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This question is an extension of Open mathematical questions for which we really, really have no idea what the answer is, although it may immediately get closed as vague and primarily opinion-based. For each Millenium Prize Problem, how confident is the general mathematical community of the actual correct answer? For example, it's my understanding that mathematicians are extremely confident that the Riemann Hypothesis is true and that $P \neq NP$, while they are much less confident of the existence and uniqueness of smooth solutions to the Navier-Stokes equation (e.g. Terry Tao has recently changed his mind on that one).

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    $\begingroup$ Not many mathematicians have doubt that the Riemann Hypothesis is true, but Wikipedia mentions Ivic and Littlewood being particular sceptical. Many mathematicians seem to believe that every finit digit sequence appears in $\pi$, although we do not even know whether every digit appears infinite many often. It cannot yet be ruled out that eventually $\pi$ contains only of the digits $0$ and $1$, for example. $\endgroup$ – Peter May 2 '17 at 22:18
  • $\begingroup$ Nearly all mathematicians seem to be sure that Goldbach's conjecture is true because of the overwhelming statistical evidence. $\endgroup$ – Peter May 2 '17 at 22:21

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