Mary Beard vividly remembers a day in her first year at Newnham College, Cambridge, when one of her friends saw a marked essay lying on her desk. He picked it up and read the tutor's comment: "This is very good; I think it would get a first." "You," he spluttered, "get a first?" "Even in the mid-70s," Beard recalls, there were "lots of men who thought that women were destined only to get 2:1s." Besides, she was studying classics, a typically male discipline, and elitist too, run by "curmudgeonly old sods". "From that moment," she laughs, "I was bloody determined to show them."

And she has shown them: Beard is now a professor at Cambridge and the best-known classicist in Britain. Her new book, The Roman Triumph, is keenly awaited, and she has been asked to give the prestigious Sather lectures at Berkeley, California, next year. She is constantly called on by the BBC and the broadsheets to comment when popular culture ventures into the ancient world - Gladiator, Troy - and has become, she admits, "a bit of a media junkie".

She welcomes all the "hundreds of movies, and hundreds of novels and cartoon strips about the Romans". "What interests me," she says, "is the idea that classics is actually quite democratic. It isn't only the toff, upper-class subject it's often thought to be. Every generation enjoys rediscovering it." At the same time, she does her best to cut through the popular myths and cruder appropriations of the ancient world, patiently pointing out that Romans didn't wear togas very often, that the animals killed in the Colosseum were more likely to be sheep than lions (also no Christians were ever put to death there), and that the Athenian version of democracy celebrated by prime ministers and presidents had severe limitations, not least the exclusion of women.

Beard is known for saying what she thinks, and for her sense of fun; she is, according to her blog, "wickedly subversive". The other day, a documentary-maker, having sought out her advice, decided she was "one of the smartest women alive ... Convivially we end up in ... a bar downing bellinis and red-pepper margaritas". But her forthrightness has also got Beard into trouble. In particular, she is still condemned in some quarters for a statement she made in the London Review of Books a few days after 9/11. "Ever after, I've been that foolish/callous/dangerous don who thought that 'the United States had it coming.'"

When the 18-year-old Mary Beard was interviewed at Newnham, she was summed up on her application form as "an only-child of elderly parents". "How about that for a put down!" Her father was "an old-fashioned liberal architect with a practice in Shrewsbury ... a raffish public-schoolboy type and a complete wastrel, but very engaging". Her mother, a headmistress, would retire to bed on Sunday afternoons with the newspaper review pages and a handful of library request cards: "It was impossible," Beard says, "to think of a world without books."

She attended a single-sex direct-grant school, and found ways in Shrewsbury to be "safely transgressive" ("if I had been properly transgressive, I wouldn't be here now"), along the customary lines of "sex and drugs and rock music". At archaeological excavations during the summer, "digging up nasty bits of pottery was the price one paid for fun in the evening". Almost despite herself, Beard eventually realised that there was "something really exciting" about the discovery of antiquity.

At Newnham she was "a swot" who "wouldn't have dared speak to" the likes of Clive Anderson and Griff Rhys Jones, that generation's stars of the Cambridge Footlights. It was a benefit to attend a women-only college at that time, she believes, though her years at university were "the first time I realised there was sexism in the world ... I had lived a protected life". Her feminism has ever since been "hugely important in terms of intellectual, cultural and university politics. Unreasonable as it might seem for me to say this sitting here" - in her elegant rooms in the college Old Hall - "you can't work in Cambridge for as long as I have without being aware that, as a woman, the dice are loaded against you."

But she detects "cant in some bits of modern orthodox feminism" and happily describes her own views as "maverick". Certainly, her recounting in the press of two of her experiences as a student have proved controversial. First, she told how, when a backpacker on a night train in Italy, she was raped by a man who had helped her buy a ticket. "I can't claim to have been particularly traumatised by what happened," she wrote, and emphasised the divergent ways she had reconstructed the event in the intervening years. A vocal response to her revelation, however, was that Beard was merely "in denial".

In another article, in which she exposed the respected Latin scholar Eduard Fraenkel as a groper of his female students, she went on to express "a certain wilful nostalgia for that academic era before about 1980 when the erotic dimension of pedagogy, which had flourished since Plato, was firmly stamped out".

When her remarks were denounced by a number of fellow academics and by student bodies, she explained that, as an undergraduate, she was regularly invited by "a senior, immensely overweight, architectural historian in my faculty" (Hubert - "Huge" - Plummer) on Saturday afternoon drives in his Mini to look around the buildings and monuments of Northamptonshire, often followed by dinner. No advances were made, and she learned a "tremendous amount", but today, "this would be a sackable offence". "It's not always easy to know where to draw the line," Beard suggests, and she regrets the closing down of "an area of sociability between dons and undergraduates".

As a graduate student, Beard picked up on new intellectual trends within the profession, including a preference for the study of social structures over political narrative, and a postmodernist questioning of the nature of evidence - the extent to which ancient writers can be read as describing reliably what their world was like. "If there was one advantage in being a woman in classics then," she recalls, "it was the licence it gave me to be more intellectually modish, to explore the edges of the discipline ... We took up Mary Douglas and said 'yippee', though it wasn't long before we began to critique anthropological methods." Beard was offered a teaching post at King's College London in 1979, where she stayed for five years before returning to Cambridge as the only female lecturer in the faculty.

Her first book, the student-favourite Rome in the Late Republic, written with Michael Crawford, drew on such innovative approaches, but was also a "marvellous crib". Classics: A Very Short Introduction, written with John Henderson, has found an even larger audience, not least because it opens up "our relationship with the ancient world".

In 2000 she published a study of Jane Ellen Harrison, also a Newnham scholar, as well as a suffragette, a Bloomsburyite, and the ideal prototype of an ebullient, media-savvy classicist. Harrison rode the wave of popularity for Greek antiquity at the end of the 19th century, giving theatrical lectures to audiences of over 1,000 on such obscure subjects as Attic grave stelae.

Yet when, in the following year, Beard herself achieved an equivalent level of fame, the experience wasn't entirely welcome. Invited alongside other contributors by the LRB to give an immediate response to the 9/11 attacks and the coverage they had received, she wrote of "the feeling that, however tactfully you dress it up, the United States had it coming. That is, of course, what many people openly or privately think" (she had just seen "an edition of Question Time with an audience that was distinctly anti-American"). All hell broke loose, with Beard becoming the focus of fierce criticism, in Britain and especially America. The London Review removed her name and address from its list of subscribers "in case somebody did something nasty".

At first she ignored all the hate mail, but then changed her mind: "Isn't intellectual life about having an argument? So I started to write back, explaining that of course I wasn't saying those people deserved to die, but simply that there was a connection, or people perceived a connection, between American geopolitics and what had happened. I had many wonderful exchanges ... and developed many email friends ... it was really moving."

Does she regret writing it? "In some ways it did me good: no one had heard of me before. But I am aware that there are people I'd have liked to have more to do with intellectually who have been put off me. Was I wrong to say it at that moment? No. You can't always worry about offending people." She adds that in today's changed political climate it is now conventional to highlight the association between terrorism and America's foreign policy.

No direct comparisons are made between the ancient world and today's political situation in The Roman Triumph, an exploration of the lavish parades held in honour of conquering generals on their return to Rome. But at the heart of the book, Beard says, is the idea that "victory is never easy". Even after a war, it is sometimes difficult to decide who has won: the defeated can become the stars. "People who exploit others come to spend an enormous amount of energy wondering about and justifying that exploitation."

She has long been uncomfortable with the accepted view of Romans as "unreflective, single-minded brutes", poor relations of the sophisticated Greeks. "How we think about Rome is how they thought about it in the 19th century. As soon as it was decided that the Greeks were not in fact nasty wimps who had dangerous sexual practices and indulged in mob rule, but were rather elevated types who invented all our institutions and were agonistic and intellectually originary, the Romans were forced to fill the role of the thuggish anti-type." To prove finally the mistaken nature of this dichotomy, Beard decided to show that even a battle ceremony was endlessly questioned, reinvented and ridiculed: "It exposes all kinds of intellectual anxieties."

And the triumph has an obvious significance for a scholar interested in how later cultures have appropriated Rome: Renaissance princes were awarded triumphs, as was Napoleon, as was Mussolini. Beard points to the ubiquity of triumphal arches, and to the frequency with which the word "triumph" is used by all of us. She even sees a parallel in victorious football teams parading through a city on open-topped buses.

The subject of her Sather lectures will be "laughter in Rome", but before she writes them, she is due to finish a book about Pompeii, which will, in part, try to think about the experience of tourists wandering around the ancient town: "What do they look at? And how do they look at it?"

Pompeii has long been a site of mass tourism and, like Hollywood blockbusters, offers itself up to an interpretation combining scholarly expertise with a willingness to be populist. Beard has had an enthusiastic response to her blog, which ranges from discussions of America as the new Rome to a list of "10 things the makers of 300 got right". Rome and Greece are everywhere, she says. "It's a great time to be a classicist."