Hyderabad Mathematician Claims To Have Proved Riemann Hypothesis

The Riemann Hypothesis or RH, is a millennium problem, that has remained unsolved for the last 161 years.

Kumar Easwaran, a mathematical physicist of Sreenidhi Institute of Science and Technology, Hyderabad.

(Photo: Accessed by The Quint)

Hyderabad based mathematical physicist Kumar Easwaran has claimed to have developed proof for ‘The Riemann Hypothesis’ or RH, a millennium problem, that has remained unsolved for the last 161 years.

The RH fundamentally helps in counting prime numbers and also gives a method for generating large random numbers. In 2000, it was designated as a millennium problem, one of the seven mathematical problems selected by Clay Mathematics Institute of Cambridge, Mass USA, the Times of India reported

It announced a reward of $1 million dollars for its solution.

Clay Math Institute Responds

Clay Mathematics Institute which instituted the million dollar prize, however, has not reviewed Dr Easwaran's proof. Speaking to The Hindu, Martin Bridson, president of the institute said, "As far as I am concerned, the Riemann Hypothesis remains open.”

He added, “I do not recall any contact from the author and I am skeptical about the merit of the review process that is alluded to in newspapers.”

How Was Dr Easwaran’s Proof Reviewed?

Dr Easwaran, who works at Sreenidhi Institute of Science and Technology (SNIST) Hyderabad placed his claims on the internet five years ago. However, the editors of international journals were reluctant to put his research titled ‘the final and exhaustive proof of the Riemann Hypothesis from first principles’ through a peer review, The Times of India reported.

In 2020, after it was downloaded a thousand times, an expert committee consisting of eight mathematicians and theoretical physicists was constituted to look into the proof developed by Easwaran.

The committee invited more than 1,200 mathematicians to participate in an open review wherein the referees had to openly reveal their names and institutional affiliations so that everything was transparent to all other experts and nothing could be done anonymously. However, of the 1000 plus invitees, only seven responded on time

‘Dr Easwaran’s Analysis Is Exhaustive’

It was based on the comments of the seven reviewers and responses of the author that the committee concluded Easwaran’s proof as correct, as per the Times of India.

While one can easily count the number of prime numbers from say 1 to 20, it becomes a tedious task to calculate the number of prime numbers till one million or 10 billion. The hypothesis was important to prove as it would enable mathematicians to exactly count prime numers

Dr Easwaran 

Professor M Seetharaman, who was formerly with the department of theoretical physics at University of Madras and one among the reviewers of Easwaran’s RH proof, told the publication.

The author’s analysis is exhaustive, unambiguous and every step in the analysis is explained in great detail and established. The conclusions of the author and his result must therefore be considered proven

Professor M Seetharaman, one of the seven who reviewed Easwaran’s RH proof

‘RH Proof Would Automatically Prove Various Theorems’

In a statement, the SNIST said, “The genesis of the problem arose from the work of the great mathematician Carl Friedrich Gauss (1777-1855) who had written down a formula which can be used to approximately predict the number of prime numbers below any given number. Georg Friedrich Bernhard Riemann (1826-1866) improved the formula by using entirely original methods involving the calculus of functions of a complex variable”.

The importance of the Riemann Hypothesis (RH) was well-known to mathematicians and it was also recognized that proof of RH would automatically lead to the proof of numerous theorems which were dependent on the truth of this hypothesis, the SNIST said in its statement.

Dr Kumar Eswaran took off from the work of JE Littlewood (1885-1977) and showed that the RH could be resolved if the analytical behaviour of a certain specially chosen function of a complex variable can be determined, the SNIST said.

(The article was edited to include the version of Clay Mathematics Institute.)