In my opinion (risky though this my be) the Riemann Hypothesis will be solved soon, maybe in the next 10 years. This is because new ways of looking at it using random matrix theory are looking very promising and are giving great new results. Of course I may be very wrong, only time will tell.
But also in my opinion the Riemann Hypothesis is not the most challenging of the big open questions for mathematicians at the moment. Far more challenging (and arguably far more useful) is the question of whether P = NP or not. This is easily the most important question in the are where maths meets computer science. Basically if we can solve this then we can solve many many more problems, including soe of the big questions in how machines can learn and solve problems. Whilst we are close to resolving the Riemann Hypothesis we are nowhere near to solving whether NP = P!
Yes, yes it will. It feels that a proof is reasonably close, but then again I would have probably said the same 10 years ago. Sometimes what looks like a “small” leftover problem actually ends up being a huge roadblock, taking decades to be solved.
And yet… it will be solved. It is a fundamental problem in mathematics with so many ramifications and consequences, and we already know a lot of things about it. I am confident that the mathematicians community will crack it, but I cannot give a timeline.
I think it most definitely will be solved (but not by me!) Michael Atiyah thought he’d solved it but his proof didn’t quite hold up. Remember though that Andrew Wiles had to alter his initial proof for Fermat’s Last Theorem so being wrong the first time doesn’t mean that it won’t ever be solved. As for when it will be solved, I’m not sure but given that one of the Millennium Prizes has already been solved I’m hopeful it won’t be too long.
I’m as certain as a mathematician can be! Some mathematicians are so tenacious (see: Wiles, Andrew) that they’ll make problems like these their life’s work. With an army of incredibly gifted people all working on the same problem, I’m sure we’ll see a solution in our lifetime.