- #1
Turtle
- 52
- 0
What is the Riemann Hypothesis? Where can I find good online literature upon the subject?![Smile :smile: :smile:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Originally posted by Lonewolf
You can help verify Riemann's Hypothesis at http://www.zetagrid.net/ if you're that way inclined.
ζ(s) = Σ 1/ns
The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It was proposed by German mathematician Bernhard Riemann in 1859 and it deals with the distribution of prime numbers. It states that all non-trivial zeros of the Riemann zeta function, which encodes the distribution of prime numbers, lie on a specific line in the complex plane.
The Riemann Hypothesis has significant implications in number theory and has connections to many other areas of mathematics such as algebra, geometry, and analysis. Its proof or disproof could also have practical applications in fields like cryptography and internet security, as well as providing a deeper understanding of prime numbers and their distribution.
Some reputable online resources for learning about the Riemann Hypothesis include the Clay Mathematics Institute's website, which offers a detailed description of the hypothesis and its history, as well as several articles and videos by mathematicians and experts. Other helpful resources include MathWorld, the website of the American Mathematical Society, and various university websites.
Many mathematicians have attempted to prove or disprove the Riemann Hypothesis, but so far, no one has been able to definitively solve it. However, there has been significant progress made towards understanding the hypothesis and its connections to other areas of mathematics. In 2018, the first ever proof of a significant part of the hypothesis was published by a team of mathematicians, bringing us closer to a complete solution.
The Riemann Hypothesis is notoriously difficult to prove because it involves complex mathematical concepts and requires advanced techniques from multiple branches of mathematics. It has also withstood numerous attempts at proof, leading many mathematicians to believe that it may require a completely new approach or revolutionary idea to solve it. Additionally, the Riemann Hypothesis has been verified for a large number of cases, but proving it for all cases is a monumental task due to the infinite nature of the problem.