Understanding Riemann Hypothesis: Know about the 161-year-old equation

Published on Jun 29, 2021 09:43 AM IST

The Riemann Hypothesis is one of seven unsolved “Millennium Prizes" from the Clay Mathematics Institute of Cambridge and has promised an award worth $1 million to the person who solves it.

The Riemann Hypothesis arose from the work of noted mathematician Carl Friedrich Gauss in the 19th century and the formula deals with understanding the distribution of prime numbers.(Shutterstock/ Representative)
The Riemann Hypothesis arose from the work of noted mathematician Carl Friedrich Gauss in the 19th century and the formula deals with understanding the distribution of prime numbers.(Shutterstock/ Representative)
By | Written by Susmita Pakrasi, Hindustan Times, New Delhi

A Hyderabad-based mathematical physicist Kumar Eswaran has claimed to have developed a proof for the Riemann Hypothesis or RH, which remained unsolved for the last 161 years. Eswaran found the solution to the problem during his service at the Sreenidhi Institute of Science and Technology (SNIST), the institute said, according to reports.

The Riemann Hypothesis arose from the work of noted mathematician Carl Friedrich Gauss in the 19th century and the formula deals with understanding the distribution of prime numbers.

Experts have said that solving the hypothesis could open the doors for the use of primes in cryptography and also impact the number theory. A number of theorems also depend on solving of the hypothesis. The solution of the Riemann Hypothesis will allow algorithms to be processed faster.

The Riemann Hypothesis is one of seven unsolved “Millennium Prizes" from the Clay Mathematics Institute of Cambridge and has promised an award worth $1 million to the person who solves it.

Here's what you need to know about Riemann Hypothesis"

--According to the Clay Mathematics Institute, German mathematician Georg Friedrich Bernhard Riemann observed that the frequency of prime numbers is very closely related to the behaviour of an elaborate function ζ(s) = 1 + 1/2s + 1/3s + 1/4s + called the Riemann Zeta function. The Riemann Hypothesis asserts that all interesting solutions of the equation ζ(s) = 0 lie on a certain vertical straight line.

--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 can be described as "esoteric and abstruse".

--Riemann showed that the primes and the zeros of the zeta function—a special L-function—are related, and though primes fail to show any respect for rules and discipline, the zeros exhibit a pattern; they all line up on 'the critical line', Research Matters noted.

--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”.

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