I don't think we (the common people) are supposed to understand this, but I would like to believe it's mind-blowingly fascinating.
What stands out to me is the quote, "You can easily do, on paper, computations that were infeasible even with a computer before."
And, "The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe."
The idea that a practically impossible problem might suddenly by solved by looking at it in a different way, perhaps using a relatively simple tool, does have broader applicability.
That maybe alternative histories (suggested in my other links) and future possibilities might be able to be calculated in terms of likelihood.
As for alternative history, scientists are at a loss to explain why global warming has not occurred as predicted. We can imagine an alternative history where humanity collectively took the issue deadly serious 20-30 years ago and drastically reduced greenhouse gas production (more drastically than we have, I mean) and now scientists would point at the lacking warming as proof that they were right.
Tangentially-related is this take on addressing the often recognized mental health issues behind mass shootings that have occurred. That's a problem that I think most shrug their shoulders at, not knowing exactly how we can address it. And there are civil liberty concerns for drugging/institutionalizing people for mental health issues. Charles Krauthammer poses a good question in response:
I know the civil libertarian arguments. I know that involuntary commitment is outright paternalism. But paternalism is essential for children because they don’t have a fully developed rational will. Do you think Alexis was in command of his will that night in Newport?
Any thoughts, ender?