Pure mathematics in our society

Solution 1:

Not an essay or book, but there is a rather informative and clear video address by Timothy Gowers (a Fields Medalist) in 2000 on the "Importance of Mathematics" for an audience containing non-mathematicians in Paris.

He specifically addresses the issue of the (enormous) benefits that mathematics yields on a (very small) investment, its intrinsic cultural value and the interconnectedness of mathematics that make the "useful" areas inseparable from the "useless" ones.

It is available for download from the Clay Math Institute's website here, you'll have to scroll down to the bottom of that page for the download link.