Like an icon: Madonna on being creative and provocative at 60

She drank alcohol but drew the line at sleeping pills. "That's a slippery slide to get on," she tells me, pulling a crossed leg toward herself and massaging her taut calf. "I've been doing back-to-back video shoots all night, standing in the freezing cold, for the past couple of weeks," she explains. I seize the opening to ask how she feels in her body these days. "You're my doctor," she says in a not particularly playful tone of voice. "I just feel tired."

She is a single mum of six now. Her second husband, Guy Ritchie, is gone, along with what her spokeswoman at the time said was $US75 million of her money. For the past few years, she has been in London less than in the hilltop village of Sintra, Portugal, where her son David Banda, 13, attended a top soccer academy and she became perhaps the world's most famous globetrotting soccer mum. She tells me she isn't yet over the release of her last album, Rebel Heart, in 2015, which sold less than her others. The songs had leaked online several months early, far from perfection. "There are no words to describe how devastated I was," she says. "It took me a while to recover, and put such a bad taste in my mouth I wasn't really interested in making music." She adds, "I felt raped." It doesn't feel right to explain that women these days are trying not to use that word metaphorically.

In Portugal, she says, she was lonely. I ask if she felt that way because she was living in a castle, which seems like the most appropriate description of the 16,000-square-foot Moorish revival mansion I read she bought, but she shoots back: "Let's not get carried away. I wasn't in any castle." She says about Lisbon, "It's quite medieval and feels like a place where time stopped in a way, and it feels very closed," adding, "There's a cool vibe there, but where I was living with my kids, I felt very cut off from a lot." She sums up her days: "It was FIFA and my kids' school and that's it. I'm fighting with the plumber."

For a moment, she almost looks shy. "I really wanted to make friends," she says.

One night, she visited a Frenchman's crumbling home on the sea for an improv session, mostly of fado musicians. "There was a vibration there that was magical and palpable, and suddenly musicians started playing," she says. They rose from couches to sing, from chairs to pluck a guitar. Listening to the variety of musicians, from Brazilian samba players and jazz quartets to a singer from Guinea-Bissau performing in Mandinka, she fell into a trance.

I listen to her describe how this scene had worm-holed her back to her younger self, particularly the one that emerged in New York City in golden early-'80s downtown Manhattan. Studio 54 was over, punk rock had come and gone and DJs like Afrika Bambaataa were figuring out how to mash up disco, seminal hip-hop albums and electro bands like Kraftwerk before sampling technology had been invented. She was the Italian-American dropout from the University of Michigan; now, she remade herself as a sexy, lovesick street urchin in pre-gentrification Alphabet City, surviving by checking coats at the Russian Tea Room and modelling in the nude for art classes.

At night, Madonna slipped cassettes of her songs to DJs at Danceteria and the Fun House. She mixed it up on the dance floor with South Bronx B-boys and graffiti-artist-musician-painters like her new boyfriend Jean-Michel Basquiat. Cindy Sherman was showing in galleries around town, spurring interest in self-invention with her photographs. "I felt she was doing some kind of parallel kind of work to what I was doing," Madonna says. "I could relate to her. Becoming other people but still herself with a sense of irony, making social commentary." The Beastie Boys were devising a tongue-in-cheek marriage of heavy metal and hip-hop rhymes and recording their first record. AIDS hadn't spread widely yet. When people talk about what New York used to be like, that's what it was like.

The conventional wisdom is that Madonna became more famous than everyone else because she was dying to become famous. What set her apart was her bottomless maw of ambition. And over the years, her statements – "I want to rule the world" – supported this theory. Today she puts it this way: "First of all, I wanted to make a living. I was tired of being broke. But second of all, all I wanted was a song to get played on the radio. That's all I was praying for. One song."

"When I was living on the Lower East Side and I didn't see many concerts, I knew about Debbie Harry and Chrissie Hynde and the Talking Heads and David Bowie, but there was no pressure for me to be anything specifically, to sound a certain way, to look a certain way," she recalls. "That's an important thing, because it allowed me to develop as an artist and to be pure, without any influences. What I try to do now is to remember that girl."

Ambition is certainly part of what keeps her going, but it doesn't seem to be all of it. When I ask her how much longer she thinks she will make music and where she thinks she will end up, she says, "Straight to the moon."

Madonna's catalogue is primarily composed of declarative anthems, mini pop arias and songs about longing or lies or mental disconnection. Madame X, her new album, her 14th, is darker than usual, though it also includes fanciful summer love songs. She experimented with musical genres like dance, fado, rap and Cape Verdean batuque and explored her anger over world leaders like Donald Trump "who seemed to be systematically removing all of our personal freedoms", she tells me. She visualises herself as a freedom fighter travelling the world to spread the gospel of love and anti-discrimination, fighting misogyny, homophobia, racism, guns, the rise of authoritarianism.

Some of Madame X was recorded in London, but she didn't build a recording studio at home – "Horrible idea," she tells me. "My house would be shaking all the time" – though she has an editing facility for videos and film. "That's good because I can drop in for an hour and then go back to see my kids, or go back to my other life, and not have to get into a car and go somewhere," she says.

To hear the album, I walk through dark-walled rooms with full bookcases and shrub-sized flower arrangements in divine red-pink-purple and down the stairs to her home screening room. Everything is perfect. The small square screening room, on the same floor as her gym, is like a Tiffany & Co jewel box, but navy rather than robin-egg blue. Every surface is velvet. Footprints cover the carpet like brush strokes on a canvas; I imagine Madonna whirling around, stretching, dancing. A set of weights rests in a corner.

The art is even more striking. Madonna spent her first major pay cheques on paintings. She has collected Frida Kahlo since the 1980s, mesmerised by the artist's cool gaze, as well as geometric Art Deco nudes by Tamara de Lempicka and works by Francis Bacon and Salvador Dalí. Near the screening room, a print of John Lennon's handwritten lyrics to Imagine hangs over the toilet – an intentionally hilarious location – and large portraits line the halls, not only of Lennon and Bob Marley but also Alfred Hitchcock pretending to strangle himself with a tie.

I first heard Madonna when I was 11. She was the opposite of what I had learnt so far about what it was to be a woman. She was sensual and playful, and I loved the way she tied her tights in her hair to make a bow on top. She was Cyndi Lauper with sex, Duran Duran with New York grittiness. And suddenly everyone looked like her – everyone wanted to be her. My friends and I were virgins singing along to Like a Virgin without understanding what the word meant. At one of her 1985 concerts at Madison Square Garden, she wrapped herself in a white wedding veil and lay down on the stage, breathily whispering "it feels so good inside" into a hand-held mike, before hundreds of balloons fell from the ceiling. It was like being present at the big bang of girl-power pop stars. Girls didn't feel the same way about Janis Joplin – they might have wanted to be her, even lusted for her, but they didn't scream as if she were Elvis.

Madonna might not have initially wanted little girls as fans, but at first she seemed to cater to the demo just like the performers at the Billboard Awards, though she attracted a lot of criticism about corrupting little girls' souls or encouraging teenage pregnancy with Papa Don't Preach.

When I tell Madonna I was at that concert, she wants to know how old I was then and says, "Wow, that's young." There is a pause, so I ask how it makes her feel when she hears people reminisce as I have – if she is proud or is unmoved because she has heard the same thing a million times before. "It depends on context," she says.

"I'm happy to hear I was a part of the beginning of your being woke as a female. That's cool." When she thinks about it now, she doesn't think the concert was ground-breaking. "I mean, my belly button was showing," she continues. "If I look back on it, I don't see it as a scandalous concert at all."

That is her first reaction, to diminish her impact, but she soon reverses herself. "A woman fearlessly expressing herself and saying, 'I'm encouraging all of you to be independent, to speak your mind, to express your sexuality freely without shame, to not allow men to objectify you, to objectify yourself' – I don't know," she says.

"All of those things seemed like the natural way of where we should be going. And strangely, a lot of feminists criticised me for it, and I got no support from that group. They thought, 'Well, you can't use your sexuality to empower yourself as a female,' which I think is rubbish, because that's part of who I am and part of me as a female and a human being, my sexuality. That's not the only thing, that wasn't my only weapon and that wasn't the only thing I was talking about."

The great, unexpected part of Madonna's career came during her seamless movement from selfish girlhood to selfless motherhood, from sexy punk simmering with barely concealed rage to earth goddess. By the late '90s, she was not only a devoted mother but an ecstatic one, regarding the birth of her daughter Lourdes as a window on transcendence. "I feel like when my daughter was born, I was born again," she told Oprah in 1998. She wore her hair loose, eschewed make-up, went to therapy, did ashtanga yoga, joined the Kabbalah Center. Ray of Light, the electronic record she gestated at the time, sold 16 million copies.

I found myself as a wife, in both of my marriages, being as I think everybody is: you try to please another person, and sometimes you find you are not being who you really are.

Relationships proved hard for her. "I found myself as a wife, in both of my marriages, being as I think everybody is: you try to please another person, and sometimes you find you are not being who you really are," she tells me. "That's the struggle, I suppose, of being in a marriage or a relationship, especially as a woman. We often think we have to play down our accomplishments or make ourselves smaller, so we don't make other people feel intimidated or less than."

As she grew older, she had young lovers, sometimes 30 years her junior. She experienced joy and wild abandon with her children. She has two biological children and adopted four from Malawi, one of Africa's poorest countries, amid a media frenzy. Her youngest two children are six-year-old girls, whom she adopted in 2017.

She is aware of the doubling effect of children, the way they reflect back your strengths and deficiencies. "If somebody said, 'Okay, you've got to give one thing up,' I would say, 'Okay, I'll stop working,' " she says. "But they like that I work. They love to come visit me and watch me work. My older children, my son, he's a painter, and my daughter's a dancer and choreographer – I can see how my work has influenced them, though they probably wouldn't like to say so. I like it. It makes me proud."

The truth is that talking to Madonna, in this dim room, about topics other than her family, then becomes increasingly difficult. In recent years, she has zoomed to the realm of demigods hellbent on doing good, like Bono, and, combined with the continued devotion to kabbalah, she has become preachy. The one-time fallen Catholic whose video was condemned by the Vatican is now religious. I respect her charity work in Africa, and I am interested in her deep concern about the spread of misogyny, fundamentalism and homophobia, but she loses me when she speaks over and over about paradoxes.

She quotes one of the Kabbalah Center's teachings – "Wherever there's the greatest amount of light, there's the greatest amount of darkness" – and explains that the more she learns on her humanitarian travels, the more complex she realises the world is. "The funny thing is, the more you know, the more passionate you feel about life, and the more joy you feel, and the more inspired you feel, but then also the more disgusted you are with humanity," she says, calling it part of "the paradox of life".

The carapace of fame often conceals insecurity, so I try to turn the conversation towards her grand influence, but she is like a cactus with spikes protecting her from anyone getting too close, particularly journalists. For years, she put boundaries between herself and the media – she had to in the pre-internet days, when people didn't have the option of following her online, so they just waited outside her building.

"It was like living in a golden prison," says her friend of 30 years, Rosie O'Donnell, about Madonna in the 1990s. "There were bodyguards everywhere we went, and people would have no qualms about telling her to her face what they felt about her black hair, and she would usually go, '[Expletive] you.' Nobody can imagine what it's like to have that much energy coming at you all the time whenever you're in public." She adds, "She keeps herself grounded by her charity and by her children, and that's the only way to stay sane in the world of fame."

Now, in the social-media era, the Greek chorus Madonna had blocked out is seeping in, saying she is too old, washed up, out of ideas, finished.

"It's not that I engage with it, but it ends up going in front of your eyes, and then when it goes in front of your eyes, it's inside your head," she says. "It comes up in your feed, and then you get pulled into it whether you like it or not. So it's a challenge to rise above it, to not be affected by it, to not get frustrated, to not compare, to not feel judged, to not be hurt. You know, it's a test. Yeah." She adds, "I preferred life before phone."

The immediacy of the criticism, that she holds it as a tangible thing in her hand, seems as though it has made her nearly paranoid. I realise I can't ask her about anything as personal as menopause, but I have to broach the topic of ageing: if I have followed her this long, where are we going next? The fact is that statements like, "I'm going straight to the moon", while inspirational, are not enough. I admire her for shaking off prejudice about what an older woman can be, for being creative, provocative and sexual over 60 – "It's almost like a crime," is the way she characterises it.

She has always been a pioneer. She tells me she has sympathy for the way middle-aged women are confused by social media, unsure of how to project an appealing image without relying on the shortcut of youthful beauty. "You can't win," she says.

When we talk about ageing, I am surprised when she turns the issue back on me. "I think you think about growing old too much," she says later. "I think you think about age too much. I think you should just stop thinking about it."

She goes on: "Stop thinking, just live your life and don't be influenced by society trying to make you feel some type of way about your age or what it is you're supposed to be doing." I tell her that's hard to do, and she agrees.

"We are a marginalised group, women. And just because it's hard doesn't mean you stop fighting against it or defying it or refusing to be pigeonholed or put in a box or labelled or told you can and can't do things." I feel a little foolish for thinking she wants to talk to me about my own concern about ageing, like an older sister. She is an icon, not a shoulder to lean on.

In early May, she arrives at the New York Hilton Midtown to receive an award from Glaad, the non-profit that advocates LGBT acceptance in the media. A screen flashes an inspirational hashtag for those maturing with HIV, #AgePositively. Men in tuxedos, including one with a pin on his lapel reading "Shoot Loads Not Guns", chat over a stereo blasting Get Together, her club hit about love on the dance floor.

While she was becoming a "creamy smooth pop icon goddess", she says, she lost many friends to AIDS, including her ballet teacher from Michigan and the artist Keith Haring. She describes the disease destroying her locals-only scene in Lower Manhattan.

"I saw people starting to behave differently toward people who were HIV-positive or who had AIDS – not wanting to shake their hands or eat chips out of the same bowl or touch the same doorknob," she says. "It made me sad. It made me feel sick. It made me want to kick everybody's ass."

After her speech, Madonna makes her way to a modified red carpet, set up just for her in a private room. Her dedicated social media photographer documents everything, and her personal hair and make-up folks bow over her like art conservators touching up a priceless painting. Women from Entertainment Tonight and other TV shows circle, waiting their turn.

"I'm hanging out backstage at the Glaad Media Awards," one says, "with none other than the pop empress herself, Madonna. How are you feeling tonight?"

I hope she might say something provocative and sexy, as she used to, but she tells the truth: "I'm tired," she says.

"You have spent your whole career using your platform to not only uplift but help marginalised people, and now you are being honoured today, and it was amazing to see you in your moment. How are you feeling?"

Madonna reckons with the tortured grammar but isn't snippy. "You know when you have a good cry?" she says. "You feel good but also drained at the same time."

"We are all so excited for your album. What would you say is the inspiration?" She looks at the floor for a moment before raising her eyes to the camera. "To thine own self be true."

Edited version of a story first published in The New York Times Magazine. © 2019 The New York Times.

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