The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles Of Our Time
ISBN: 0465017304
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I'll recommend reading the chapter on the Riemann Hypothesis from the book: The Millennium Problems by Keith Devlin.
https://www.amazon.com/Millennium-Problems-Greatest-Unsolved...
That has about 42 pages of prose describing the problem in layman terms. I'd think someone who tackled high school math should be able to follow it. Dr. Devlin also has a good Coursera course on an introduction to mathematics.