The idea is interesting -- copyright periods should be chosen to maximize some quantity (I think it's called "welfare" in the original paper), and this paper does it. It's basically a theoretical economics paper, and it looks accessible to someone with first-year calculus and common sense under their belt. I won't criticize the paper, because it's twenty-nine pages and I haven't read it.
What bothers me is the headline. Mathematics is not some sort of magic bullet! The paper makes a lot of assumptions about things in the "real world" which may or may not be true. Just because this thing spits out "14 years" doesn't mean that's the optimal copyright period -- see page 24 of the paper, which states
With α = 0.12, γ = 0.129, then θ ≈ 0.93. With our defaults of a discount rate of 6% and cultural decay of 5% this implies an optimal copyright term of just over 14 years.
Those are a lot of arbitrary-sounding constants. If they were a little different, would the answer be different? Of course.
It does, however, suggest that the current copyright periods of, say, life of the author plus fifty years are too long.