It’s noon at Carmen Herrera’s home in downtown Manhattan. Time for a drink. “Would you like a cup of tea, or a scotch?” she asks. Scotch, please. She smiles. It’s the answer she was looking for. We rummage among the boxes – bottle after bottle of the finest single malts – before settling on the super-peaty Lagavulin. We clink glasses.

At 101 years old, Herrera is in her artistic prime. She has been a working artist for the best part of a century, but it wasn’t until 2004, at the age of 89, that she sold her first painting. For the past four months, there has been a gorgeous exhibition of her work at New York’s Whitney gallery, soon to transfer to the Wexner Center in Ohio. The Cuban-born artist has belatedly been recognised and her pieces are selling for hundreds of thousands of dollars. Good job, too, she says. It’s not cheap getting old.

Carmen Herrera at work in Havana in 1941. Photograph: Jesse Loewenthal, courtesy of Carmen Herrera

Herrera has a lovely, raspy voice, and segues between English and Spanish when the mood takes her. Her friend Tony Bechara, also an artist, is here to translate. Her help, Maria, lays on the biscuits and pours the whisky. But there is no mistaking who is boss here.

Herrera was born in Havana in 1915, to journalist parents. Her father was the founding editor of the newspaper El Mundo, her mother a reporter and columnist. Herrera, one of seven siblings, says she grew up surrounded by journalism. Were her parents political? “Oh yes! Which I think is terrible. They were always against the current government.” Many of her relatives were imprisoned for anti-government activity.

The Cuba of her childhood was governed by Gerardo Machado, a former army leader who was elected to the presidency in 1924 and went on to become a despised dictator. “It was a very cruel time,” Herrera says. She left Havana to go to finishing school in Paris and returned to study architecture at university. But, she says, the political climate was not conducive to a good education. “There were always revolutions going on, and fighting in the streets. The university was closed most of the time, so it affected my studies.”

Carmen Herrera in 1948. Photograph: Victor Laredo, courtesy of Carmen Herrera

Was it unusual for a woman to study architecture in the 30s? “We were breaking down that business of staying home for women. We were breaking through.” So, despite the dictatorship, Cuba was enlightened when it came to gender? “Oh yes! Machismo was not such an issue there.”

Bechara cannot believe what he is hearing. “Oh come on, Carmen! Machismo was not an issue in Cuba?”

“No! The men I knew were not like that.” Herrera regards Bechara as a son, though they bicker like a long-married couple.

Her degree in architecture was disrupted by the two most important discoveries of her life: love and art. In the late 30s, she met Jesse Loewenthal, an English teacher visiting from America, and in 1939 they married. She abandoned her studies and moved to New York. Did she leave Cuba for politics or love? “I’m not telling you,” she cackles. By the time she reached America, she had realised that she had a calling; she was destined to be an artist. Herrera says this as if it is a curse. Why? “Because I knew it was going to be a hard life.” She smiles and sips her scotch.

The trailer for the 100 Years Show, a documentary about Carmen Herrera the100YearsShow.com

Perhaps her most formative years were spent in postwar Paris, between 1948 and 1953. Here, Jesse, an urbane multilinguist, taught English, and she refined her style. She limited herself to two or three colours, painting interlocking abstractions where ovals met rectangles and triangles and semicircles, often set within a circular whole. Her art seemed architectural from the start, influenced by painters such as Kazimir Malevich and the early Russian suprematists whose work she saw in Paris at the Salon des Réalités Nouvelles. Herrera herself exhibited at the salon, though she never came close to selling a piece.

France was more progressive than 1940s America. In Paris, she and Jesse lived on the Left Bank in Montparnasse, and befriended many artists and writers. Herrera was close to the scandal-loving writer Jean Genet. “He was a good friend, a good person, a sweet gentleman.” She pauses. “But he could be very unsweet, too. A bitch. There was an American woman who came over to him in a cafe and said she admired him so much and felt such a connection with him, and he replied, ‘Madame, if you are so much like me, then you must be a pederast yourself.’ She didn’t even know what that meant.” Herrera bursts out laughing. “He was actually a sweet person. I had a pearl necklace and the pearls all fell on the floor. He was there until he had picked up the last one.”

Carmen Herrera with her husband, Jesse Loewenthal, in Paris in the late 40s. Photograph: Courtesy of Carmen Herrera

Herrera used to see Jean-Paul Sartre and Simone de Beauvoir all the time at the Café de Flore. And she became friends with the parents of artist Yves Klein, both painters themselves. “They shared a studio, and they had an easel and one would paint on one side and the other would paint on the other side. His mother, Marie Raymond, was better than he was, and did better than him. They always used to talk about ‘Bébé’. We thought it was a little child until we met him. Yves was the only child. They said we have to go home to feed Bébé, and Bébé turns out to be a martial arts expert and painter in his 20s.”

Did she know Samuel Beckett? No, she says, but she did see the first production of Waiting For Godot. “That was terrific. When the audience came out, they were incensed: ‘This is terrible. I don’t understand anything.’ It was really funny. People were fighting with each other.” What did she think? “Good for him. Yes, I liked it.”

Herrera returned to New York in the mid-50s and her work gradually became more minimalist: the voluptuous curves flattened into sharp lines that taper off to nothingness or stretch to infinity. She calls it a process of purification, trying to make her art ever more simple. “I never met a straight line I did not like,” she once said.

What is their appeal? “I like the form of things,” she says simply.

“The clarity of it,” Bechara says. “You often speak about the clarity of the straight line.”

Herrera gives him a look. “It’s my vision, not yours,” she says.

“I know, I’m just helping out,” he says.

“Sorry, Tony. Sorry.”

Iberic, 1949. Photograph: Ken Adlard/Courtesy of the artist and Lisson Gallery © Carmen Herrera

It was hard enough back in the mid-20th century for any female artist to succeed, but particularly one whose work was so defiantly unfeminine. “You were supposed to do maternity scenes or watercolours, but not something as tough and decisive as what you do,” Bechara says.

Herrera was not to be deterred. She continued to paint, and the world continued to ignore her. She recalls visiting one avant garde gallery to discuss her work and as she left, the owner, Rose Fried, called her back. “She said, ‘You know, Carmen, you can paint rings around the men artists I have, but I’m not going to give you a show because you’re a woman.’ I felt as if someone had slapped me on the face. I felt for the first time what discrimination was. It’s a terrible thing. I just walked out.”

Fried said she had to give the men shows because they had families to maintain. “It was a lame excuse,” Herrera says. She and Jesse did not have children. Had they ever wanted a family? “That is my business, not yours,” she says curtly.

Green and Orange, 1958. Photograph: Collection of Paul and Trudy Cejas © Carmen Herrera

Why does she think art was virtually a closed shop for women back then? “Because everything was controlled by men, not just art.” She says well-known female artists were resented. “I knew Ad Reinhardt and he was terribly obsessed with Georgia O’Keeffe and her success. He hated her. Hated her! Georgia was strong, and her paintings were exhibited everywhere, and he was jealous.”

On her desk is a framed photograph of Jesse: he’s a handsome man, formally dressed, with a resemblance to the poet TS Eliot. Herrera calls him a saint. “He was very patient and very supportive, and he would encourage me, and if he didn’t like something, he would keep his mouth shut rather than be too critical.” Jesse died in 2000, aged 98, little more than a year after Herrera’s first solo exhibition in America (sure enough, she still didn’t manage to sell a sausage).

Male artists such as Ellsworth Kelly and Barnett Newman (a neighbour and friend, with whom she used to breakfast every Sunday) were ploughing a similar furrow and being rewarded for it, but success continued to elude her. It seemed that geometric abstractions were just dandy, so long as you weren’t a woman.

She can see now that the men fared better not simply because they were men, but also because they were more streetwise. “They were better than me at knowing how to play the system, what to do and when. They figured out the gallery system, the collector system, the museum system, and I wasn’t that kind of personality.”

***

Herrera has lived in the same apartment for 49 years. In the 60s and 70s, New York’s artists would hang out at the nearby restaurant and nightclub Max’s Kansas City; Warhol’s Factory was down the road. The area was glamorous, in a bohemian, beaten-up kind of way. She and Jesse got by on his wage.

At the end of the living room is a long desk facing the street. This is Herrera’s workspace, covered with industrial-sized metal rules, pencils, piles of paper, scissors and colour charts. Pots of orchids sit on the windowsill. Every day she goes to the desk and works. She sketches in miniature, hangs the drawing on the wall (there are a few at any one time), stares at it for a few weeks, reworks it and, if she likes it, develops it into a larger piece.

Estructura Roja, 1966/2012. Photograph: Courtesy of the artist and Lisson Gallery

Not surprisingly, she cannot work on her own these days. For one thing, she is arthritic and wheelchair-bound. So when she is ready to develop a piece, she calls her assistant, Manuel Belduma, who buys the canvasses and places them horizontally on an old architectural drafting table that rotates, enabling Herrera to work on it bit by bit. She tells Belduma where to place the sticky tape that sections off areas of the painting, and then they paint the piece between them.

“Manuel is unsophisticated about art, and doesn’t want to be an artist,” Herrera says. “He does exactly what I tell him, and he does it well. I wouldn’t work with somebody who wanted to be an artist. He would go straight out of the window.”

She has only one complaint about Belduma. “He is very religious.” I look around the room in disbelief as she says this: there is Catholic iconography everywhere. But you’re a Christian, too, I say. “Yes,” she says. “But he is too religious. He doesn’t work on Sunday.”

I ask if her art has ever been figurative. Rarely, she says. “In Cuba, I did sculpture which was figurative.” That makes sense, I say, because even now there is something three-dimensional about her paintings: some look as if they could be turned into buildings. She and Bechara glance at each other, a look that verges on the conspiratorial. “That is something she is working on,” he says.

“You see,” she says to me, “you know everything!”

Herrera has a grumpy exterior, but when she softens she verges on the coquettish. At 101, there is still something girlish and playful about her. She dresses stylishly (the shirt she is wearing today could be based on one of her three-colour abstractions), has a white bob and the longest fingers I have ever seen.

Men were better at playing the system. They figured out gallery, collector, museum. I wasn't that kind of personality

In her Whitney show, there are a few sculpted pieces: two slightly off-kilter Ls that fit together to make a skewed rectangle. The deliberate imperfection humanises the work; it could be a couple cuddling or making love. For such precise, arithmetic art, it is surprisingly sensual. Lines come at each other from all directions, narrowing like arrows, touching, or almost touching. The perfect kiss, or the kiss denied.

Does she see emotion in her paintings? “Yes,” she says. Are they images of love? “Yes.”

Herrera talks about the carpenter she used to work with, who helped realise her sculptures – a lovely man, she says, but in the end he let her down. How? “He died. People really shouldn’t die like that! Very inconsiderate.”

She says this with a straight face. Did she always have a good sense of humour? Her face lights up. “That is nice of you. Thank you. I’m not laughing about Cuba, though.”

After she moved to America, members of her family continued to trouble the authorities. By now, though, they were dealing with Fidel Castro rather than Machado. “My brother had a way of getting to jail all the time, and I was running all over trying to get him out. He was put in jail for anti-government activities by Castro in 1960 and sentenced to 20 years.” She spent a great deal of time back in Cuba in the early 60s trying to help him. “Whenever I arrived back there, they’d say, ‘Ah, you’ve come about your brother.’” Is this why she hates politics? “Yes, to me it is something horrible that happens.”

Is there anything in her art that is for ever Cuban? “Maybe through colour there is an expression of nationality.” Despite her fondness for black backgrounds, it is the bright, life-affirming yellows, oranges, greens and reds that dominate her paintings. I ask whether she feels more Cuban, French or American. “I’m an American now.”

Equation, 1958. Photograph: Collection of Stanley Stairs and Leslie Powell © Carmen Herrera, courtesy Ikon Gallery

“But you’ve just had a Cuban lunch,” Bechara says.

She giggles. “I know. Hehehehe! Rice and black beans.” She looks at Bechara tenderly. “He is a terrible friend, you know.”

It was Bechara who kickstarted Herrera’s career when she was in her late 80s. He found her a dealer in 2004; the market and museums came running, and she never looked back.

We are looking at a book of her work. Some of her earlier, curvier pictures remind me of Matisse’s cut-outs. She creates them in a similar way: cutting out shapes and placing them at different angles. She smiles when I mention the French postimpressionist. Herrera is a voracious reader and, as it happens, is just reading a book about Matisse and Picasso. “I don’t like Picasso,” she says. “He is dangerous. Matisse is a nice person. I saw Picasso many times, but never made friends with him. I was near Notre Dame one day, looking along the Pont Neuf, and I saw a tourist painting Notre Dame and as he paints, he is explaining to this gentleman what he is doing and the gentleman just keeps nodding and looking. The gentleman was Picasso.”

That’s a sweet story, I say. She looks horrified. No, she says, there is nothing sweet about it. “It was Picasso stealing, as he always does, from everybody. I will never allow in my lifetime a book with Picasso’s paintings in my house, because they are bewitched. When people look at his paintings, they start painting like him. I like Matisse better as person, personality, art, everything.”

The first press coverage of Herrera’s work appeared in 1998 – a short review of a small exhibition in a gallery in East Harlem dedicated to Latin American art. The paintings on display were atypical of Herrera’s work: two dozen black-and-white pieces, described by the New York Times art critic Holland Cotter as “an abstract art of quietly jazzy linear patterns”. In 2004, the year she sold her first painting, Cotter wrote about her again in the New York Times, this time in a tiny review of a Latin American three-woman show, alongside Colombian Fanny Sanin and Mira Schendel, who lived in Brazil. “The senior artist, who is also the least well known, is Carmen Herrera,” Cutter wrote. In 2009, Herrera was given her first solo show in Europe, at Birmingham’s Ikon Gallery. Observer art critic Laura Cumming wrote: “Carmen Herrera is the discovery of the year – of the decade... How can we have missed these brilliant compositions?”

Carmen Herrera: ‘I am not a teacher. An example, yes; teacher, no.’ Photograph: Chris Buck for the Guardian

Your story is such an inspiration, I say. It teaches us all to not give up; to have faith in ourselves. She shakes her head. “No,” she says. “I am not a teacher. An example, yes; teacher, no.”

What is the best and worst thing abut getting old? “There is nothing good about getting old. It is a disaster that cannot be avoided.”

“People say age gives you wisdom,” Bechara cajoles.

“Pah,” she replies. “Who said that?”

In her particular case, age has given her power. If she had not lived so long, she would have been unable to enjoy her success. Do people treat her differently these days? Do they say, I always believed in you and knew you would be a star? She smiles. “With real friends, I cannot tell the difference. They are the same as they were 20 years ago. The only difference is that there are not as many of them. I’m outliving them. Would you like some more scotch?”

Just a wee dram. We clink glasses again, and talk about the artists she likes. She mentions the 20th-century British painter Ben Nicholson and the Baroque Spanish artist Francisco de Zubarán, famous for his religious paintings.

It is time for her to rest. As I leave, I ask who is her all-time favourite artist. She thinks long and hard. “Carmen Herrera,” she eventually says. She tilts her head back and rocks with laughter. “Yes, Carmen Herrera is my favourite.”