US Open 2020: Serena, Azarenka and Pironkova - the trailblazing women making motherhood normal

Even the hardest heart must have been touched just a little to see Olympia Ohanian's legs kicking with glee as she celebrated her mother Serena Williams' third-round win over Sloane Stephens at the US Open.

The three-year-old celebrated her birthday in New York this week, and "Mama", the tournament's third seed, has loved being able to see her little girl in the stands.

"I hope that she saw her mama fighting!" said Williams after the match.

Three days on from that, Williams has beaten Maria Sakkari in round four as well - and is joined on the second day of women's singles quarter-finals by two other mothers.

One is Victoria Azarenka, who has also been spotted watching the action from her suite overlooking Arthur Ashe Stadium with her son Leo.

And one is the woman Williams is facing for a spot in the semi-finals - Tsvetana Pironkova of Bulgaria, who is playing her first tournament in three years after giving birth to son Alexander in 2018.

Three out of eight quarter-finalists is a pretty good percentage. It's a far cry from the fuss that was made about Kim Clijsters' return after maternity leave, when she won back-to-back US Open titles as a mother in 2009 and 2010.

It seems a little late to realise it, but in 2020, provision is finally being made for women to be top-class professional athletes and mothers as well.

Azarenka was one of the players on the WTA council who fought for maternity rights, meaning that any player who took time out to have a baby would have some kind of rankings protection on the tour.

And Pironkova is one of the women who have benefited from it, using that allowance to enter the US Open as her first tournament back.

"I'm glad that our women have this protection," Azarenka said in a press conference this week. "I'm not the only one who fought for that, but one of the players who fought for this rule that we are more protected and feel more comfortable because it's such a life-changing experience that you have.

Admittedly, it has led to the unedifying spectacle of the non-mothers in the draw being questioned in press conferences about their future family plans.

Naomi Osaka, 22, was unsurprisingly stunned to be quizzed on this, managing to reply, "Honestly, that's so far ahead in the future, I haven't really thought about it."

Actually, 32-year-old Angelique Kerber was similarly taken aback, answering thoughtfully: "When you can come back and playing on a high level after having a baby, of course it's a great thing, and you can see that everyone loves the sport. This is always important. About me, I don't know. I mean, I'm not thinking about this yet. For me, it's more important now to play good tennis and stay in the moment."

But after an eternity in which their male counterparts have been able to combine fatherhood with elite competition, it's good that the women are getting the chance to do so as well if they wish - and thriving.

And perhaps this year isn't a one-off. Perhaps this trailblazing generation - who have fought hard for their rights just as their predecessors did - are going to make it entirely acceptable to be a mother in professional sport, if that's what a player chooses, and entirely unnoteworthy.

Because, after all, they're not there to have their kids cooed over, or their parenting admired.

"I don't identify myself on the tennis court as a mother," said Azarenka. "I still identify myself as a tennis player. Me being in the quarterfinals, I didn't get there by being a parent, I got there by being a tennis player."

And perhaps the next generation might be led by a little girl whose mother has taken on the world - and won - 23 times and counting so far.

"I'm like, 'I gotta put my career aside and get her a racket in her hand'," said Serena of her small tennis fan.

"Seriously, that's what I told my husband yesterday. I'm like, 'We got to get a racket in her hand."