A mathematics problem formulated over 150 years ago, and considered to be one of the most important unsolved problems to this day, may have inched closer to a solution with the publication of a new paper in the journal Physical Review Letters on March 30.
The paper’s authors are Carl Bender of the Washington University, Missouri; Dorje Brody, Imperial College, London; and Markus Müller, Western University, Ontario. They have taken on the Riemann hypothesis, which is one of the Clay Mathematics Institute’s seven Millennium Problems. Solving each one of these problems fetches the solver a cash reward of $1 million, not to mention international plaudits. The list was introduced in 2000.
The Riemann hypothesis is rooted in number theory and can be traced to the work of the Swiss mathematician Leonhard Euler, who laid its foundation in the 18th century. In 1859, Bernhard Riemann expanded on Euler’s work to develop a mathematical function that relates the behaviour of positive integers, prime numbers and imaginary numbers. Because of these connections, Riemann’s function shows up in multiple areas of mathematics, including analytic theory and cryptography.
As a result, proving or disproving the Riemann hypothesis is expected to have wide-ranging consequences for the practice of modern mathematics. Its historical significance and underlying complexity is the reason it is listed among the Millennium Problems. … (The Wire)