Maths whizz Lily Miyazaki feels like her number has finally come up after qualifying for the US Open.
The Tokyo-born Brit had a wild card for Wimbledon last year, but has now reached the main draw of a grand slam under her own steam for the first time.
Miyazaki, who earned a masters degree in mathematical science in the United States four years ago, beat Slovakia’s Viktoria Hruncakova in the final round of qualifying at Flushing Meadows.
The 27-year-old now has to solve the puzzle of how to get past Russian Margarita Betova on Monday for a first grand slam match win.
“Playing Wimbledon last year was amazing,” said Miyazaki. “But I think that, as a wild card, I don’t know how to explain it, but I don’t know if you truly believe like you belong.
“And I played Caroline Garcia, obviously she’s a pretty good player and I was really nervous going into that match. So hopefully this time I feel like I belong here. So that experience definitely helped me.”
Miyazaki joins Katie Boulter and Jodie Burrage as the British contingent in the women’s draw.
She also shares a coach, Craig Veal, with British number two Burrage, who was in the stands supporting her compatriot.
“For her to qualify, it was killing me,” said Burrage, 24. “When she was one-set all, I had to go to practice and throughout it I was shouting at my physio asking what the score was.
“I was hardly focusing on my practice because I wanted to be there watching her, but it’s so good she has qualified, with me and ‘Boults’ being in the main draw.
“It’s nice when you are friends and you can enjoy success with them and hopefully next week we can do some damage in the main draw. We’ve all got the games to be able to.”
Burrage faces Russian Anna Blinkova on Tuesday, while British number one Boulter meets France’s Diane Parry.
Sabalenka sets up Swiatek rematch at Madrid Open
Aryna Sabalenka will face Iga Swiatek in the Madrid Open final for the second year running after beating Elena Rybakina 1-6 7-5 7-6 (7-5) in a semi-final classic on Thursday.
Fourth seed Rybakina made a flying start and took the opener within just 25 minutes, but Sabalenka hit back in a topsy-turvy second set featuring five breaks of serve to force a decider.
Both players were imperious on their own serve from there, with a tie-break required to split them. Sabalenka's power looked likely to overwhelm Rybakina as she raced into a 5-1 lead, but the former Wimbledon champion clung on by saving two match points on her own serve.
Sabalenka would not be denied third time around, though, a huge serve giving Rybakina no chance as the defending champion teed up a rematch with Swiatek, who she beat in the Spanish capital in last year's showpiece match.
Data Debrief: Sabalenka's unwanted record
Sabalenka has dropped 60 games at this year's Madrid Open. That makes her the player with the most games dropped en route to reaching the final since the tournament's inception in 2009.
The world number two had to dig deep in a match which saw Rybakina win more total points (99 to 95), but she will not mind one bit if she goes on to capture a third Madrid Open title on Saturday.
Lehecka into maiden Masters semi-final after Medvedev retires hurt
Jiri Lehecka progressed to the first ATP Masters 1000 semi-final of his career as Daniil Medvedev retired hurt on Thursday at the Madrid Open.
Lehecka, who beat the great Rafael Nadal in the last 16, had just taken the first set 6-4 when Medvedev threw in the towel.
Medvedev had earlier received treatment from the physio, having seemingly struggled when moving to his right side.
"It's never easy in a match like this," Lehecka said. "If I were to choose the way how to win this match, it wouldn't be like that.
"So of course, it's never easy to see your opponent struggling, but at that moment, you just need to focus on yourself, trying to get the maximum level out of yourself."
Lehecka will face Felix Auger-Aliassime, who progressed thanks to a walkover following Jannik Sinner's withdrawal, for a place in the final.
Data Debrief: Czech mates
Lehecka is the third Czech player to reach the semi-finals in Madrid, following Jiri Vovak and Tomas Berdych.
Should Lehecka reach the final, he will move into the top 20 of the ATP rankings for the first time.
Swiatek races into Madrid Open final with dominant win over Keys
Iga Swiatek cruised into her second Madrid Open final on Thursday, maintaining her ominous form by beating Madison Keys 6-1 6-3 within 71 minutes.
Swiatek had been forced to fight back from a set down against Beatriz Haddad Maia in the quarter-finals, but there was no slow start on Thursday as she broke Keys' serve to love at the first attempt.
Only in the fifth game, when Keys failed to convert two break points, was Swiatek troubled in a 31-minute opener, and she carried that momentum into the second set with another early break.
Having eliminated Coco Gauff and Ons Jabeur on a deeply impressive run, Keys had no answer for Swiatek's power as she clinically worked her way through the second set, the American's forehand running long on match point to seal a routine win for the world number one.
Having lost last year's final against Aryna Sabalenka, Swiatek could face a rematch against the defending champion, who takes on Elena Rybakina in Thursday's other semi-final.
Data Debrief: Swiatek surpasses Serena
Saturday's final will be Swiatek's 11th at WTA 1000-level, the Pole going all the way on 37.9 per cent of her 29 main-draw entries at that level. That is a better ratio than 23-time grand slam champion Serena Williams managed in her glittering career, the American doing so at 18 of 49 WTA 1000 tournaments (36.7 per cent).
Swiatek has now played eight matches in 2024 without dropping a single game on her own serve, a tally only matched by her possible final opponent Sabalenka on the WTA tour.
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