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The Riemann Hypothesis is a conjecture made by mathematician Bernhard Riemann in 1859 that states that all non-trivial zeroes of the Riemann zeta function, which is a complex function that encodes the distribution of prime numbers, lie on the critical line of 1/2. The conjecture is considered one of the most important unsolved problems in mathematics and has yet to be proven or disproven.
There have been many efforts to prove the Riemann Hypothesis over the years, but so far, no one has been able to provide a definitive proof. Many mathematicians have made significant progress in understanding the conjecture and its implications, but a proof remains elusive.
Some of the notable efforts to prove the Riemann Hypothesis include:
In 1859, Riemann himself provided evidence to support the conjecture by showing that the first few non-trivial zeroes lie on the critical line.
In 1911, the mathematician G.H. Hardy proved that an infinite number of non-trivial zeroes lie on the critical line.
In the 1970s, the mathematician A. Selberg proved that an infinite number of non-trivial zeroes lie in the critical strip, which is a slightly wider region around the critical line.
Despite these advances, a proof of the Riemann Hypothesis remains elusive and it continues to be one of the most important unsolved problems in mathematics. Some of the most recent and notable progress on the Riemann Hypothesis has been made by researchers using computational methods such as the Turing method and the Gram-Schmidt orthogonalization method, but the proof is not yet proven.
It's worth mentioning that the Riemann Hypothesis is considered an important problem in mathematics, and solving it could have far-reaching implications for many areas of mathematics and physics, including number theory, cryptography and prime number distribution.
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