What progress has been made on the Riemann Hypothesis since 2004?

In summary, there have been no updates since 2004 on the topic of DeBranges and Riemann. However, on the Purdue University website, there are links to papers written by DeBranges himself on the subject. These papers can be found on the bottom of the page, but may be difficult to understand for some readers. Additionally, there is an apology posted on the Purdue Math Department website, along with a collection of downloadable PDF papers.
Physics news on Phys.org
  • #3

1. What is the Riemann Hypothesis?

The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It is a conjecture about the distribution of prime numbers, which are the building blocks of all whole numbers. Specifically, it states that all non-trivial zeros of the Riemann zeta function lie on the critical line with real part 1/2.

2. Why is the Riemann Hypothesis important?

If proven true, the Riemann Hypothesis would have far-reaching implications in mathematics, particularly in number theory and analysis. It would also have practical applications in cryptography and computer science. Additionally, solving this problem would provide a deeper understanding of the fundamental nature of prime numbers.

3. How long has the Riemann Hypothesis been unsolved?

The Riemann Hypothesis was first stated by German mathematician Bernhard Riemann in 1859. Since then, it has remained unsolved despite numerous attempts by many mathematicians. It is considered one of the most challenging and important problems in mathematics.

4. How can the Riemann Hypothesis be proven?

There is no definitive answer to this question as the Riemann Hypothesis is still an unsolved problem. However, some mathematicians believe that the key lies in understanding the behavior of the zeta function near the critical line, while others have proposed alternative approaches such as using the theory of modular forms and L-functions.

5. Has anyone come close to proving the Riemann Hypothesis?

Over the years, many mathematicians have claimed to have solved the Riemann Hypothesis, but all attempts have been met with skepticism and ultimately disproven. Some of the most notable attempts include those by G.F.B. Riemann, John Edensor Littlewood, and Atle Selberg. Currently, the Riemann Hypothesis remains an open problem and one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute.

Similar threads

Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
15
Views
7K
Replies
8
Views
4K
  • Linear and Abstract Algebra
Replies
6
Views
4K
  • Astronomy and Astrophysics
Replies
4
Views
1K
Replies
3
Views
1K
Replies
4
Views
5K
Replies
33
Views
5K
  • Quantum Interpretations and Foundations
Replies
25
Views
1K
Replies
2
Views
1K
Back
Top