So, Mary Beard and Hillary Clinton, together at last.

Since the Cambridge professor began presenting TV programmes on the Romans nearly a decade ago, she has become world famous, as well as wildly popular for her robust refusal to stand for misogynistic online abuse. Trolls are publicly challenged; one was memorably shamed into taking Beard to lunch to apologise for calling her “a filthy old slut”. Her latest book, Women & Power: A Manifesto, brings an illuminating historical perspective to the contemporary abuse of powerful women.

I have that book. Maureen sent it to me as a surprise.

The pair met briefly four years ago when both received honorary degrees at the University of St Andrews University in Scotland. Beard had been advocating a more combative strategy towards trolls than Michelle Obama’s famous injunction to “go high… when they go low”. The latter having failed to work for Clinton, she and Beard fall at once to discussing how women in public life can deal with misogyny…

Mary Beard What I remember us talking about when we met was the sense that it was extremely important to say: “Hang on a minute, mate, you are not right.” Or: “Please take this tweet down.”

Hillary Clinton Learning about the ongoing grief you took over standing up for women’s rights and accurate history was quite enlightening to me.

MB It’s gone on, too, actually.

HC Well, as you rightly point out, it has only continued, and in some ways gotten worse. The ability of people in public life or in the media to say the most outrageous falsehoods and not be held accountable has really altered the balance in our public discourse, in a way that I think is endangering democracy.

MB To me, what’s really interesting is that, although they look as if they’re going for what we said, what they’re really going for is the fact that we dared to say anything, almost. It’s not about having an argument about, say, migration. It’s about telling you to shut up.

HC That’s right. I know that very well, and so do you, and we have perhaps thicker skin than a lot of other people. But it is still distressing to be told, either explicitly or implicitly: “Go away. You have nothing to say.”

MB The friendly advice when it happens to you is always: “Don’t pay attention. Don’t give them oxygen and publicity. Block them and just move on, dear.” And you think, sorry, that is what women have been told to do for centuries. If somebody accuses you of having a smelly vagina that stinks of cabbage, you’re supposed to say: “Just block him.” Actually, no. Somehow, even among the people who are trying to support you, it’s basically saying: “Shut up.”

HC It’s interesting you say that, because, in my book, I try to talk about the dilemma that a woman faces between “be calm and carry on”…

MB You’re quite good at that!

HC Yes, I’ve had a lot of practice. You know, when Trump was stalking me [in the 2016 televised presidential debates] and leering and, oh, just generally trying to dominate me on this little stage, my mind was like: OK, I practised being calm and composed, you know, because that’s what a president should be. But, boy, would I love to turn around and say: “Back off, you creep.” But I didn’t, because I thought then his side will say: “See, she can’t take it. If she can’t take Donald standing there like the alpha male that he is, then how’s she going to stand up to Putin?” A ridiculous argument, but nevertheless one that might get traction. And, as you say, even your friends are like: “Oh, come on, don’t take the bait. Don’t take the bait.”

They have a good extended conversation about taking the bait, taking it and running with it.