Riemann Hypothesis/Historical Note

Historical Note on Riemann Hypothesis
The Riemann Hypothesis was stated by in his $1859$ article.

It is the last remaining statement which has not been resolved is the Riemann Hypothesis.

This problem is the first part of no. $8$ in the Hilbert 23, and also one of the Millennium Problems, the only one to be in both lists.

In 's words, in his posthumous papers:
 * [ These theorems ] follow from an expression for the function $\map \zeta s$ which I have not simplified enough to publish.

As put it:
 * We still have not the slightest idea of what that expression should be. ... In general, Riemann's intuition is highly geometrical; but this is not the case for his memoir on prime numbers, the one in which that intuition is the most powerful and mysterious.

In $1914$, proved the Critical Line Theorem, that there exist an infinite number of nontrivial zeroes of the Riemann $\zeta$ function on the critical line.

This was again demonstrated in $1921$, by together with.

In $1974$, demonstrated that At Least One Third of Zeros of Riemann Zeta Function on Critical Line.

By $1983$, systematic exploration of the critical strip with the aid of computers had shown that the first $3 \, 500 \, 000$ nontrivial zeroes were all located on the critical line.

While this is compelling, it is far from being a proof.

In December $1984$, it was announced that had found a proof, but this was shown to be flawed.