Sage-Tips

Will the Riemann hypothesis be proved?

Most mathematicians believe that the Riemann hypothesis is indeed true. Calculations so far have not yielded any misbehaving zeros that do not lie in the critical line. However, there are infinitely many of these zeros to check, and so a computer calculation will not verify all that much.

Why is proving the Riemann hypothesis important?

Considered by many to be the most important unsolved problem in mathematics, the Riemann hypothesis makes precise predictions about the distribution of prime numbers. If proved, it would immediately solve many other open problems in number theory and refine our understanding of the behavior of prime numbers.

Is the Riemann hypothesis true?

Given that evidence, most mathematicians think the Riemann hypothesis is true. But trillions of confirmations do not a proof make. One way to get some idea of why is related to prime numbers (and thus, why the Riemann hypothesis in related to primes) is to re-write in the form of an infinite product, instead of an infinite sum:

Does Atiyah’s work prove the Riemann hypothesis?

Firstly, it’s become clear that the work presented by Atiyah doesn’t constitute a proof of the Riemann Hypothesis, so the Clay Institute can rest easy with their 1 million dollars, and encryption on the internet remains safe.

Is Xian-Jin Li’s preprint a proof of the Riemann hypothesis?

Proof of the Riemann Hypothesis? Last night a preprint by Xian-Jin Li appeared on the arXiv, claiming a proof of the Riemann Hypothesis. Preprints claiming such a proof have been pretty common, and always wrong.

Did Opeyemi Enoch prove the Riemann hypothesis?

Only some claimed proofs get this level of attention though, and this one has been somewhat unique in that it was taken a lot more seriously than usual. You might remember that a few years ago, the BBC reported that Opeyemi Enoch had proved the Riemann hypothesis, and we immediately said “no, he hasn’t”.