The world breaks everyone, and afterward, many are strong at the broken places. —Ernest Hemingway
In All the Bright Places, Finch and Violet are constantly referring to famous writers who killed themselves. What better way to start the book, then, than with a cameo from Papa himself—Ernest Hemingway, who shot himself in 1961.
The quote is from A Farewell to Arms. It's a sad one, isn't it? But at the same time, it's hopeful. In the words of Kelly Clarkson, what doesn't kill you makes you stronger.
It also sounds like Violet; the world breaks her twice (with the deaths of her sister and Finch), and she has to find strength within herself to survive.
The key word in the quote is many. "Many"—not all—"are strong at the broken places." Though it's not included in the epigraph, it's worth noting the line that comes next: "But those it will not break it kills."