Jeffrey not only understood the hard science of debt relief but had enough moral outrage to demand it be done.

--- How should I understand "hard science" in this context?

Well, economics is often dubbed the "dismal science", but there is enough obsure mathematics in economic modelling today, that I suppose it could be called a "hard science"...
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"Hard science" in your given context means Jeffrey has the in-depth knowledge based on science and real, rigorous facts, to understand about debt relief.

By the way, is "Jeffrey" here "Jeffrey Sachs"?

Yes, it's Jeffrey Sachs.