The first time I saw Mary Beard, I was 17. It was 1989, and she was speaking at a joint open day for the Oxford and Cambridge classics faculties. She was utterly unlike the other speakers, who, as I recall them, were Oxbridge dons straight from central casting: tweedy, forbidding, male. Instead of standing at a lectern like everyone else, she perched rakishly on the edge of a desk. She was dressed in a vaguely hippyish, embroidered black dress, and a cascade of black hair tumbled around her shoulders. Greg Woolf, now director of the Institute of Classical Studies at the University of London, recalls another one of those open days, in the early 1990s. “I spoke, and then another big hairy bloke like me spoke. And then Mary came on and said: ‘Well, you’ve heard what the boys have got to say.’ And you could see that she’d already won everyone’s hearts.”

Everyone who has met Beard seems to have a story about encountering her for the first time – usually involving her rigorous intellect, her total lack of formality, and her sense of mischief. One of her former students, Emily Kneebone, remembers supervisions – one-to-one or two-to-one teaching sessions – at Newnham, the women-only Cambridge college to which Beard has been attached for most of her adult life, first as a student, then as a don. She would teach from a chaise longue: “At first she’d be in a normal position, but as the hour progressed she would gradually slide further and further down so you could only see her feet.” One junior colleague still remembers Beard introducing herself, at a conference almost 25 years ago, with the overture, “Give us a fag, darlin’.”

In public, in private and in her academic writing she is sceptical, wary of consensus, the kind of person who will turn any question back on itself and examine it from an unexpected angle. She is not afraid to take apart her own work: at that same conference in the early 1990s, she presented a paper that repudiated one of the scholarly articles that had helped make her name a decade earlier, an influential study of Rome’s Vestal Virgins. It was an extremely unusual thing for a scholar to do. “She doesn’t let herself off – she’s not one of those scholars who is building an unassailable monument of work to leave behind her,” Woolf said. “She is quite happy to go back to her earlier self and say, ‘Nah.’”

The learned but approachable figure you see on TV translating Latin inscriptions, carving up a pizza to explain the division of the Roman empire, or arguing about public services on Question Time, is precisely the Beard you encounter in private, except that in real life, she swears magnificently and often. (“She’s always spoken fluent Anglo-Saxon,” said Woolf.) In a Greek restaurant in London one January afternoon, her long grey hair uncharacteristically glossy and fresh from the stylist, Beard talked about everything from Islamic State to academic freedom. At one point, she sketched out an argument for a second referendum on Britain’s membership of the EU. Her case rested on the very nature of democracy, for which the presence of a ballot box was a necessary but not sufficient condition. Democracy cannot properly operate without knowledge, she said – which the entire electorate of summer 2016 lacked. (“Aristophanes knew that!”) The referendum then, should not be treated as the final word, she said, but as a straw vote. “Sure, say we want to leave, but you can only in the end say we are going to leave when we know what it means. Otherwise,” she said, “it’s just wanking in the dark.” Thinking I had misheard, I asked her to repeat. “Wanking in the dark,” repeated Beard, at volume. Later in the conversation, she told me she was planning to get a pink streak in her hair. “I’m fucking well going to have one: it just feels like such fun.”

Beard is a celebrity, a national treasure, and easily the world’s most famous classicist. Her latest book, Women and Power, about the long history of the silencing of female voices, was a Christmas bestseller on both sides of the Atlantic. In the eight years since her debut TV documentary, Pompeii, she has conquered the small screen. She is one of a trio of presenters who will, in March, front Civilisations – a new, big-budget version of Kenneth Clark’s 1969 series Civilisation, the most revered cultural TV series in the BBC’s history.

A mark of her leap into the celebrity stratosphere is the avalanche of daily requests she receives. These have included, aside from several politely declined offers of a makeover from the Daily Mail, invitations (also politely declined) to appear on the diving show Splash!, on the celebrity version of The Great British Bake Off and on Celebrity Mastermind. Of the last she said: “God, just imagine it. Either you’d look like a complete nerd or everyone would be saying, ‘She doesn’t know a thing.’”

Out and about, she is regularly flagged down by fans, often, but not always, young women. (One admirer, Megan Beech, published a poem called When I Grow Up I Want to Be Mary Beard – a phrase that now adorns T-shirts worn by her fans. Characteristically, Beard befriended Beech after they connected on social media, and Beech is now studying for a PhD at Newnham.) Caterina Turroni, a television producer who has worked with Beard since the Pompeii documentary, recalled filming with her in Tiberius’s villa on Capri in 2013, when a party of English schoolgirls spotted the cameras. “You could hear them saying, ‘What if it’s her?’ ‘Do you think it’s really her?’ and then they saw her and they went insane – it was like they’d seen a boyband.”

As recently as a decade ago, it would have seemed unlikely, even outlandish, that a middle-aged classics don, her appearance a million miles away from the groomed perfection expected of women in the public sphere, would end up so famous and, by and large, so loved. That unlikeliness was summed up by notorious reviews of her early programmes in the Sunday Times by the late TV critic AA Gill, who mocked what he called her “corpses’ teeth” and, in 2012, declared that she ought to be “kept away from cameras altogether”. But it was Gill who was out of tune with the times. Beard hit back in the Daily Mail, pointing out that “There have always been men like Gill who are frightened of smart women who speak their minds”, and that “The point is not what I look like, but what I do.” She struck a chord. “I thought that most of the readers’ comments would be negative,” she told me in December, “but many more of them were positive. The Mail’s demographic, after all, is women my age – and who look like me, not like Joanna Lumley.”

Since then, Beard has become a standard-bearer for middle-aged women, and beloved by the young – indeed, by anyone who wants to be seen in terms of their ideas, not their looks; anyone who think it’s cool to be smart; and by those who relentlessly ask questions and never reject a contrary opinion out of hand. Beard’s intellectual style, which suffuses all her scholarship – a commitment to rigorous scepticism that refuses to be cynical – has made her a model for those who worry that the shouting and bullying of the digital world make reasoned political debate impossible.

Beard radiates authority and expertise, but she does not hesitate to get mixed up in messy public arguments, which often puts her on the frontline of the culture wars. Last year, when a far-right conspiracy theorist attacked a BBC cartoon that showed a man of sub-Saharan appearance as a Roman in Britain – political correctness gone mad! – Beard calmly stepped in to explain there was in fact “plenty of firm evidence for ethnic diversity in Roman Britain”. Her expert intervention was met with a what she later described as a “torrent of aggressive insults, on everything from my historical competence and elitist ivory tower viewpoint to my age, shape and gender”.

For most people, this would be a cautionary tale; for Beard, it was evidence that such battles cannot be shirked. Embedded in her refusal to be silenced, in her endless online engagement, is a kind of optimism: the idealistic, perhaps totally unrealistic, notion that if only we listened to each other, if only we argued more cogently, more tolerantly and with better grace, then we could make public discourse something better than it is.

Beard exemplifies something rare, said Jonty Claypole, the BBC’s director of arts and one of the executive producers of the new Civilisations. “It’s never about her,” he said. “To be a true public intellectual is like offering a form of public service. A lot of people don’t realise that: they confuse being a public intellectual with their ego.” He counted off those he regarded as her predecessors: “Bertrand Russell, Kenneth Clark, Susan Sontag, Robert Hughes, Germaine Greer, Stuart Hall, Simon Schama … ” Figures like these emerge only once in a generation, he said. “She looks at the world through the deep lens of the ancient world, and she shifts arguments.”

In 1995, the year she turned 40, Beard’s academic career looked as if it was going nowhere in particular. “You would have said: ‘Pity about Mary, she looked so promising,’” she told me at her house in Cambridge, a cosy clutter of books and oriental rugs. In her 20s she had produced some significant scholarly articles on Roman history – the kind featuring great chunks of untranslated Latin, German and Greek, and thick wads of footnotes. They included, in 1980, her pioneering work on the Vestal Virgins, which, fashionably, used techniques borrowed from anthropology to reshape thinking about the priestesses who served the Roman goddess of the hearth. But she did not turn her PhD, on state religion in the Roman republic, into a book, nor produce a serious monograph setting out her stall, as an ambitious young scholar would usually do. Her first books, when she got round to writing them in the late 1980s and 1990s – on Roman religion, on Rome in the late republic, and an introductory book on classics – were, unconventionally, written with fellow scholars.

Mary Beard around 1978. Photograph: MMP Cambridge

It wasn’t that she was slacking: Beard has always been hardworking to a fault. But in 1985, the year after she returned as a lecturer to Cambridge, after a brief stint at King’s College London, she had her first child; then, two years later, her second. (Zoe and Raphael Cormack are both now academics, working on South Sudanese anthropology and Egyptian literature respectively.) With her husband, art historian Robin Cormack, working in London, she lacked the uninterrupted stretches of time needed to concentrate on serious research. The family was also struggling for money, “so I had to supervise my arse off, because you are paid extra for that”. But, in retrospect, all that teaching – quite broadly spread through archaeology, ancient history and Latin literature – had its advantages: she was amassing knowledge, not least of how to make the ancient world seem exciting. Even in those apparently unpromising days, the Beard of 2018 was being forged.

It was not until 1989 that she published the first book under her name alone – and it was nothing to do with classics. It was called the Good Working Mother’s Guide, a practical handbook that included advice on maternity benefit, how to interview a nanny, and the best way to hand-express milk (“First of all stroke or massage your breasts for a few minutes, starting from the top and working down and round towards the nipple … ”). It was an unlikely project for a young classics don, but was an example of Beard’s pedagogical instinct in action: reading it, you can sense she didn’t want to waste painfully acquired knowledge if it could be useful to others. “It’s true,” she told me, “that millions of women have sussed this and don’t immediately think: ‘I’ll write a book about it.’ But it seemed a fun thing to do.”

This work of no-nonsense feminism was a first step beyond the academy. She had pitched it to Duckworth, which had already taken one of her co-authored classics books. Its boss, an old-school publisher called Colin Haycraft, hosted famously dissolute parties, the kind of event at which you would drink too many champagne cocktails and get introduced to authors whose books you had read. “It was part of a world of literary drunken glamour that I didn’t, as a good girl growing up in Shrewsbury, know existed,” said Beard. “It was eye-opening. Proper 1980s lunches: you’d wake up at 7pm on Colin’s sofa and think: ‘Fuck, I’d better go home.’”

In the late 1980s, she started writing for both the London Review of Books and the Times Literary Supplement – and in 1992, Ferdinand Mount, then editor of the TLS, asked her to take over its classics coverage. She found that this kind of public writing could be conveniently slotted in around parenting duties, and it had the attraction of being immediate: “You could see the fucking thing in print the next week. Not like writing an article for the Journal of Roman Studies.”

Her natural frankness was well suited to addressing an audience beyond academia. So was her ability to make eye-catching connections between the ancient and contemporary worlds, and her tendency to argue from an unexpected position. Some of her articles were controversial enough to be reported in the papers, generally with the nuance stripped out. She began to acquire a certain notoriety.

One piece described her own experience of sexual assault, by way of demonstrating that rape is not just an act, but a story – and frequently a contested one. Another outed Eduard Fraenkel, a famous Oxford classicist, as a “serial groper”, but in doing so aired the uncomfortable truth that relationships between teachers and pupils (since Socrates and Agathon, you might say) have often had an erotic tinge. A short response to the September 11 attacks in the LRB brought a torrent of complaint from those who thought she said “America had it coming”. (She didn’t write that, precisely, but said that some people might think that it had – and argued that one should try to understand the terrorists’ ideology.) In 2005, at the behest of Mount’s successor at the TLS, Peter Stothard, she gamely agreed to try another new form, the blog. She took to it with ease, and her vivid, informal journal, A Don’s Life, has flourished ever since – unlike so many similar projects that have quietly faded away. Recent topics have included the future of #MeToo, her views on book blurbs, and the museums she enjoyed on a recent trip to Bologna.

The TLS gave her a reason to get out of Cambridge. “I was able to meet a London crowd – a whole world, people you’d never dream of being in the same room as. I was starstruck.” She remembers wandering up to Martin Amis and asking who he was – then being “crushingly embarrassed” that she hadn’t recognised him. Around that time, in 1990, she won a one-year fellowship, which she hoped would give her space and time for research. “I wrote absolutely fuck all. Another example of total failure by Beard. When you’ve been looking after two small kids, the idea that you have a year off from teaching and you’ll now be able to write – well, after about six months you become human again. But the idea you sit down again and say: ‘Great, chapter one, off we go’ – no. I wrote pages of crap. I couldn’t do it. I wept over endless drafts.”

Her career stands, in a way, as a corrective to the notion that life runs a smooth, logical path. “It’s a lesson to all of those guys – some of whom are my mates,” she said, remembering the colleagues who once whispered that she had squandered her talent. “I now think: ‘Up yours. Up yours, actually.’ Because people’s careers go in very different trajectories and at very different speeds. Some people get lapped after an early sprint.” She added softly, with a wicked grin: “I know who you are, boys.”

Mary Beard with a statue of the Emperor Constantine in Rome while filming with the BBC. Photograph: Caterina Turroni/BBC

Whatever she is doing – writing books, or reviews, or blogging, or tweeting, or working on TV programmes – she takes the same intellectual approach. “For Mary, everything is a two-way street,” said Stothard. “She doesn’t shut people out. Arguments never finish; criticism is never over, and it’s always about the process, and not the thing itself.” This is also how she teaches – with an unusually sincere attachment to the principle that the pedagogical process should be rooted in an encounter, a relationship and a dialogue.

“She thinks of the primary academic mode as the one-to-one supervision,” said Tim Whitmarsh, professor of Greek culture at Cambridge. “It’s not just about feeding a student information. It’s about how you relate to that person as a person, how seriously you take them, how much support you give them.” When she engages with those who challenge her, on Twitter or on Question Time – when she argues her case with humour and knowledge, when she listens to the views of the other side, when she takes no shit – she is making the whole world her undergraduate.

The classics faculty in Cambridge is a modest, 1960s building on the leafy Sidgwick Avenue – the same street as Newnham, which was convenient for Beard during the child-raising years. One morning in November I watched her lecture around 60 undergraduates. She was dressed in a bright-blue mac and perched on a high stool at the edge of the dais. The ostensible subject was how the emperor Augustus solidified his power, but it could easily have been titled “How Autocracy Works”.

One-person rule, she said, “does not just operate through political reform or by military power, important as they may be. It works by inscribing the autocrat indelibly into the world of his or her subjects.” She referred to Augustus’s autobiography, Res Gestae (“Things Achieved”) – a rather indigestible account of peoples conquered and temples restored. “It is a piece of enormous self-justification,” Beard explained. “He is saying: ‘I liberated the state.’ And it is full of strategic omissions. He doesn’t say: ‘I tore out someone’s eyeballs with my bare hands.’” (Suetonius, his biographer, later claimed he did.) It would not have taken much to have transformed the lecture into a television programme – the tone, smart and clear but not condescending, was very BBC2.

Beard describes herself as academically “flighty”. Instead of burrowing into one small area – a single Latin author, for example, or Roman religion in a given period – she has darted between topics; and, perhaps because of her gregarious nature, has preferred those topics not to be especially obscure. She turned to the Vestal Virgins, she told me, because she realised that state religion in the Roman republic “wasn’t much of an opener at a party”. After The Good Working Mother’s Guide, her next sole-authored book was a biography of one of her foremothers at Newnham, the early 20th-century classicist Jane Harrison. She has written about the Romans’ sense of humour, the Triumph (a ritual victory parade undertaken by Roman generals), and the Parthenon. Her next, more academic, book, after a TV tie-in for Civilisations, is another departure – about images of the Caesars in art since the Renaissance.

This eclecticism has given her the means to range widely through the ancient world in her public work. So has the fact that her scholarship has been relatively mainstream, rather than at the bleeding edge of academic fashion. “She often represents herself as quite traditional though she also likes also to think of herself as transgressive,” said Greg Woolf. “The traditional bit is dominant: she does think you need to know Latin and Greek to be a classicist. She’s not about demolishing classics as a subject. She likes to do interesting things from the canon.”

That position, poised between tradition and transgression, holds true for public life, too. The notion that she is “wickedly subversive” – as the tagline of her blog has it – is always tempered by the fact that she emerges from a discipline with an enormous weight of inherited cultural capital. That she is able to draw on this double identity – a fierce feminist with an unassailable expertise in Latin; someone whose leftwing politics are twinned with a deep knowledge of Cicero – is part of the reason she appeals so broadly. She is as much of interest to the readers of the Telegraph as the Guardian.

Beard receiving an OBE medal at Buckingham Palace in 2013. Photograph: WPA/Getty

As time has passed, her writing style, compared with the early, careful academic articles, has become more like her spoken voice. The Beard of the first Vestals article of 1980 would never have used, as an epigraph, a quote from a Procol Harum lyric – as did the Beard of the later Vestals paper repudiating her earlier ideas. “I saw eventually that you could write ‘scholarly articles’ in a style that felt right for you and didn’t feel significantly different from the way you wrote a review,” she told me.

Her breakthrough book, Pompeii (2008), combined her academic methods with a relaxed, approachable address. The idea had come from the late Peter Carson, a classicist and her editor at Profile Books. At first, she’d been reluctant – Pompeii has its own cohorts of specialised scholars, and she had never excavated there. But eventually, not least because she was short of money, she decided to give it a go, realising she could use it at a place “to really get into Rome”. It was a work of sceptical history that debunked myth after myth, and battled against received opinion. She argued that Pompeii was not “frozen in time”, as often claimed – it was more complicated than that, a city that for centuries had been “disrupted and disturbed, excavated and pillaged”, even bombed during the second world war. At the same time, its traces provided vivid glimpses of the lives of ordinary people, from unlucky lovers to hotel guests pissing in their beds.

Janice Hadlow, then controller of BBC2, read the book on holiday, and persuaded Beard to turn it into a TV programme. “I was terrified there’d be lots of people dressed up in sheets,” said Beard. But it was her moment: at the time, the BBC was being sued for age discrimination by presenter Miriam O’Reilly and the paucity of older women on air was becoming painfully obvious. “Janice said: ‘You’ve complained there are loads of wrinkly, crusty old men presenting documentaries and no women over 35, and now I’m offering you the chance – you’re not going to tell me you’re not going to do it, are you?’” It was a turning point. Hitherto, her readers had numbered in their thousands. The documentary was watched by 3.4 million.

The scepticism that defines Beard’s intellectual approach – so clearly on display in Pompeii – was drummed into her early, when she was a student. Her tutor was Joyce Reynolds, who is now 99 years old. “She is probably working in the library right now,” said Beard. Reynolds would say to her: “Do you really know that, Miss Beard? Is that the only way you can interpret the evidence?”

But once you have stripped away the myths, the misapprehensions and the (literal) mistranslations that come between us and an understanding of the ancient world – once you have acknowledged that much can never be known for sure – the problem becomes what, if anything, to put in that void. One of Beard’s solutions has been to change the goalposts of “knowing”. We cannot ever know, for example, the motives of Brutus in assassinating Julius Caesar. But we can know a great many other things: how, for example, Roman parents commemorated their dead children on tombstones; how Cicero fashioned an image of himself as the saviour of the Roman state; how Augustus wanted to be remembered.

Beard’s view, in other words, is that it is fruitless to make ancient sources into a kind of window through which, if you try hard enough, you will be able to discern a clear picture of the classical world – which has been the traditional means of doing classics. The sources themselves – the original texts and artefacts, as well as the accretions of later scholarship – combine to create our view of the past, and they can be unpicked so that they offer up clues about the anxieties and worldview that formed them. When she, with her co-writer John Henderson, first put such ideas forward in A Very Short Introduction to Classics (1995), it was surprising and fresh to read not that classics was about discovering what Greece and Rome were “really like”. Instead, they wrote, “classics exists in that gap between us and the world of the Greeks and the Romans”.

This approach was neatly displayed in her bestselling history of Rome, SPQR (2015). The early history of Rome, the era of its fabled seven kings, is notoriously difficult to untangle. There are few, if any, contemporary sources. The whole story slides frustratingly away into legend, with the later Romans just as confused as we are about how an unremarkable town on a malarial swamp came to rule a vast empire. One way of handling this material might have been simply to have started later, when the historian’s footing among the sources becomes more secure. Instead Beard asked not how much truth could be excavated from the Romans’ stories about their deep past, but what it might mean that they told them. If the Romans believed their city had started with Romulus and Remus, with the rape of the Sabine women – in a welter, in other words, of fratricide and sexual violence – what can we learn about the tellers’ concerns, their preoccupations, their beliefs? According to Greg Woolf, “One of the things Mary has taught is to look at the window, not through it, because there isn’t really anything behind it.”

Women and Power begins with a tribute to Beard’s mother – who lacked the opportunity to attend university, became a teacher and, very unusually for the 1950s, continued working after having children. Beard’s father was an architect specialising in historical buildings, and the family lived in Shropshire. In her teens she started to take part in local excavations, at places like Wroxeter, where there are the remains of a Roman town. “It’s a bit naff, but there is something exciting about pulling a bit of pottery out of the ground that’s 2,000 years old.” She decided to study classics for the simple reason that she was good at it, and therefore liked it. Her school steered her to Newnham.

As an undergraduate, she “went out and got pissed – sex, drugs, rock’n’roll and all that. But I worked really, really hard. I am not of the view that people get firsts effortlessly.” These were different times. She found herself drawn to older, sometimes married, men. “I had relationships with people who were technically in different levels, in positions of power,” she said, “and I am fucking well not having my agency removed from that. You could say: ‘Beard, you are engaged in massive self-deception, you were being exploited within a power structure and you’ve just not seen it.’ But when I look back at the late 1970s and early 80s, that’s not how my relationships with these guys felt. You can accuse me of, and I can never defend myself against, mammoth miscognition.”

She doesn’t feel damaged by scenarios that would plainly be unacceptable today, she said, though “on the other hand you’d have to be blind as a bat to see it didn’t work like that for everybody”. One of the great problems of today, she said, was deciding how far current rules of behaviour could be projected back on the past. This question also informs her academic work: she is more likely to point out how different we are from the Romans than how similar. “As soon as you say things were different 40 years ago, people start to say you’re a harassment denier. But actually, they were. I do not think that the lives of women of my generation as a class were blighted by the way the power differentials between men and women operated. We wanted to change those power differentials; we also had a good time.”

Beard in Pompeii filming her 2016 series for the BBC. Photograph: BBC/Lion Television/Caterina Turroni

As a young don, Beard was just the kind of female colleague that the men liked – “a woman who answered back. Feisty, a bit gobby,” as she puts it. The feisty gobbiness was partly a performance, an identity forged to fit into the world of work. “I got the best out of them by being pushy. It was a strategy, but also a strategy that felt like me.” There was, she said, a lot of predictable sexism, “the day-to-day gendered world of the office, about who chooses the curtain material, who helps clear the tea away”. But, she said: “My colleagues were structurally male and really male, but what they didn’t do was treat me as anything other than an intellectual equal.”

Sometimes, she overcompensated for her femininity. After her first baby, she decided to continue with her duties as secretary of the Cambridge Philological Society, a fortnightly faculty club where papers were presented. Her job was to read out the minutes from the last session. “I thought: I’m bloody well not going to let them say I had ratted on that obligation. Four or five days after Zoe was born, I went and read the minutes, and after a few minutes of the paper I slipped away.” For the rest of the term, she did the same: read the minutes, and discreetly slipped away to feed the baby, feeling utterly heroic. But heroism, it transpired, was not what the blokes saw. They saw a shirker. A decade later, she was in the pub with a colleague. “And he said: ‘Oh yes, you were the one who used to turn up, and then not hear the paper.’” Beard recalled: “My breasts were exploding.”

The presiding genius of the classics department was Keith Hopkins, the late ancient historian, who was notorious for his withering put-downs of colleagues’ work. “He was adversarial, terrifying and inspirational all at once. He used to say: ‘Mary, this is boring. There is an argument here, but it’s dull.’ He’d say, in a way that would get him sacked now: ‘Seduce me.’” Not everyone took to this aggressive environment. “He would be disciplined now, undoubtedly, for inappropriate behaviour – probably including hands on knees. He was very rough, and very tough … What we don’t see is those who were so traumatised by it that they just basically gave up.”

Fortunately for her, she flourished – and, necessarily, developed a thick skin. When, after an appearance on Question Time in 2013, she received death threats and ugly misogynist abuse, she felt shocked – almost physically winded, she said, “as if I’d been hit in the back with a tennis ball”. Still, it would have felt worse, she said, if someone “had been through one of my articles and pointed out that all the footnotes were wrong”.

One reason Beard is so widely beloved is that her interventions in public life – whether one agrees with her or not – offer an alternative mode of discourse, one that people are hungry for: a position that is serious and tough in argument, but friendly and humorous in manner, and one that, at a time when disagreements quickly become shrill or abusive, insists on dialogue. Still, it is these precise qualities that can, equally, land her in deep water. The point of her notorious 9/11 article was that one could simultaneously deplore the terrorists’ murderous violence, and try to understand their position. After the deluge of angry emails arrived, she tried to reply to most of them, even making a couple of friends along the way. When I asked her if she would countenance taking Isis’s ideology seriously, she said: “That’s the wrong question. There is no argument that I won’t take seriously. Thinking through how you look to your enemies is helpful. That doesn’t mean that your ideology is wrong and theirs is right, but maybe you have to recognise that they have one – and that it may be logically coherent. Which may be uncomfortable.” Few would think it worth arguing with Arron Banks, the Ukip donor, when he said the Roman empire had collapsed because of immigration. Beard pulled him up on Twitter, suggesting he might like to read a bit more classical history – and then went out to lunch with him.

Trying to calm the fury and aggression of public speech is, quite possibly, a futile endeavour. Friends worry about the toll such a publicly exposed existence takes on her. The time she devotes to email alone is daunting; she tries to respond to everything. Withstanding appalling online abuse is draining. Still she keeps going. She abhors a comfortable consensus. “She is very suspicious of received wisdoms, conventional views,” said Peter Stothard. “If everyone is saying X is Y, her instinct is to say, are we sure it isn’t P?” For Beard, the very point of being an academic in the public sphere is the ability to be a kind of intellectual awkward squad – unlike elected politicians, who inevitably seek popularity. “The right to be unpopular is important – that’s what academic freedom is about,” she said.

Once, in a different political age, she used to get students to argue that the USSR was more democratic than the UK and US. “It got them to see that the other side wasn’t barking mad, but they had a different set of criteria for assessing what was democratic. That was helpful when you got to Athens – which called itself democratic without women having the vote. There’s hardly anywhere in the world that doesn’t claim to be a democracy.” Being a classicist helps this way of thinking. The point of the discipline – the study of people at once familiar, since they have haunted western culture for so long, and at the same time deeply alien – is to “turn the focus on you, and make you an anthropologist of yourself”. It is to make us seem strange to ourselves.

Before Christmas, Beard ran me through her previous week’s diary. On the Sunday, she had worked on voiceovers for Civilisations. On Monday, she had been to Brussels to talk at the EU’s annual human rights conference. Tuesday morning was lecturing, seeing graduate students, and working on her Civilisations book; she also met the new Cambridge vice-chancellor, and did a public event with the American studies professor Sarah Churchwell in Bloomsbury. On Wednesday, she filmed with the author Robert Harris for a new BBC documentary about Julius Caesar. On Thursday, she did some writing, then hosted the Odyssey translator Emily Wilson at an event at Newnham. Friday, she saw curators from the Ny Carlsberg Glyptotek in Copenhagen, whom she is advising on a redisplay of classical sculpture. Then she and Cormack drove to Houghton Hall in Norfolk for a talk in aid of children’s hospices. On Saturday, she wrote her undergraduate lectures for the following week, and made the Christmas pudding. Sunday was voiceovers again. Between all this she was replying to an avalanche of correspondence, jabbing out replies to email on her iPhone.

She is never tempted, she told me, to abandon the day job and focus purely on her media career. Cambridge is grounding. It is her home. She is respected by her peers: perhaps because her media success came late, she has never lost academic credibility, and her colleagues regard her as an invaluable standard bearer for the subject. As her former Newnham colleague Helen Morales – now at the University of California – said: “She might be meeting Manolo Blahnik in the morning, but it’s the Res Gestae in the afternoon.” (She has an unlikely friendship with the shoe designer, whom she met at a party; she has several flat pairs of his shoes, her favourites being “my little red Manolos”.)

Beard is also aware that her time in the limelight may one day come to an end. No one knows better than she that empires rise and fall. One day late last year, in her office in the classics faculty, she said: “When all this has gone I’ll be in the university library, writing, and I’ll be quite happy. And I’ll think, as I ride home on my bicycle: ‘Didn’t life used to be busy?’”

Mary Beard will be in conversation with Charlotte Higgins at a Guardian Live event at the Shaw Theatre in London on Friday 16 March. Details: theguardian.com/guardianlive

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