It is couture week in Paris. I am in a vast suite at the Plaza Athénée hotel, sitting in front of two of the finest sights the city has to offer. One is the Eiffel Tower. The other is Maye Musk, the 74-year-old model who has a jawline to make a 20-year-old jealous and who is proof positive that, with genes like hers, neither gray hair nor wrinkles need wither you.

“People are booking me for my wrinkles,” she says of her determinedly Botox-free state. “No one has asked me to change.”

As for the hair, it was only when she went gray and then cut it all off, in her late fifties, that her modeling career went stratospheric.

Musk is now a celebrity, but that doesn’t come close to the fame, if not notoriety, of the eldest of her three children, Elon Musk. More on the CEO of SpaceX and Tesla in a bit.

Musk – this Musk – is looking devastating, clad head to toe in Dior, courtesy of her gig as a Dior Beauty ambassador. “They treat me like a goddess,” she says, her accent South African with a transatlantic edge.

In recent years Musk has appeared on a number of high-profile magazine covers, most notably a faked-up take-off of Demi Moore’s naked pregnancy cover for New York magazine. The latest cover was her Sports Illustrated Swimsuit debut in May, an experience she describes, eyes twinkling, as “terrifying”.

“Who wants to do one of those when you are my age?” she deadpans. “I was never one of those swimsuit models whose bums go into their thighs.” When she was in Korea in June, autograph hunters held out copies of the cover for her to sign. “I think they sell them.” To men or women? “I don’t know.”

“People are booking me for my wrinkles.”

Last year she acted as wingwoman when Elon hosted a Mother’s Day edition of the American national institution that is Saturday Night Live. That wasn’t terrifying at all, she insists. “It didn’t bother me. All I had to do was read the cue cards.” Sample line: “I am excited for my Mother’s Day gift. I just hope it’s not dogecoin.” Elon’s reply: “It is!” (Dogecoin is, along with bitcoin, one of three cryptocurrencies her son owns.)

Then there’s the best-selling book A Woman Makes a Plan, a charming and surprisingly inspiring portmanteau of memoir and guidance with the subtitle Advice for a Lifetime of Adventure, Beauty and Success. It was published in 2019, has been translated into 30 languages and is particularly big in China, Russia and Turkey, apparently.

There is another book in the offing that will focus more on her childhood, when her father, “a great man”, would fly his family around in a single-prop canvas plane and summer holidays would be spent looking for “the lost city of the Kalahari”. Her father’s motto was “Live dangerously, carefully”, half of which could now be taken as her eldest son’s.

After Paris, Musk is returning to New York, which has recently become home and where she likes to walk her dog in “old clothes, a shabby coat, a hat and dark glasses”. For much of her life she has dressed “terribly”. She landed in the city after the exhaustingly peripatetic-sounding existence detailed in the book. “My place is not big,” she says. “I don’t need big. I don’t need wasted space because with it come responsibilities. I feel like I am settled in and I said to my kids, ‘This is the nicest place I have ever lived.’ ”

There have been quite a few places: Canada, South Africa, Canada again, then America, ping-ponging between one coast and the other. “It’s horrifying when you look back.” Then there were the ongoing money issues after the end of her marriage. When her luggage was lost after she and her three children emigrated to Canada, “I had to wear Elon’s and [her daughter] Tosca’s clothes, because I couldn’t afford to buy new clothes.” Her bags turned up five months later.

Her marriage sounds plain traumatizing. Errol Musk, who has been branded “evil” and a “terrible human” by Elon, is now married to and has two children with his stepdaughter from his second marriage in 1992. Musk herself describes him as “dreadful”.

“Every day he would scream at me and say, ‘You’re ugly. You’re stupid. You’re boring.’ I would think, I can’t be that ugly. I am modeling. But then he would beat me up, so you don’t argue back.

“It kept on getting worse. I had three kids in three years. But aren’t they the best three kids in the world?” Whom do they take after? “All my children are like me,” she says. “They have a really good sense of humor. And they work hard. He did work hard.” She doesn’t use her ex-husband’s name. “He was a good engineer. He really was a good engineer.”

For decades Musk’s day job was her nutritionist practice, the modeling a sideshow. “I am a geek,” she says. “I used to look like a geek. Now I am a geek in disguise. And no one cares that I am a geek. I wanted to make my book all about nutrition, but they made me leave it to the fifth chapter.”

So the world’s most famous geek, not to mention the richest, is a chip off the old block? Her nickname for Elon was Genius Boy. He “remembered everything he read. He was always absorbing information. We could ask him anything. This was before the Internet. I guess now we would call him the Internet.”

“Every day he would scream at me and say, ‘You’re ugly. You’re stupid. You’re boring.’ I would think, I can’t be that ugly. I am modeling.”

She knew she had a genius on her hands by the time he was three. “But you still don’t know if he’s going to do great things because many geniuses just end up in a basement being a genius, but not applying it.” In 1983, at the age of 12, Elon came up with a computer game. “I showed it to some university students. They were surprised that he knew all the coding shortcuts. These guys were in their second and third year in computer science and they were very impressed.”

It is Elon’s younger brother, Kimbal, a restaurateur and entrepreneur who is on the board of SpaceX and Tesla, whom she credits with ensuring Elon made it out of the basement. “In the beginning, Kimbal was with him in the first company [a web software enterprise called Zip2] and Kimbal could explain what a computer is, what’s a cursor, what’s a mouse and the background as to why the program is so great.” The sale of Zip2 put $22 million worth of wind in Elon’s sails.

These days, Elon can “mix with people who are also shy”, says Musk. “All his engineers are shy and nerdy.” When she visits him at Boca Chica, SpaceX’s Texas HQ, “I have to sleep in the garage. You can’t have a fancy house near a rocket site.” Is her son interested in possessions? “No, not at all in that sense.”

Maye Musk and Elon Musk arrive at the Met Gala 2022, celebrating the Costume Institute’s opening of “In America: An Anthology of Fashion.”

In her book she writes that “when the kids were young I always taught them to ask for what they wanted”. Elon’s success – and Kimbal’s and their younger sister Tosca’s (the founder of the streaming service Passionflix) – stems, Musk says, from her “letting them follow their own interests” and keeping her nose out unless asked. “When they wanted my advice, I gave it,” she says. “I am very short with my own answers.”

Elon might now be down to his last billion if he had always listened to his mother. “He should do whatever he wants,” she says. “I told him not to do an electric car as well as rockets and he didn’t listen to me.” As it is, he has, at the time of writing, another $270 billion to spare.

Musk doesn’t seem that fussed about traveling to Mars. “You have to have six months of preparation and isolation and that just doesn’t appeal to me,” she says. “But if my kids want me to do it, I will do it.”

She remains her son’s biggest cheerleader and peppers her social media accounts with #proudmom. The recent Wall Street Journal allegations that Elon had an affair with the wife of his old friend Sergey Brin, the co-founder of Google, had not broken when we met. But Musk readily took them on via Twitter, her son’s recently abandoned business proposition, when they did. “@WSJ It wasn’t alleged, you made it up. As always,” she tweeted. “Who is paying you to lie this time?”

What does she have to say about all those troublesome tweets of her son’s, in which phrases such as “paedo guy” get bandied around? “He has a quirky sense of humor and he doesn’t always understand that some people might not like it or don’t understand it.” So it’s a context thing? “Yeah. He might be joking, but sometimes you put it in a tweet and it doesn’t relay properly.” On occasion there is a certain disconnectedness, a kind of time delay, in Musk’s own humorous sallies, though in her case these come across as endearing rather than incendiary.

It may be Elon’s idiosyncratic romantic life that is in the spotlight at the moment – he has, among other things, been married three times, twice to the same woman – but his mother is typically frank about her own romantic failures. Friends call her “a jerk magnet”. After the end of her marriage at 31, “Men would ask me out and then they would turn mean.” She isn’t looking for a partner anymore. “People have said to me, ‘You will find love when you least expect it.’ I least expected it most of my life, but I’ve never found love. I’ve tried, but did not find a man who made my life better than I can myself.”

When I ask Musk what is the most surprising thing about her, she says, “I am not naturally lean. I am really careful with my eating habits and it’s worth it.”

After the end of her marriage she went up to 208lbs. “I loved eating fried, fatty, sweet foods, but I was eating them out of unhappiness and stress,” she says. “I had back problems, then I had knee problems, then I had high cholesterol. So I could take painkillers or cholesterol-lowering drugs and all the side effects that they have. Or I could get my weight under control.”

These days she is a US size 6. “That’s considered really big on the catwalks,” she says. “The girls are naturally lean. A size zero.” Isn’t that a problem? “That’s a model. You don’t have to be that way.” When I try again to get her to engage with what, to my mind, is one of the biggest issues in fashion today, the absence of almost anything other than ultra-thinness on the catwalks, she turns playful. “Yes, I think it’s a problem.” Pause. “Because I should be walking in all the shows!”

She is, she says, still “very below what I naturally am. I could be 200lbs if I let myself go.” Elon, who might be described as cuddly, if it weren’t for his spiky online presence, was accused of “eating badly” by his father last month. He might want to get his (nutritionist) mother on the case.

For most of Musk’s modeling life, she landed work of the “commercial” variety, which is looked down upon by snooty fashion types. At 28 she was already being cast as “mother of the bride”. At 41, when she moved to Toronto, “medications” were added to the client list. “Insulin, arthritis and diabetes, hypertension. Those paid a lot.” She was modeling for hypertension in her forties? “I was the oldest model in Canada.”

At 50, she was living in a rented studio flat in San Francisco. “We couldn’t afford to have a birthday party. Then one of the investors in Elon and Kimbal’s company said we could use her home. So the kids picked up not so fancy food and they gave me a little wooden house and a little wooden car and promised me that one day they would buy me the real thing.

She knew she had a genius on her hands by the time he was three.

“I said, ‘That’s so sweet,’ thinking it would never happen. Next thing you know, that is what they did.” That was after the sale of Zip2. “But it still took a long time not to live with the fear.” The fear? “There were hard times. Tosca and I were joking the other day about how we all lived in a one-bedroom apartment for a year. For a long time after I left my marriage, I had a pain in my gut. I was so terrified about not being able to feed my kids.”

What does it mean to have so much wealth in her family now? “It doesn’t change anything,” she says. “My kids are still kind and caring. I still appreciate being here. When I first came to Paris at 21, I had $5 a day. I stayed in a room with one lightbulb hanging down.” What with all the chandeliers, I count 40 lightbulbs in her suite’s sitting room alone. And she won’t be paying a bean.

When Musk first embraced what is now her signature barnet, “I remember the agent I was with at the time said, ‘We can’t send you out like that. Nobody will book you.’ ” Wrong! Suddenly she was a magazine cover star. At an age when many women are lamenting their supposed invisibility, she says she is “way, way more visible than I have ever been before”. One chapter in her book is entitled Silver is the new blonde.

Brand Maye Musk was in its infancy when I first met her years ago. I remember her as someone clearly on the outside looking in. And I remember her as delightful, excitable company. It would seem that both adjectives still apply today – far from the norm in the higher echelons of fashion, where ennui can set in rapidly. Musk can’t get over the fact that she now turns left on a plane. “From the age of 68 I started flying business class. Every time I feel thrilled that I am flying business class.”

To my surprise, she also recalls our first encounter. “I knew no one,” she says. Now she is a star, I say. “I know. I am a supermodel. It’s ridiculous.” So is she like Linda Evangelista, not getting out of bed for less than…? “Well, with inflation, you’ve got to go for it.”

There’s some chat about a new, hyped restaurant she was taken to the night before. “What! You haven’t been to Gigi?” she exclaims in faux horror. “Do you know what? You are not as special as me.”

Her life has transformed since we last met, I say. Mine, not so much. I am jealous. “Good,” she laughs. “I make you jealous. That’s important.” Pause. “Jealous of a 74-year-old?” More laughter. “Shame on you.”

Anna Murphy is the fashion director for The Times of London and the author of How to Not Wear Black