The title is a quote from a Jim Holt article entitled, "The Riemann zeta conjecture and the laughter of the primes" (p. 47).^{1}
His example of a "long-standing conjecture" is the Riemann hypothesis,
and he is cautioning "those who blithely assume the truth of the
Riemann conjecture."

. What are examples of long-standing conjectures in analysis that turned out to be false?Q

Is Holt's adverb "often" justified?

^{1}Jim Holt.

*When Einstein Walked with Gödel: Excursions to the Edge of Thought*. Farrar, Straus and Giroux, 2018. pp.36-50. (NYTimes Review.)

blithelyassume RH. Looks like an educated non-fiction writer's good-faith construction. $\endgroup$ – paul garrett Jul 25 '18 at 23:40whomexactly?) is the story of the Zagier-Bombieri wager. According to du Sautoy's bookThe Music of the Primes, Don Zagier, number theoristnon pareil, moved from a position of semi-skepticism/agnosticism about the truth of RH to one of firm belief, after he lost his bet with Bombieri that the first 300 million non-trivial zeroes would yield one off the critical line (he had thought the odds were about 50-50). Of all the conjectures to warn about... $\endgroup$ – Todd Trimble♦ Jul 26 '18 at 0:43he thinkshe's saying is justified. Whatever he thinks analysis (and its scope) is, it's likely to be pretty different from what mathematicians understand it to mean. $\endgroup$ – Todd Trimble♦ Jul 28 '18 at 14:30