In the middle of the 1859 paper on prime numbers, Riemann writes a sentence almost in passing. Speaking of a function linked to zeta, whose real roots correspond to the zeros of zeta on the critical line, he says: It is very probable that all the roots are real. One would of course wish for a rigorous proof of this; but I have, after some fleeting vain attempts, provisionally put aside the search for one, since it did not seem necessary for the next objective of my investigation. — Bernhard Riemann, On the Number of Primes Less Than a Given Magnitude (1859)