Fry is an eminent professor — we meet after a busy day of lecturing at University College London (UCL). Having studied mathematics and theoretical physics at UCL, she completed a PhD in fluid dynamics in 2011 — four years of wrestling with the equations that describe the way fluids move, from drops of honey to the formation of galaxies. She is now a professor in the mathematics of cities at UCL’s Bartlett Centre for Advanced Spatial Analysis. She has written four books, and was awarded both the Christopher Zeeman medal and the Royal Society David Attenborough award for her work in engaging the UK public with mathematics. Oh, and this year that “nubile young woman” — now 40 — was appointed president of the Institute of Mathematics and its Applications.

She’s also all over the TV, and if you’re one of the half a million followers of her @frysquared account (“All math and no trouser”) all over Instagram, where she crunches complex ideas — or just revisits fun moments in scientific history — and explains them with a conspirational wink. There’s The Sky at Night, The Joy of Data and Stargazing Live on the BBC; The Maths of Life on 6 Music; and the podcasts Uncharted and Curious Cases. She has just appeared in a mudbath alongside Fearne Cotton in a (presumably lucrative) ad campaign for Samsung, and made films for Bloomberg (sponsored by Nokia). One of her latest “collabs” is presenting the Google DeepMind podcast with Demis Hassabis and John Jumper — who only went and won a Nobel prize earlier this month.

Respected by her peers and a role model for aspiring brainboxes — including my own ten-year-old daughter — her graduation from dusty lecture theatre to the mainstream has been confirmed with recent slots hosting Have I Got News for You and running the numbers in the Peter Snow/Jeremy Vine role for Channel 4’s live election night coverage in July. “I’m a proper politics nerd,” Fry says. “I listen to so many political podcasts, it’s the background music to my life. It’s like a soap opera. I mainly did it because I want to be best friends with Emily Maitlis. I did not achieve my goal, though, as she was at her desk for 24 hours. Damn it.”

She has also since 2021 recovered from cervical cancer and masterminded what she calls a “grade A” divorce. So she’s really not bothered about how people — “guys going crazy on Twitter” included — perceive her. “It’s changed as I’ve got older,” she says. “There was definitely a time when I was, like, I’m not showing any flesh at all. I was really careful, but as time has gone on I just don’t give a shit any more.

“In everything I do, it’s always about what I’m saying or doing that’s interesting, it’s never about how I appear,” she continues. Nevertheless she was nervous about the photoshoot for this interview. “It’s really emotionally exposing. You strip all that intellectual armour away and it’s just what you look like. I find that very stressful. You can’t look clever in photos, can you?”

Growing up in Hoddesdon, Hertfordshire, she was the middle child of three sisters. Her English father worked in a hydraulics factory and her Irish mother stayed at home. Fry describes it as a strict household. “My mum is the most Catholic person I’ve ever met — including any priests,” she jokes.

“My parents have an unhealthy respect for authority — very meek,” she says. “I never acted out in my teens, I didn’t have the opportunity. I really think my mum thought that if she gave me any rope at all I would immediately be a pregnant drug dealer. I think the only men I knew until I was 18 were my dad and the priest. I always thought, I’ll never subject my daughters to that.”

As a result of her upbringing she was a “goody two-shoes” and spent a lot of her free time studying. She even took extra modules in her further maths A-level at the local state school, Presdales, just for the fun of it — gaining straight As, of course (“I told you, prefect energy”). She always enjoyed the challenge of the world of numbers. “I’ve got this friend Matt Parker [an Australian mathematician and author] and he says that mathematicians don’t find maths easy, they just enjoy how hard it is. I really think that’s it. It takes this toxic stubbornness. That’s a driving force with most things that I do.”

• Maths is the new ‘cool’ subject. Here’s how schools got so good at it

Until 2014 Fry assumed she would spend her entire working life in academia. Then she gave a TED talk on “the mathematics of love”, which went viral and has nearly six million views. “I was really scared of the world then,” Fry says. “I can’t tell you how hard I tried. It was slightly traumatic.”

Soon after came motherhood. She has two daughters, aged seven and five, with whom she is more relaxed than her parents were with her. “With kids of course you don’t want them to put themselves in danger, but you can end up making them anxious about everything, so I try to stand back and let them make their own mistakes.”

This laid-back attitude chimes with Fry’s admission in an interview for this magazine’s Life in the Day column last year that she can be a slightly messy mum who often eats Haribo for lunch. “By the way, I’m quite bad at remembering to feed my children. They never starve, but it can get to 2.30 and one of them will be grumpy and I’ll be, like, ‘What is wrong with — oh shit, I haven’t fed you.’ ”

Home life for Fry is a “two-household family” in south London with her ex-husband, Phil, a sports writer from whom she split in 2022 after a nine-year marriage. It all sounds terribly civilised: he lives three doors down and they share parental responsibility. “There have been very few hiccups, but if such a thing is possible we’ve basically had a grade A, gold-star divorce,” she says, ever the high-achieving swot. “I have a new partner, Oli, who I met last year and they’ve met and are on very good terms. The reason why we broke up — there was no nastiness or great drama — was just that we weren’t suited. So you can separate from somebody while respecting them.”

Fry met Oli on Hinge, soon after being banned from the dating app for supposedly impersonating herself. “I set up a whole new profile on a different mobile number to get around the ban,” she says. “I think there’s something quite amusing about the fact that I didn’t commit identity fraud on their platform until they accused me of it.”

True to type, she has a scientific explanation for the success that soon followed: “I strongly suspect that relaunching as a ‘new person’ with a brand new sparkly profile did make a difference to the algorithm, which still puts you in “buckets” with people who are a similar level of attractiveness to you. Those buckets are really difficult to escape, even when you add better pictures and wittier prompts. Put it this way — I wasn’t getting to see men as good as Oli before being banned, and I met him almost immediately afterwards. I mean, correlation isn’t causation, except sometimes it is!”

The initial split from Phil came after a shock: her diagnosis, then recovery, from cervical cancer at the age of 36. That’s a lot of personal turmoil to endure in a short space of time, I suggest, stating the obvious. “Yes, but they’re not unconnected, are they?” she says. “You wake up from that first one and you’re, like, ‘OK, I’m going to firebomb my life.’ ”

In early 2021, after a routine smear test, Fry was diagnosed with cervical cancer and underwent a radical hysterectomy, in which the uterus, cervix, both ovaries, the fallopian tubes and nearby tissue are removed. She documented her experience in a film for the BBC, Making Sense of Cancer with Hannah Fry. In the intimate footage we see her in tears as she receives her test results — and ultimately the all-clear — and watch her navigating family life during the pandemic with her two young daughters.

• Hannah Fry on her cervical cancer, divorce and Haribo for lunch

As part of her hysterectomy Fry had a number of lymph nodes removed as a precaution in case they too were cancerous. This resulted in her developing lymphoedema — a chronic condition that causes swelling of the limbs. For Fry, managing that involved further surgery and Pilates, which she has to do weekly to keep the symptoms at bay.

Applying her understanding of risk and probability, she questions in the film whether the risk-averse route taken was worth it. Even after she was given the all-clear in 2021, she was told there was a 10 per cent chance of her cancer coming back, and if it did it would be incurable.

In the film she questions our treat-at-all-costs approach to diseases such as cancer. “I never wanted to tell people if they should or shouldn’t have treatment,” she says. “But I do think that when it comes to uncertainty and risk, only you can make the decision about what matters to you. I don’t think the way we’re doing it at the moment prioritises that.”

Last year she had a scare when she went for a scan and they found a lump. “It turned out to be OK but it looked for a moment … I had got into this habit of not really thinking about it, so that was a really sharp shock.”

After her initial diagnosis in 2017 she had spoken to one of her Irish cousins, who told her, “One day I hope you’ll see the gift in it.” “I was, like, ‘OK, thanks,’ ” Fry says, deadpan. “It was really annoying.”

As time has gone on, though, Fry says she has started to see what her cousin meant. “I read about women in their fifties and sixties who finally get the confidence to not give a shit any more and I think it accelerated that process for me. To have that in your late thirties and to be healthy is an extraordinary gift. But you do slip back into the old pattern of forgetting that life is finite. The scare [earlier this year] jolted me in a positive way.” I wonder if some of that came into play when she talked herself into doing this shoot. “Absolutely,” she says. “Put me in a bin bag!”

The study of Stem subjects — science, technology, engineering and mathematics — is still a male-dominated field. The percentage of female graduates with core Stem degrees is just 26 per cent, but Fry is seeing more female students in her lectures and believes that universities are trying hard to change things.

Her biggest run-ins with sexism have been in television, however. When I ask for an example, she lowers her voice and leans in to emphasise the point. “In terms of outright despicableness … Do you want me to tell you a story?” I do.

She was preparing to host a new TV programme and turned up the day before to meet the director, the co-host and the cameraman, and was confronted with a “massive wall of men”. She was having a tour of the studio when she told the director that she and the co-host had grown up near each other. At this point the co-host made a move towards Fry. “He grabs my arm, turns me around and when I’m facing the other way he’s, like, ‘Oh, now I recognise her’ [clearly insinuating that he had previously had sex with her — of course they hadn’t]. In front of everyone. And literally no one said anything.”

Fry was fuming. She didn’t sleep that night and planned to go to work the next day and say something “because that’s normally what I’d do. But TV is so stressful that I let it go. If that happened now I would expect that the guys would say, ‘That’s not OK.’ ”

Fry may be one of the UK’s coolest nerds, but she is not alone in what’s becoming a burgeoning industry. Indeed, this could well be the Age of the Nerd, where brainy quiz shows such as Only Connect pull in millions of viewers and the podcast The Rest Is History sells out world tours.

The day Fry and I meet, two her of her podcast buddies — the British computer scientist Demis Hassabis, a chess prodigy who co-founded the AI company Google DeepMind, and his American colleague John Jumper — have been awarded the Nobel prize in chemistry for their “revolutionary” work applying artificial intelligence to understanding proteins, the building blocks of life.

Does she lie awake at night worrying about AI and what could happen with it in the hands of people perhaps less altruistic than Hassabis and Jumper?Is there a difference between the tech bros and the proper scientists?

“Yes, definitely,” Fry says. “I wanted to work with [Hassabis and Jumper] because they are scientists to their core. There is a reason why they wanted to be in London instead of Silicon Valley. They publish in peer-reviewed journals, they release their findings for free to genuinely advance science. I’m not saying they will be perfectly successful in shielding that from people who just want to make some money or want to actively do harm, but I do think they are at least treading carefully.”

Although academic research has taken a bit of a back seat in the past couple of years, Fry says she will always be “an active professional mathematician. To be honest, I’ve spent too much on nice fountain pens and fancy dotted notebooks over the years to ever give it up.”

Now she just needs her daughter to get the memo. Lately the woman who has switched much of the country on to the power and beauty of numbers has been struggling to inspire her seven-year-old to do her maths homework.

“I have none of my existing weapons with her,” she says. “I have so many cool things to tell her but she says, ‘No.’ ” I sense that Fry will find a way. And if not, there’s always her younger daughter? “Yes, there’s always the little one. I’ll get her.” Series two of BBC Radio 4’s Uncharted is available on BBC Sounds, alongside the latest series of Curious Cases with the new co-host Dara Ó Briain