Solution to Riemann hypothesis

"What we have done in our paper," said Ken Ono, a number theorist at Emory University and co-author of the new proof, "is we revisited a very technical criterion which is equivalent to the Riemann hypothesis … and we proved a large part of it. We proved a large chunk of this criterion."
A "criterion which is equivalent to the Riemann hypothesis," in this case, refers to a separate statement that is mathematically equivalent to the Riemann hypothesis.
It's not obvious at first glance why the two statements are so connected. (The criterion has to do with something called the "hyperbolicity of Jensen polynomials.") But in the 1920s, a Hungarian mathematician named George Pólya proved that if this criterion is true, then the Riemann hypothesis is true — and vice versa. It's an old proposed route toward proving the hypothesis, but one that had been largely abandoned.
Ono and his colleagues, in a paper published May 21 in the journal Proceedings of the Natural Academy of Sciences (PNAS), proved that in many, many cases, the criterion is true.
But in math, many is not enough to count as a proof. There are still some cases where they don't know if the criterion is true or false.
"It's like playing a million-number Powerball," Ono said. "And you know all the numbers but the last 20. If even one of those last 20 numbers is wrong, you lose. … It could still all fall apart."