Days after media reports emerged that an Indian mathematician had proven the Riemann Hypothesis, Clay Mathematics Institute, the grantor of the Millennium Prize, has rejected the claim. The Reimann Hypothesis has remained unproven for over 160 years.
Published in 1859, Reimann Hypothesis attempts to predict the occurrence of prime numbers using a mathematical function. Prime numbers do not follow a pattern of occurrence. After you find one, it is impossible to predict the occurrence of the next prime number. Mathematical greats like Euclid, Euler, and Gauss are among many who attempted to address this problem.
Bernhard Riemann, a student of Gauss, found a pattern in the frequency of prime numbers. He found them to follow a closely follow pattern that could be explained with a function, which he called Riemann zeta function.
ζ(s) = 1 + 1/2s + 1/3s + 1/4s + ...
The hypothesis states that all interesting solutions of the equation:
ζ(s) = 0
lie on a certain vertical straight line.
The Clay Math Institute claims that this hypothesis has been checked for the first 10,000,000,000,000 solutions. What needs to be proven is proof that shows that the zeta function is true for all solutions.
News reports suggested that Indian mathematical physicist Kumar Easwaran had published his proof in 2016. However, internationally reputed journals refused to put his proof through a peer-review process, a requisite for claiming the Millenium Prize.
Is there still hope?
Reports also claimed that an open review was conducted on Easwaran's claims by seven mathematicians and found it exhaustive and the proof should be considered as proven.
However, the President of the Clay Math Institute, Martin Bridson, questioned the merit of the review process and asked publications to refrain from calling the hypothesis proven.
As per the Institute's rules, the proposed solution must be published for at least two years in a reputed journal and be accepted by the mathematical community at large.
In 2018, award-winning mathematician Sir Michael Atiyah had claimed to have proven the Reimann hypothesis. The recent clarification from Clay Math Institute has put that to rest as well.