These things are kind of like landing on the moon. The act of actually walking on the moon is fairly symbolic and ultimately the more important things were the achievements required to get there.
What the current state of the problem demonstrates is there's some unknown quantity of cutting edge work required that has yet to be done; maybe there's a cunning conceptual error in some field that has somehow missed everyone's eye or maybe there's an entirely new mathematical concept or tool which makes the problem straight-forward, but nobody has "invented it" yet.
One day, the time we are in right now will be "150 years ago". Contemporaries of any time think all fundamental things have been exhausted and discovered for whatever reason. It was as true in 1874 as 2024.
And they've always been wrong. Doesn't mean you or I can get there. It'll take some brilliant individual or team years of sweat equity, skill and profound luck but one day, right now too will be 150 years ago and people will look back on us as we look back on 1874 mathematics.
There's another possibility: that everything discoverable by humans as been discovered.
Before long, AIs and organizations will be claiming to prove things that no human has the capacity to verify with reasonable confidence, or humans will run or of capacity or make progress. We just had the 1000 page Geometric Langlands proof.
"everything discoverable by humans as been discovered" again, this claim is made by every generation like clockwork, going back as long as humans have been making claims that can be recorded.
What the current state of the problem demonstrates is there's some unknown quantity of cutting edge work required that has yet to be done; maybe there's a cunning conceptual error in some field that has somehow missed everyone's eye or maybe there's an entirely new mathematical concept or tool which makes the problem straight-forward, but nobody has "invented it" yet.
One day, the time we are in right now will be "150 years ago". Contemporaries of any time think all fundamental things have been exhausted and discovered for whatever reason. It was as true in 1874 as 2024.
And they've always been wrong. Doesn't mean you or I can get there. It'll take some brilliant individual or team years of sweat equity, skill and profound luck but one day, right now too will be 150 years ago and people will look back on us as we look back on 1874 mathematics.
Problems like Riemann is how we forge ahead.