As in... science.
What we should do about it (if there is something we should do) is politics, an entirely different topic.
It's important to consider absolute quality of life in addition to inequality. "Equality" is a relative measure, but what matters in the end is how well each individual is doing.
I'm in favor of policies that would help the less fortunate, though we need to be careful to implement them in an effective way.
I do think manufacturing will shift from globalization to localization once enough of the process can be automated. Once shipping costs start to exceed production costs, manufacturing will move back home. Of course, if the manufacturing is automated, it means those jobs aren't coming back. This also depends on whether it's cheaper to ship the raw materials vs the finished product, and where those materials can be sourced from.
That being said, a lot of the recent rise in inequality has been driven by government policy. Some things like housing are becoming prohibitively expensive to most due to short term focused policy by the Fed and perhaps congress as well.
The policy reaction we've seen has been quite effective, but is creating many potential asset bubbles that can cause bigger problems down the line.
These bubbles obviously inflate the wealth of the rich and lead to much greater inequality (often described as the k shaped recovery).
Hyper targeted policy, and letting things reach equilibrium through mostly free market forces often produces healthier outcomes in the long run.