Every once in a while, a teenager plays their way into a major championship. Even rarer still, every once in a while a teenager is able to make the cut in a major championship.
In the history of the four modern men's major championships, the youngest player to make the cut the Guan Tianlang. The Chinese player was just 14 years, 5 months, 18 days old when he got to the weekend in the 2013 Masters and completed the tournament. (Curiously enough, he's also the last player in Masters history to receive a slow-play penalty stroke.) He also remains the youngest player to make the cut in any PGA Tour event.
In US Open history, the youngest player to make the cut since World War II (1945) is Beau Hossler. Hossler actually had a share of the lead briefly in 2012 at The Olympic Club at the age of 17 years, 3 months. He finished tied for 29th place, behind ultimate winner Webb Simpson.
At the PGA Championship, the lone championship designed only for professional golfers, there have been dramatically fewer teenagers to get in the field. The youngest player to compete in the PGA Championship is Gene Sarazen, who was just 19 years old when he competed in the 1921 PGA Championship. Even more remarkable, Sarazen won the championship the next year, in 1922, at the age of 20 years, 5 months, 22 days, making him the youngest champion to capture the Wanamaker trophy.
In the British Open Championship, the oldest of the four majors, there have been a number of teenagers to get through the tournament. However, the youngest player to make the cut at the Open Championship is Matteo Manassero, with the Italian getting through the 36-hole cut at the 2009 British Open Championship at Turnberry's Ailsa Course.
While Guan Tianlang is the youngest player to make the cut in a men's major championship, the youngest person to make a cut in any major championship is Michelle Wie. Wie was 13 years, 5 months, 17 days old when she made the cut in the 2003 Kraft Nabisco Championship, now known as the ANA Inspiration. Wie is consequently also the youngest golfer to make a cut on the LPGA Tour, shooting 2-over 146 on a sponsor invitation to qualify for the weekend.