It was quite something to watch the opening moments of Marta Kostyuk’s third-round match at the Australian Open on Thursday night. She was playing Elina Svitolina, of Ukraine, the bettors’ favorite to win in Melbourne, and arguably the most consistent top player in the women’s game over the past year—with Serena Williams not yet back after giving birth to a daughter late last summer, and most of the rest of the best sloshing tidally from the near reaches of No. 1 to six or maybe sixteen or lower, and then back. Kostyuk is from Ukraine, too, but she and Svitolina are not well acquainted. Svitolina, who is twenty-three, spends most of the year on tour and much of her downtime in London. Kostyuk is based in Zagreb, Croatia, where she works with Ivan Ljubičić, a former tour pro who has coached Roger Federer. She is fifteen, the age of an American ninth grader. And she was torching Svitolina, breaking her quickly in the opening game without dropping a single point.

Kostyuk is not especially tall, and she does not have the kind of muscular lower body that some shorter players do. She does have broad swimmer’s shoulders, and these, together with her precocious timing and pronounced weight transfer, back foot to front, provide her flat groundstrokes with what comes across as easy power. One of her forehand winners was clocked at ninety-four miles per hour. Madison Keys, the twenty-two-year-old American star, and another favorite to win the Australian Open, is thought to have the biggest forehand in women’s tennis, one that regularly reaches eighty miles per hour. Did I mention that Kostyuk is fifteen?

She began playing tennis at the age of five. Her mother, a former tour player, was her coach—and still is. Kostyuk says that it was not uncommon for her to have days when she spent twelve hours on the court. She hated to lose. She raged. She was a perfectionist, by her own account. She didn’t enjoy herself, she’s said. She did get better, and better. Last year, she won the Australian Open girls’ singles championship. Fourteen is young to accomplish that. Grand Slam junior tournaments are open to anyone up to age eighteen.

That win earned her an invitation to qualifying week at this year’s main event. She won all three of her qualifying matches and, this week, entered the main draw. She dispatched the twenty-fifth-seeded Peng Shuai, of China (6–2, 6–2), on Monday. Then, on Wednesday, she took out Australia’s Olivia Rogowska, a wild-card entry ranked No. 168 in the world—which sounds unimpressive until you understand that Kostyuk entered the tournament ranked No. 541. By defeating Rogowska (6–3, 7–5), she became the youngest player to reach the third round in Melbourne since Martina Hingis, in 1996. That win brought Kostyuk to center court Friday afternoon, at Rod Laver Arena, where the temperature was a hundred and seven, and the sun seats were mostly empty. But the rest of the tennis world, in cooler places—and mostly in time zones where it was still Thursday—was brimming with anticipation.

What is so thrilling, at the moment, about watching a teen-age tennis phenom appear? It has something to do, I think, with the dominance, in this era, of Federer, Nadal, Djokovic, and the Williams sisters: all in their thirties, as dominant players so rarely used to be. They are all destined to be legends, and all having seemingly—or, if you are in your twenties, or younger, not so seemingly—been with us forever. It’s exciting to be introduced to someone new. The sensation of last year’s U.S. Open was undoubtedly Denis Shapovalov, the eighteen-year-old Canadian with the oversized backward cap, one-handed backhand like something choreographed by Trisha Brown, and the winning—in every sense of the word—court presence. We fans know who we love. We want a crush. Shapo!

For older fans, like this one, there is nostalgia, too, for a time when teen-agers came out of nowhere to win—or come close to winning—Grand Slams. Boris Becker grabbed the trophy at Wimbledon in 1985 as an unseeded seventeen-year-old (and then rested it on his mop of red hair). Maria Sharapova was seventeen, too, when she stunned Serena, at Wimbledon, in 2004. Most vivid for me, watching with newly made friends as I began college, was Chris Evert, at her first Grand Slam, in 1971, at the U.S. Open at Forest Hills, where, at that time, the main stadium had three grass courts, with matches rotating among them to preserve the turf. Evert was sixteen, with a long ponytail and a lacy tennis dress. Grass was not her surface and never would be. But she reached the semis, where she lost in two hard-fought sets to Billie Jean King, the eventual champion. Bud Collins called the match, effervescently. It was the dawn of the tennis boom, or felt like it—or feels like it now.

The truth is, there weren’t all that many teen-age champions even then. Add in Tracy Austin, Steffi Graf, Hingis, Serena, Michael Chang, Mats Wilander, Pete Sampras, and you still have little more than a handful in the entire Open era. It tends to take awhile for a promising teen to get really good.

Therein lies another reason that fans get so absorbed by the play of teen-agers—especially those of us who spend our weekends hacking away on some club court. The youngest newcomers to the pro tour confirm how difficult tennis is. A brilliant fifteen-year-old still sprays shots, tightens up on big points, grows clueless about court position, muffs volleys, and gets grumpy or impatient or both. They’re still becoming—which means they’re erratic.

And so Marta Kostyuk was, soon enough, in the biggest match to date in her young, young life. She would double fault nine times. She would mutter and shake her head. She would lose the form she displayed in the first game by the second game, and never regain it. She would wind up losing (2–6, 2–6) in under an hour, and by the time she had grabbed her racquet bag and reached the tunnel, she was biting hard on the towel around her neck and appeared to be almost running. She looked, all of a sudden, like a child.