There is a good popular math book about Kepler's Conjecture: "Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math

There is a good popular math book about Kepler's Conjecture: "Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World", by George Szpiro. I enjoyed it and recommend it if you want a historical perspective on this problem.