If the last few days have shown anything about Coco Gauff, it is a fragility to her game and her emotions. 

Tears on the court, difficulties with her serve, and the realization that she is just 21; a young athlete carrying immense expectations, striving to handle the mounting pressure.

However, under the warm Saturday sun at Arthur Ashe, none of these struggles were visible as Gauff displayed determination and focus, effortlessly defeating No 28 seed Magdalena Frech in straight sets, 6-3 6-1.

What a transformation in just two days. After describing her play as ‘the worst I’ve ever felt’ during Thursday’s challenging match against Donna Vekic, Gauff was back in top form, thrilling the enthusiastic crowd who had paid a premium for the most sought-after ticket in town.

‘It’s been an emotional week,’ Gauff told the crowd after Saturday’s big win, ‘but I think I needed those tough moments to move forward. I was putting so much pressure on myself, but today I showed I was really having fun out there.’ 

The narrative surrounding the American at this year’s US Open has been on her struggling serve, with the two-time Grand Slam champion firing coach Matthew Daly and hiring serving guru Gavin MacMillan just six days out from arriving in the Big Apple.

Coco Gauff looked in imperious form as she demolished Magdalena Frech in straight sets

Gauff’s serve looks better in every match under new coaching guru Gavin MacMillan

And so, she has been learning on the go, working it all out in front of 23,000 fans on the biggest stage. And little by little, it seems to be working.

A 61% first serve percentage in round one was improved to 69% in round two, and Gauff’s motion looked back to its best against Frech, with 76% of her first serves in play.

As for double faults: 10 in her first match, eight in her second, and just four here. With each passing day, she looks ever more impressive. 

Not that her Polish opponent didn’t rise to the occasion herself. In her debut on Arthur Ashe, she embarked on a series of grueling baseline rallies with the world No 3, matching her stride for stride and at times silencing the partisan American crowd.

Frech was making her Arthur Ashe debut but she couldn’t provide an upset in New York

Thousands of fans descended on Arthur Ashe to watch Gauff open Saturday’s proceedings

The defining moment of the first set came on Frech’s serve at 3-4. Having each been broken once, Gauff fought back from 30-0 down, finally converting a third break point to take a 5-3 lead and give herself the chance to serve for the set.

And that she did, seeing it out with relative ease to spark a rare scream of emotion from the 21-year-old, the entire crowd rising to its feet in unison.

Now, Gauff was well and truly in the New York Groove, and try as Frech might it is almost impossible to stop her when she’s in this mood.

The Pole managed – just – to hold her serve in the opening game, before Gauff unleashed a furious 20 minutes of tennis. 1-1, 2-1, 3-1, 4-1, Frech hardly given a chance to steady herself against the brutal pace of her opponent.

Saturday’s performance was in stark contrast to Thursday night when Gauff cried on court 

The 21-year-old American waves at the crowd after making it through to the fourth round

With the match nearly out of her grasp, Frech rallied back to deuce in the next game, but Gauff once again proved too strong with a looping forehand to secure a 5-1 lead. 

From there, the home favorite saw it out in style, breaking again to see the second set out 6-1. Next up is the fourth round, and a blockbuster meeting with Naomi Osaka – a match many had hoped for when the draw was first made.

‘I can’t put into words how privileged I feel to be out here in front of you guys,’ Gauff beamed as she came off court.

If she continues to improve like this, there may be no stopping her.