In terms of the struggle for gender equality, the symbolism of the birth of Neve Te Aroha Ardern Gayford is impossible to ignore, and is rightly being celebrated around the world.

Possibly the most important article about the significance of Ardern having a child while prime minister was published in the Hindustan Times – see: Jacinda Ardern to Benazir Bhutto: A tale of two pregnancies in power. As the title suggests, the article emphasises the difference between Ardern's experience and that of Pakistan's prime minister Benazir Bhutto, who gave birth to daughter Bakhtawar in 1990 while in office.

The contrast is stunning and worth quoting at length: "It was all a far cry from 1990, when Bhutto, the first woman to head a democratic government in a Muslim-majority nation, told almost no-one she was pregnant until Bakhtawar was born on January 25. 'None of us in the cabinet virtually knew that this prime minister was about to deliver a baby,' Javed Jabbar, a member of her cabinet, told the BBC recently. 'And then lo-and-behold suddenly we learn that she has not only gone and delivered democracy she's also delivered a baby.' Opposition leader Syeda Abida Hussain had called Bhutto 'greedy' for wanting to have 'motherhood, domesticity, glamour, and whole responsibility' rather than make sacrifices for her country."

The article recounts how the Pakistani prime minister feared "she was in danger of being overthrown" and had to go "incognito to a Karachi hospital, underwent a Caesarean section, then returned to work." According to Bhutto, "The next day I was back on the job, reading government papers and signing government files".

Bhutto was assassinated in 2007, but had she lived "Thursday would have been her birthday."

It would be a mistake to see the contrast between Bhutto and Ardern's experience as simply being down to cultural and national differences between New Zealand and Pakistan. After all, western developed countries haven't produced many female heads of government since 1990, and it's remarkable that Ardern is only the first to give birth while in office.

Ex-prime minister Helen Clark, writes in the British Guardian: "What lessons are there in this for our world? In my view, New Zealand is showing that no doors are closed to women, that having a baby while being prime minister can be managed, and that it's acceptable for male partners to be full-time carers. This is very positive role modelling for the empowerment of women and for gender equality" – see: Jacinda Ardern shows that no doors are closed to women.

On Ardern being unmarried, Clark says "Conventional wisdom may have said that this combination of factors would not have been helpful to a political career at the highest level. Fortunately, that has proved to be wrong. Ardern is a remarkable woman who crashes through glass ceilings with apparent ease."

Lots of commentaries on the birth have quite rightly been using words such as "momentous" and "groundbreaking". For example, see Michelle Duff's Jacinda Ardern had a baby, and we should all be proud.

According to Duff, the importance of this historic event is that: "It normalises powerful women and nurturing, caring men. It decimates outdated ideals of where a mother 'should' be – at home, with the children, while dad earns the money."

She says the country has mostly embraced the PM's pregnancy: "New Zealand's reaction to its Prime Minister's pregnancy has basically been a collective 'Sweet as'. As a country, we're mostly cool with this, which suggests we're well on our way to true equality."

National Party blogger David Farrar came up with one of the best lines on the significance of it all, saying, That's one small step for a woman, one giant leap for womenkind. He stated: "There is of course nothing unusual at all about a woman giving birth, but for many it is quite monumental to see that being pregnant and giving birth is not incompatible with the highest office in the land. It is motivational and aspirational.

Similarly, veteran political journalist John Armstrong reflected on the significance, declaring: "There are moments in a country's history which transcend the ordinary; moments when the stars are in alignment with one another to produce the truly extraordinary. The birth of the Prime Minister's first child has been such a moment" – see: There are moments in a country's history which transcend the ordinary.

Armstrong explains Ardern's influence: "Ardern is the very embodiment of how a modern society seeks to unshackle women in order to harvest their potential contribution to the greater good to the maximum possible. It is impossible to measure Ardern's influence as a role model. But it will already have been vast. Yet, she is incurably modest about it all. And she does not seek to exploit her success and the consequent high regard in which she is held to ram a message about gender equality down people's throats."

Positivity about the birth, and about the breaking down of barriers, has been far from partisan according to Armstrong: "No matter one's political leanings, it was near impossible not to succumb to the euphoria. The symptoms of Babymania were easy to spot."

Newspaper editorials also reflected on what Neve Gayford's birth said about the modern liberal nature of New Zealand. For example, The Press said that "In an unmarried Prime Minister who gets to take maternity leave, we could see the progressive, tolerant, open-minded nation we like to think we are" – see: Jacinda's baby represents hope, humility and the best of our values.

Of course, some have questioned how progressive the nation really is and whether we should read too much into the birth. For example, Heather du Plessis-Allan reminded us that we didn't actually vote a pregnant woman into office, and it was really down to Winston Peters giving the nod to Ardern instead of Bill English. She argues that, although the nation loves to bask in the reputation of being socially progressive, there's plenty of evidence to the contrary – see: It's not hip to be square.

Coming from a completely different point of view, leftwing blogger Steven Cowan wonders if Labour Party types are simply trying to make political capital about how great it is for elite women in this country, while ignoring the struggles of most women. He says, "It is trickle down feminism, the kind of feminism that neoliberalism can embrace" – see: Jacinda Ardern and the feminism of the one percent.

Ardern has been at pains to acknowledge that not all women or families have the privileges that will allow her to lead the nation while being a new mother. And David Farrar elaborates on this in his blog post:

"Jacinda is fortunate that she has the support of not just her partner who will be primary caregiver, but also her parents. On top of that she has a staff of 25, VIP Transport, the DPS etc who will all be supporting her in her role as PM and mother, so she can do both. Her baby and partner/support persons will be transported around NZ with her. That is at it should be, but not every mother will have that support. So other parents shouldn't feel pressured that they are lacking something if they are not back at work so soon."

And these issues are fuelling debate around the world. For instance, in the UK, Victoria Smith has written in the Independent newspaper that, as much as we should celebrate what New Zealand's prime minister has achieved, there is a danger in assuming – or pressuring – every women to be able to do the same thing when it's simply not possible for them – see: Why you shouldn't uphold Jacinda Ardern as proof that working mothers can 'have it all'. Smith worries that other mothers who are not working will now be asked: "So what's your excuse?".

Her main point is this: "I'm delighted at the example Ardern sets, and look forward to her continuing to demonstrate that pregnancy, motherhood and care work can and should be embedded in political life. The more we see mothers as full participants in public discourse and social change, the better. It's important, though, to be clear about realities for other women in the here and now. Being shown what can be possible is not the same as being offered it. Pregnancy and motherhood should not exclude us from career success, but the truth is, they do."

Finally, Jenna Lynch looks back at some of the politicians who have lead the way for Ardern – see Jenna Lynch's Mothers in Parliament: The women who paved the way for Jacinda Ardern, and Anna Bracewell-Worrall investigates how Parliament is becoming more child-friendly – see What it's like having a baby at Parliament.