In the film of the English Patient, Ralph Fiennes' character Almásy can't be separated from his copy of Herodotus' Histories. But in our ever more pressured efforts to educate future generations, is it time to leave the Greeks behind?

Last night, I was witness to a chromosomal abnormality at the Royal Society that speaks to this situation. In one of its rooms, the L’Oreal/UNESCO Women In Science Awards were handing £15,000 each to four young researchers, to spend on “whatever they may need to continue their research, from buying scientific equipment to paying for childcare or travel.” A few paces away, in another room, an all-woman panel and a female chair discussed the merits of Athenian democracy.

It’s lucky the unusually large number of women didn’t create a queue outside the toilets. That would have given them a chance to cast their eyes over a display showing off the Royal Society’s 44 new fellows for the year. Just two are women.

When that was announced back in April, Cambridge University’s Athene Donald, chair of the judges for the Women in Science Awards, declared it “deeply disappointing”. But the scientists should take heart: at least the Society is helping to address this imbalance. It’s not clear that the Athenians are much help to the beleaguered heiresses of their tradition.

While last night’s prizegiving was in progress, an audience invited by the University of Durham’s Institute of Advanced Study listened to enraptured discussions of the unparallelled public involvement in the running of Athenian society. The audience also enjoyed the irony that the five enthusiastic classicists leading the discussion on this pioneering democracy would not, being female, have been allowed to vote.

The classicists believe the merits of the Athenian system – its ethical codes, its theatre, its citizenry – illustrates exactly why schoolchildren should be studying classics. Perhaps, though, Labour MP Andy Burnham had a point on the BBC's Question Time programme when he criticised Michael Gove's idea of an English baccalaureate that “found room for Latin and ancient Hebrew, but not for engineering or ICT". With a limited timetable, should we spend more time looking where we have come from than where we are going?

That depends on the merits of each. The Athenians are certainly fascinating – especially to someone like me, who knows his superconductors but not his Sophocles. I’m left wondering, though: is there any evidence that studying them has shaped our world for the better?

We heard much last night about how Athens gave us drama and the theatre. Panellist (and classicist) Charlotte Higgins, chief arts writer at the Guardian, declared when theatres want to do something dangerous, or politically subversive, they go back to the Greek plays, which teach moral lessons to do with leadership, responsibility, accountability and good decision-making. But our political classes, I would suggest, seem to have evolved immunity to such proddings from the stage.

A fixation with the Greeks may even have done harm: Higgins confessed she had spent the day writing about the misogyny of the London stage; female actors are struggling to find work. The spirit of Athens lives on in the arts, then: the original Greek actors were exclusively male. The actors' union, Equity, has asked 43 artistic directors of theatre companies how they are planning to improve the lot of female actors. Only eight bothered to reply, a response Equity has described, perhaps channelling Athene Donald, as “disappointing”.

Perhaps it’s a scientist’s bias, but I don’t see that the answers to modern dilemmas will necessarily be found in the study of ancient societies. Modern science owes a debt to millennia of thought in which the Greeks played a crucial role. Modern political, moral and philosophical thought owes a similar debt to the Greeks. But application is key: it’s no good knowing it all, but not putting any of it to work to change – if I may use a classical phrase – the status quo. That’s why I have to applaud the Royal Society – which is actively working to make science more female-friendly – L’Oreal (while urging them to stop putting chemicals in animals’ eyes) and UNESCO. Four female scientists are today finding the playing field a little more level than it was yesterday. My suspicion is that London’s female actors will still be fighting for equal work opportunities for a long time to come.