Fast-forward to 2014 and it is now eight years since a teenager won a grand slam title, when Maria Sharapova the U.S. Open at 19.
Since then, only three teenagers - Sharapova at the Australian Open in 2007, Ana Ivanovic at the French Open the same year and Caroline Wozniacki at the U.S. Open in 2009 - have even made it to a grand slam final.
More promising teenagers have bitten the dust in the first two rounds of the Australian Open but there are signs that youth may be coming of age.
Five teenagers ended last year inside the world's top 50, led by number 12 Sloane Stephens, and the sight of 16-year-old Belinda Bencic pushing world number four Li Na hard on Wednesday suggests big things for her future.
Having won through qualifying, she looked overwhelmed as she lost the first set but took Li to a tiebreak in the second before going down 6-0 7-6, impressing the Chinese in the process.
"She played exactly like Martina Hingis, I feel," said Li, a compliment Bencic is yet to tire of hearing. "She gave me a very tough time at the end of the second set."
A junior champion in Paris and Wimbledon last year, Switzerland's Bencic already has 11 sponsors, including Rolex, and is coached by Martina Hingis's mother, Melanie Molitor.
Like all juniors, Bencic is restricted in the number of WTA events she can play, a rule designed to avoid the burnout that affected the sport in the 1980s and 1990s.
BEST PERFORMANCE
A 16-year-old is usually restricted to 12 events on the WTA Tour, but by reaching two junior grand slam finals (she won them both) and finishing in the top five of the junior rankings, she can add three events, making a total of 15.
"It's not frustrating now," she told reporters, referring to the restrictions.
"It's OK, because I get three extra tournaments.
"I think I showed also in qualifying I can beat players and also some people in the main draw. It's great I had this experience at the age of 16."
Eugenie Bouchard, who turns 20 next month, saw off Virginie Razzano of France 6-2 7-6 to reach the third round, clinching victory on her seventh match point to equal her best grand slam performance to date.
The Canadian, a former Wimbledon junior champion, is developing a large following wherever she goes and was given a cuddly koala by one of her fans after the match.
Seeded for the first time at a grand slam, Bouchard admitted that breaking through at grand slam level is far from easy.
"It think it's still really tough," she told reporters. "There are some of us who are kind of breaking through a little bit but we still have a lot of tough moments.
"I think the older, experienced players are still dominating but as time goes on, I think I'll do better.
"I've gained experience in the past year and hopefully I can start doing better right away."
Miami-based Puerto Rican Monica Puig and America's Madison Keys were both beaten by experienced opponents but another American, Alison Riske, a little older at 23, believes the new crop of Americans have the ability to push on close to the top.
"The atmosphere in the locker-room with the Americans is awesome," she said after crushing Yanina Wickmayer of Belgium 6-1 6-1.
"We're all doing well and pushing each other on. To be able to do this together is really exciting. It's a win, win."
(Editing by John O'Brien)
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