He has published three books on mathematical puzzles: Mathematical Puzzles: A connoisseur's collection (A K Peters, 2004, ISBN978-1-56881-201-4, translated to German and Russian), Mathematical Mind-Benders (A K Peters, 2007, ISBN978-1-56881-336-3), and Mathematical Puzzles (A K Peters, 2021, ISBN978-0-36720-693-2). And he is widely considered to be a pre eminent scholar in this domain. He was the Visiting Distinguished Chair for Public Dissemination of Mathematics at the National Museum of Mathematics (MoMath), gave topical talks at the Gathering 4 Gardner conferences, and wrote novel papers related to some of these puzzles.
Winkler's book Bridge at the Enigma Club[6] was a runner up for the 2011 Master Point Press Book Of The Year award.[7]
According to a story included in Chapter One of "The Man Who Loved Only Numbers / The Story of Paul Erdös and the Search for Mathematical Truth",[9]Paul Erdős attended the bar mitzvah celebration for Peter Winkler's twins, and Winkler's mother-in-law tried to throw Erdős out. [Quote:]
"Erdös came to my twins' bar mitzvah, notebook in hand," said Peter Winkler, a colleague of Graham's at AT&T. "He also brought gifts for my children--he loved kids--and behaved himself very well. But my mother-in-law tried to throw him out. She thought he was some guy who wandered in off the street, in a rumpled suit, carrying a pad under his arm. It is entirely possible that he proved a theorem or two during the ceremony."[9]