known as Carl Friedrich Gauss in 1790, 1890 Jacques Hadamard, and Charles Jean de la Vallée Poussin, who proved it independently. Thus Riemann Hypothesis is very important because it gives us the chaos about the prime numbers and estimates the remainder term in the prime theory theorem.
Advantages of Riemann Hypothesis –
- If the hypothesis has been proved then the prime numbers wouldn’t produce a number-spectrometer.
- It estimates the work of prime numbers and provides us proof work.
- The theorem gives the assumption of true statements.
- Gives precise predictions about the distribution of prime numbers.
- Tries to solve the unsolved problem in mathematics.
- Refine the understanding of the behavior of prime numbers.
Disadvantages of Riemann Hypothesis –
- The zeros will be negative even integers and show the complex numbers in the real part.
- It is the question of the Zeta function.
- Hard to solve and find the solution.
- Hardest mathematical theorem on prime numbers.
- Hard and very rare to prove the hypothesis.
Hence the toughest mathematical theorem of the Riemann Hypothesis was solved by the Russian mathematician Grigori Perelman. He had solved the Millenium problem and most complicated math problems several years ago.
Even though this was solved by brilliant-minded mathematicians, still it gives us complexity and finds it hard to resolve math problems. The magic of the number itself gives us mysterious twists. Playing with the number is not a fun game but it gives us the direction to solve the problem. For every toughest problem, we have got answers and therefore the Millenium had solved the hypothesis and gave the answer of distribution of prime numbers on an equal basis.
The above article showcases the Riemann Hypothesis in a complicated way but trust me, it’s one of the wonderful mathematical problems to hunt for solutions.