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.
Sinner inspires comeback to help Italy reach Davis Cup semi-finals
Jannik Sinner kept Italy's hopes of retaining the Davis Cup alive after winning matches in the singles and doubles to inspire a 2-1 comeback triumph over Argentina on Thursday.
Sinner and Matteo Berrettini edged Maximo Gonzalez and Andres Molteni 6-4 7-5 in the deciding game to set up a rematch of last year's showpiece against Australia in the final four.
However, the Italians started off on the back foot when Francisco Cerundolo downed Olympic bronze medallist Lorenzo Musetti 6-4 6-1 in an hour and 29 minutes.
Musetti converted just two of the eight break points he was presented with, as Cerundolo put Argentina on the brink of reaching the semi-finals for the first time since 2016.
But two-time grand slam champion Sinner, who won the ATP Finals last weekend, carried his momentum forward from Turin against Sebastian Baez.
The world number one breezed to a 6-2 6-1 win over his opponent, serving seven aces to the Argentine's one, while also saving all four break points he faced.
Sinner then returned to the court alongside Berrettini, with the pair replacing Simone Bolelli and Andrea Vavassori in the must-win clash.
The pair won 90% of their first-serve points and fended off all five break points they faced, earning a key break at 5-5 in the second set before surging to victory.
"It was a must-win match," said Sinner. "Very different conditions. The court is very, very fast and tough to play.
"I haven't had so much time to adapt to the conditions, but I'm happy about today."
Data Debrief: The Italian Job
Italy edged closer to becoming only the sixth nation to retain the Davis Cup since the final stage was introduced 52 years ago, and first since the Czech Republic in 2013.
But they were inspired by Sinner once again, who proved why he will end the year at the summit of the ATP rankings.
And after leading Italy to their first Davis Cup title since 1976 with a victory against Australia's Alex de Minaur last year, he will fancy his chances this time around.
Ebden and Thompson send Australia to third straight Davis Cup semi
Matthew Ebden and Jordan Thompson booked Australia's place in the Davis Cup semi-finals after the pair clinched their deciding match against the United States to win 2-1.
The pair, who won gold at the Paris Olympics, beat Tommy Paul and Ben Shelton 6-4 6-4 to put Lleyton Hewitt's side into their third successive semi-final at the men's team event.
Australia, who have won the tournament 28 times, largely had Thanasi Kokkinakis to thank after his remarkable triumph over Shelton in the first match of the day.
Kokkinakis saved four match points and let slip six of his own before eventually prevailing 6-1 4-6 7-6 (16-14) in an engrossing encounter that lasted two hours and 14 minutes.
However, in the rematch of a recent ATP Finals group-stage match, Taylor Fritz emerged victorious over Alex De Minaur as he did in Turin a week ago.
Despite De Minaur going 2-0 up in the second set, Fritz roared back to earn a 6-3 6-4 victory to send the tie the distance in Malaga.
But Australia held their nerve, and will discover their opponents later on Thursday when reigning champions Italy take on Argentina.
Ebden and Thompson’s win came after United States’ captain Bob Bryan opted for a late change, with Paul and Shelton replacing Austin Krajicek and Rajeev Ram.
“We were expecting the other pair, but we knew they’ve got incredible players who can play doubles,” said Ebden.
“We were ready. A slight adjustment obviously. More huge serving singles players than the doubles craft, maybe, but it was just as big a challenge as any.
"Out here, finals live match, just to play with Jordan here was real fun. Following what Kokk did, unfortunately Alex went down, but what a day. So fun, so happy.”
Data Debrief: Australia ready to right Davis Cup wrongs
Australia have failed to win the Davis Cup since 2003, but they will be confident of halting that streak this time around.
If they take the trophy, they will have reason to thank Kokkinakis, whose tie-break win against Shelton was the longest an Australian player had featured in at the tournament, surpassing Pat Rafter's win over David Rikl in the 1997 quarter-finals of the competition (15-13).
Ebden and Thompson also shone when it mattered most, serving four aces compared to Paul and Shelton's two, while also winning 92% of their first-serve points.
Paolini and Bronzetti seal fifth Billie Jean King Cup for Italy
Victories for Jasmine Paolini and Lucia Bronzetti handed Italy their fifth Billie Jean King Cup title as they overcame Slovakia in Wednesday's final in Malaga.
Italy, who were beaten in last year's final by Canada, overcame Poland in the semi-finals on Monday as Paolini partnered Sara Errani for a decisive doubles win over world number two Iga Swiatek and Katarzyna Kawa.
The showpiece contest began with Bronzetti triumphing 6-2 6-4 against Viktoria Hruncakova, before Paolini took to the court to face Rebecca Sramkova.
The world number four – who won doubles gold at the Paris Olympics in August to cap her breakout year – eased past Sramkova by a 6-2 6-1 scoreline to ensure a doubles match was not required.
Speaking after Italy claimed the trophy for the first time since 2011, Bronzetti heaped praise upon her team-mate and revealed she had struggled to sleep before playing in front of 12-time grand slam champion King.
"Jasmine raised her level really high this year. She's an example for all of us," Bronzetti said.
Asked about King's presence in the crowd, Bronzetti added: "She is a great person, a great legend. I didn't sleep very well.
"You're not playing just for yourself. You're playing for your team and your country. We all want this trophy, and it is our dream, all Italians."
Data Debrief: Five-star Italy
Italy have claimed their fifth Billie Jean King Cup, having previously triumphed in 2006, 2009, 2010 and 2013.
Only the United States (18), Czechoslovakia/Czechia (11) and Australia (seven) have won more. Spain and Russia (also including the USSR and Russian Tennis Federation) have also tasted success five times.
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