I think that you might be comparing apples to oranges. There's a chance that someone will think about the Riemann Hypothesis in a new way, or a new tool will be invented , and it will be proven or disproved. But the biggest historical mysteries result from a lack of information. Sometimes more information is found: advances in archaeology are explaining more about the collapse or disappearance of the Native American pre-columbian states, like the Maya. But often that is very unlikely to happen- we are unlikely to recover/ discover an account of the African explorations of the Carthaginian Hanno, or find a long-lost 6th c. account of the Battle of Badon and the guy later known as King Arthur.

However there are energetic debates over theories, and these are perhaps more comparable. There's the Turner Thesis, that the settlement /colonization of the American frontier was intrinsically important for creating Democracy ( unproven: it didn't do that for the Spanish) There's the Rising Gentry theory: that the Yeoman landowners in England were rising in wealth and importance but lacking political power in 17th c. England, and became Puritans and started the Civil War as a result ( unproven: they seem to have been gentry on both sides of the war, and aristocrats as well).

And there are debates over simple narratives, causes... A very big one , now, is over how WWI was started in Europe. Much of it is over the place of Germany- chief instigator, or just a blunderer like everyone else? There's plenty of source material, and it is not likely to end anytime soon. Certainly, it won't have a simple and elegant proof.