Siri Hustvedt is laughing. “I feel so much urgency,” she says, her long legs folded beneath her on an armchair. We are on the ground floor of the Brooklyn brownstone she shares with her husband, Paul Auster. The room is decorated with paintings of typewriters. There is a vase of fresh flowers. Hustvedt, who has just published her seventh novel, Memories of the Future, is figuring out which of her many projects to tackle next. “I want to write another novel, but I also want to write this philosophical book, and I have many, many essays now that I should put together in another collection.” A day earlier she’d given a eulogy for an old friend, the American magician Ricky Jay. “I was talking to two people I know, both at least as old as I am, and I was asking what they were doing, and they were both saying, ‘Well, we’re not doing that much at the moment,’ and I just said, ‘You know, I’m working for my life.’” She drops her voice to a whisper: “I’m a little nuts, I am working like a maniac to get it in before I die.”

Her days start early, at 5.30am with some meditation; she is at her desk by 7am. “Morning brain is the best brain,” she says cheerfully. “I can feel my sharpness declining after six or seven hours.” Hustvedt spends the afternoons reading, mostly academic papers that form the basis of her many lectures on neurology and psychology. She and Auster have been married for 38 years, and still read aloud to each other. They are great lovers of fairytales, as is their 31-year-old daughter, Sophie, a singer of slinky, soulful pop songs. There are other writer couples, of course, but few that have stayed together so long.

“I remember we bought this house many years ago,” Hustvedt says, wistfully. “We walked in the door and Paul looked at me, and he said, ‘Not bad for a couple of poets’.” Like a fantasy of the novelist’s life made flesh, one pictures the couple working away on their manuscripts, and then coming together for dinner, before settling in to watch a movie. “We have one of those DVD things,” Hustvedt says. “We are partial to movies from the 1930s. There’s an energy to those films, and also the roles for women are infinitely better.” As a history student at St Olaf College in Northfield, Minnesota, she saw Katharine Hepburn and Cary Grant in George Cukor’s Holiday, and remembers being blown away. “I was Katharine Hepburn for an hour and a half,” she said. “She was the outsider in that film.”

Without my strangeness, I might not have become a writer

As an actor, Hepburn was often accused of being austere and haughty, in some ineffable way not “feminine” enough. “I never realised until lately that women were supposed to be the inferior sex,” she once quipped. Hustvedt has often found herself pushing back against the same prejudice, a result she thinks of the way arts are seen as inherently feminine, soft, imaginary, and unserious. “A male novelist hardens and dignifies the form, while a female novelist is doubly penalised as a woman working in an unserious form,” she says. The distinction, she thinks, may explain why male writers have an equal number of men and women readers, while female writers are read primarily by women. Hustvedt’s 2014 novel, The Blazing World, longlisted for the Man Booker prize, was a kind of revenge fantasy in which she imagined a marginalised female sculptor, Harriet “Harry” Burden, playing an elaborate trick on the art world by persuading three male contemporaries to present her work under their names to show how gender, not talent, was the industry’s yardstick.

At the memorial service for Ricky Jay, Hustvedt had addressed the challenges of her own life as an intellectual woman in a misogynistic society. “I gave a rather forceful speech, saying that, as a woman, and worse as an intellectual woman, and even worse as an intellectual woman writer married to a man writer of some note, I have negotiated social spaces with an earned cynicism from facing lordly condescension, instant dismissal, and long lectures on subjects that I have been studying for years.” The point of the speech was to emphasise a singular quality of her late friend. “He knew all about prejudgment, and people seeing what they expect to see, because that’s what magic is about,” says Hustvedt. “And I ended up saying that because he knew all about this, he was free of it.”

As Hustvedt recalls her eulogy she meanders frequently down other paths – how Dickens would visit the Paris morgue whenever he was in the city, as well as her interest in hunger artists (“especially girls who starve themselves in different ways”) and with Christian mysticism. She also urged me to find a video on YouTube in which a man dressed as a gorilla walks across a basketball court, turns to the audience, waves his hands, and then walks off. She tells me that: “75 to 80% of the people do not see the gorilla.” The official term for this phenomenon is “inattentional blindness.” A good magician uses inattentional blindness to his advantage. The gorilla is staring at us, but we are so focused on something routine and commonplace – the shuffling of cards, say – that we miss it.

Hustvedt was 13 when she got the writing bug. Her father, a professor of Norwegian, had taken his wife and four daughters with him to Reykjavík, where he was studying the Icelandic sagas. They would drive around squashed into a Volkswagen Beetle, while their father would gesture to random spots, and shout things like, “And this is where Snorri died,” before heading to the next landmark. “It was perpetually light because it was the summer, and I couldn’t sleep, for the first time in my life,” Hustvedt recalls. “My circadian rhythms were completely screwed, so I just stayed up and read.” She was graduating from children’s books to what she calls “little print”, and immersed herself in the classics. She read an abridged version of The Count of Monte Cristo and barely stirred through its 800-odd pages. But one book, in particular, stood out. “I was so moved by David Copperfield, the horrible stuff about Mr Murdstone, and Peggotty, and Aunt Betsey, and the blacking factory, the horrors of all of it. I remember walking to the window, looking out at the creepy, little city of Reykjavík and thinking, ‘If this is what books are, this is what I’m going to do.’” She began writing that year. The fact that Copperfield is memoir dressed up as fiction was evidently not lost on her.

Memories of the Future is a Pandora’s box of ideas within ideas, but principal among them is the question of whether we should take a memoir at its word. We get a warning early in the novel: “If you are one of those readers who relishes memoirs filled with impossibly specific memories, I have this to say: those authors who claim perfect recall of their hash browns decades later are not to be trusted.” Readers of Karl Ove Knausgaard’s six volumes of memoir, My Life, with their endless descriptions of routine chores, may take note. “Many successful memoirs have dialogues that goes on for page after page after page, dialogue that nobody could possibly remember, unless you are a savant of some kind,” Hustvedt says. “And that’s extremely rare, so what are we talking about? You can’t possibly believe the memoir writers have that kind of memory.”

‘Not bad for a couple of poets’: Siri Hustvedt with her husband Paul Auster, a novelist, and daughter Sophie Auster. Photograph: Shawn Ehlers/WireImage

While memoir is too conventional to interest Hustvedt, memories do make their way into her novel in which a protagonist by the initials of SH shares much, but not all, of the writer’s biography. Like SH, Hustvedt really did see the great poet John Ashbery reading in Greenwich Village at the Ear Inn; a tin of Campbell’s soup really did roll under the seats of the auditorium during a lecture on Shelley and Rousseau by the since-discredited and now long-dead academic Paul de Man.

On the other hand, Hustvedt did not live next to a witches’ coven. And although she was near-broke and hungry for a period, she was never reduced, as SH is, to lifting a cheese sandwich from a rubbish bin. “The poverty stuff is not exaggerated,” says Hustvedt. “I didn’t have enough money to get by, and I think about this with a kind of amazement now, but, like SH, I was too proud to ask.” She recalls being so pale with hunger that a professor eventually urged her to visit the university office and ask for an emergency loan. “It saved my life,” she says. “I got $200, and they didn’t ask me to pay it back.”

Hustvedt’s novel evokes a New York that has vanished, a city that feels both smaller and shabbier, yet also richer, with an intellectual life that no longer feels plausible in the suburbanised city of today, in which public spaces have eroded and people gather in cafés not to debate ideas, but to plug in. But the city has become safer. A pivotal scene in Memories of the Future culminates in an attempted rape. Nothing quite so terrible happened to Hustvedt, although she bore her share of horrors. “I was never mugged, but I was molested on the subway, someone grabbed my genitals,” she replies matter-of-factly. “I actually did get my elbow into his side before he left the train, and he cried out, which was extremely gratifying.” She also recalls being handed a whistle at Columbia University library after reports of a flasher lurking among the shelves, a precaution she finds hysterical today.

Sometimes Hustvedt wonders if her compulsion to write is neurological. She thinks a lot about the Danish philosopher and poet Søren Kierkegaard, who may have had temporal lobe epilepsy. “This man wrote 7,000 pages in a journal, and that’s not including his many books, and he died in his 40s,” she says. “Without my strangenesses, I might not have become a writer, so as with many afflictions sometimes there are reasons to celebrate.” By “strangenesses” Hustvedt is referring to a history of crippling migraines, one of which lasted a year, and that started during her honeymoon. “I had a seizure that threw me against the wall, my arm went up in the air, and then I had auras, uncanny clarity of vision and then the crash and the pain,” she says. “I still have them, but not nearly so often, and I control them with deep meditation.” In 2009, she published a well-received book, The Shaking Woman, about another neurological condition that she first experienced in 2007 when she found herself shaking uncontrollably as she gave a eulogy for her father. The shaking recurred on subsequent public engagements, and she now takes Propranolol, a beta blocker that seems to keep things in check. “I’m usually most interested in myself as somehow an object of study,” she says wryly. “Generally, it takes the form of seeing myself as ridiculous. And that is very helpful, on the road of life, to put things in a certain perspective.”

Hustvedt lives so deeply in the world of ideas that it can be hard to keep pace with her thoughts, but there is no pretension in what she says, because none of it is said for effect. She has spent her life carving out a career as a writer of intellect in a field where that distinction is still largely claimed for men. Reversing that double standard is a kind of mission. “Over the years, I have found myself deeply amused by enthusiastic responses to high-flown allusions, intellectual references, and complex forms in books by man novelists as signs of their cleverness and genius and the denigration or ignoring of the same play in works by women,” she says. In an email sent after we parted, she reminds me of a line in Memories of the Future, in which one character advises another: “Remember this: the world loves powerful men and hates powerful women. I know. Believe me, I know. The world will punish you, but you must hold fast.”

Behind the facade of a townhouse that sits just south of Brooklyn’s Prospect Park, Hustvedt is holding fast.

Memories of the Future by Siri Hustvedt is published by Hodder & Stoughton at £18.99 on 19 March. Buy it for £16.71 at guardianbookshop.com