Over the past couple of years, as he has ploughed an often lonely furrow for Australia at grand slam events, Alex de Minaur has been at pains to state that things would come good, sooner rather than later. Numbers, it’s all about numbers, he suggested, referring to the increasing presence of Australians in the men’s top 100.

It has been a long time coming, but if this year’s US Open is anything to go by, then the pyramid effect – the more players you have, the more likely some of them will push higher – looks like it is working.

For the first time since 1997, Australia has four men into the third round at the US Open. De Minaur has been joined in the last 32 by Alexei Popyrin, Jordan Thompson and Chris O’Connell, four Sydneysiders whose friendship, work ethic and camaraderie is pushing each of them to new levels. If Popryin, who is due to play the 24-time major winner Novak Djokovic, and O’Connell, who takes on world No 1 Jannik Sinner, face uphill battles, then Thompson and De Minaur have good chances to go further. Things are happening.

“I think Australia has shown through years and years, the rich history it has in the game,” De Minaur says. “There was a stage where maybe we lost a couple of those numbers, but I think recently we’ve shown the strength in the country.

“With this new wave of players, we’re really flying the flag proudly, not only with our numbers. We’re a grand slam nation, but in population, we don’t have that many people, and we’ve made the final of the Davis Cup two years running with what some would say is not the strongest team.

“But we just show what it means to play for Australia. I know all these boys out there, they’re flying the flag very proudly. It’s great to see them all doing well.”

With Nick Kyrgios still on the sidelines through injury, most of Australia’s hopes have landed on the shoulders of De Minaur, with Rinky Hijikata the only other Australian to make the last 16 of a slam in the past two years. De Minaur often talks of his privilege to be the leader of Australian men’s tennis, setting an example through his work ethic and professionalism, for the others to follow. The 25-year-old sets standards that Kyrgios, for all his talent and success, arguably did not.

“Look, I think just watching him achieve what he has at this level, I think ‘Demon’ is the epitome of hard work and perseverance,” says Popryin, who in Montreal earlier this month became the first Australian to win a Masters 1000 title since Lleyton Hewitt in 2003. “He is definitely a really hard worker and showed us that if you’re able to put your mind to it and your brain to it and your body to it, then you can achieve some [big] things.

“He was one of the first people to congratulate me after I won [in Montreal], and that’s the kind of person that he is. We’ve known each other for a very long time, we’ve come up the ranks together. Him being in the top 10 and me being at my career-high [ranking] is a great thing for us. It’s something that as kids, you know, we never really thought about at the time, but it’s definitely what we wanted.”

Australians have always produced good doubles players – Kyrgios, Thanasi Kokkinakis, Matt Ebden, Max Purcell, John Peers, Hijikata and Jason Kublev have all won men’s doubles titles at slams in the past decade – but now they’re performing even better in singles.

Thompson’s win over Hubert Hurkacz in the second round of the US Open was his first over a top-10 player at a major; O’Connell took out the No 26 seed Nicolas Jarry in round one and Kokkinakis knocked out Stefanos Tsitsipas, the 11th seed and twice a runner-up at grand slams, in the first round. Australia has 10 men in the world’s top 100 and three – De Minaur, Popryin and Thompson – in the top 32.

The Australians are a close-knit bunch and all good friends, something that can’t hurt especially when they are such a long way from home. Hanging out together at an Australian coffee shop in Manhattan or just relaxing in the player lounge at Flushing Meadows, they enjoy each other’s company. And while they are all competitive, they are also pulling for each other to do well.

“There’s always an Aussie doing well each week,” says Thompson, who plays Matteo Arnaldi on Saturday. “So it’s like, if an Aussie does well one week, you’re like, OK, why couldn’t it be my week the following week? That’s sort of how it is and I’m sure all the other guys are thinking the same thing.”