HYDERABAD: City-based mathematical physicist, Kumar Eswaran, has claimed to have found proof for Riemann Hypothesis (RH), a mathematical problem unsolved for the past 161 years.
Considered the top-most mathematical problem of the top 10 unsolved mathematical problems by American mathematician Stephen Smale, the RH fundamentally helps in counting the prime numbers and also gives a method of generating large random numbers.
In 2000, it was designated as a millennium problem, one of the seven mathematical problems selected by the Clay Mathematics Institute of Cambridge, Mass, USA.
It announced a reward of $1 million dollars for its solution.
Kumar Eswaran, a mathematical physicist at Sreenidhi Institute of Science and Technology, Hyderabad placed his research titled ‘the final and exhaustive proof of the Riemann Hypothesis from first principles’ on the internet almost five years ago.
In spite of all this, there was a reluctance on the part of the editors of international journals to put the paper through a detailed peer review.
Following thousands of downloads, an expert committee consisting of eight mathematicians and theoretical physicists was constituted in 2020 to look into the proof developed by Eswaran.
“While one can easily count the number of prime numbers from say 1-20, 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 the prime numbers,” said Eswaran.
The committee invited more than 1,200 mathematicians to participate in an open review wherein the referees would be willing to have their names and institutional affiliations openly revealed, so that nothing is done anonymously, nothing can be said that would not be openly available for all other experts to see.
So seven international scholars responded in time.
The committee then examined the comments of the seven reviewers and the responses of the author and concluded that Eswaran’s proof of the RH is correct.
“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,” said professor M Seetharaman, formerly with the department of theoretical physics at University of Madras, who was one among many who reviewed the RH proof by Eswaran.