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Hyderabad-based Mathematician Claims to Have Solved 161-Year-old Riemann Hypothesis

Image Credits: Facebook/Kumar Eswaran

Image Credits: Facebook/Kumar Eswaran

The Riemann Hypothesis is one of seven unsolved 'Millennium Prizes' from the Clay Mathematics Institute of Cambridge.

Hyderabad-based mathematical physicist, Kumar Eswaran has claimed that he has found proof for Riemann Hypothesis (RH), the famous mathematical problem that has remained unsolved for 161 years. First posited by Bernhard Riemann in 1859, the Riemann hypothesis is one of seven unsolved “Millennium Prizes" from the Clay Mathematics Institute of Cambridge and worth $1 million to the person who solves it.

According to Times of India, Easwaran, who is a mathematical physicist at Sreenidhi Institute of Science and Technology, Hyderabad, had placed his research titled ‘The final and exhaustive proof of the Riemann Hypothesis from first principles’ on the internet almost five years ago. However, editors of international journals were reluctant to put the paper through a detailed peer review.

Eswaran told Deccan Chronicle, “It was, in fact, back in 2016, that I first gave proof for the formula improved by the great mathematician Georg Friedrich Bernhard Riemann in the 1800s. I had put it on the web for open review and downloads after working on it for about six weeks. During 2018-19, I gave several lectures on the proof."

After the research was downloaded thousands of times, an expert committee consisting of eight mathematicians and theoretical physicists was constituted in 2020 to look into Easwaran’s proof. He told Times of India, “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."

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According to Research Matters, the Riemann Hypothesis, from a technical point of view, is a prediction about the solutions of an equation involving ‘L-functions’, which, at best, can be described as esoteric and abstruse.

The expert committee had invited more than 1,200 mathematicians to participate in an open review and seven international scholars responded in time. Professor M Seetharaman, formerly with the department of theoretical physics at the University of Madras, who was one among many who reviewed the RH proof by Eswaran told Times of India, “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."

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first published:June 28, 2021, 12:42 IST