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.