Still making a big noise: A season of Michael Frayn plays is set to reaffirm the brilliance of his work

There's more to come from this great polymath, says Paul Taylor

If there is one thing that is certain to be bursting out all over in the early spring, it is the theatrical mastery of Michael Frayn. In March, Sheffield Theatres unveil a mighty Michael Frayn season, masterminded by artistic director, Daniel Evans, and his associate, Paul Miller. In addition to a programme of rehearsed readings, it will consist of major revivals of a trio of key plays from the past three decades – Benefactors (1984), Copenhagen (1998) and Democracy (2003). There can be no better way of assessing how these works throw light on each other than by catching them at this cannily constructed festival where, on certain days, they will be playing across three auditoria.

Meanwhile, down south, there is the West End transfer to the Novello Theatre of Noises Off, Frayn's farce about putting on a farce that is now celebrating its 30th year of commercial and critical success. In April, though, we'll be given the chance to take a fresh look at his 1993 play, Here. Lisa Spirling's revival at the Rose, Kingston (with Alison Steadman on board) is its first significant airing since it flopped at its Donmar Warehouse premiere. I was in the tiny minority of critics who thought the play pulled off a delicious balancing act between deceptively profound playfulness and poignancy.

It will be fascinating to see it again because the piece now invites reconsideration in the light of The Human Touch: Our Part in the Creation of a Universe, Frayn's amazingly panoptic 500-page tome of philosophy, published in 2006. And not content to have excelled as dramatist, novelist, columnist and thinker, he has recently won the 2011 PEN/Ackerley Prize for best memoir. The book, My Father's Fortune, is a beautifully written, belated tribute to his father, Tom Frayn, an asbestos salesman in south London. It tells of the devastating effect on the family of the death of his mother, when the author was 12, and his father's slow recovery from the paralysis of grief. Is it a back-handed compliment, though, that it has nabbed a prize for best autobiographical writing? You can hardly leave yourself out when writing a biography of a parent and the effects on parents of their progeny is a much less often explored subject than the reverse. But where do you draw the line between portrait and self-portrait; foreground and background; the unduly retiring and the overweening?

That's just the kind of comical fretting over necessarily fuzzy demarcation disputes and criteria that Frayn's characters are temperamentally drawn to. And it is true, above all, about Here. A three-hander, it focuses on a young couple as they move into and colonise a room in the home of an elderly widow. For them, this space is a blank slate, their future a vertigo of choice. For the funny-sad interfering landlady, it's a museum of anecdotal evidence to support her view that those embarking on connubial bliss are not to be envied. Frayn's indecisive duo ponder such burning questions as where to position a toy dog. The man is given to brooding over such imponderables as whether, had the Earth cooled slightly differently 5,000 million years ago, you might well not be in this particular room with this particular partner. And because everything is so momentous, enjoying living in the moment is damnably tricky. He's an irritating and oddly moving object lesson in the impracticality of "practising" philosophy round-the-clock.

I've just reread a profile by me of Frayn that was published in these pages around that time. I am happy

to be reminded of such Frayn gems as "To be perfectly honest, what I feel bad about is that I don't feel worse", which exemplifies his acute comic ear for liberal humbug and his conviction that anything taken to excess can be dangerous, liberalism included. People who go to see Charlotte Gwinner's production in Sheffield of Benefactors, Frayn's Eighties play about a do-gooding architect of high-rise estates and his wife, will be treated to a marvellously sharp take on the déformations professionelles of being a card-brandishing liberal, culpably purblind with piety.

I still agree with most of what I said in the profile, but I realise now that I gave this author, who was then pushing 60, no leeway for growing in ways that might surprise us. This was a mistake because it turned out that his two greatest stage plays (indeed, two of the greatest plays of the postwar period), Copenhagen (1998) and Democracy (2003), were still to come at that point. Almost all non-science journalists use the phrase "quantum leap" inaccurately, as Frayn is ideally placed to know, being the author of a play that trains a brilliant eye on quantum physics both in terms of its history and outcomes and in terms of the way it can generate metaphors for capturing the deep mysteries of human motivation. So it's in the spirit of playful mischief that I claim that Frayn the dramatist made a quantum leap with this pair of works. Evans, prime mover behind the forthcoming Sheffield festival, reminded me of something that Nick Hytner, the National Theatre's artistic director, has said about this senior generation of playwrights – Frayn, Alan Bennett and Tom Stoppard. They have all made huge emotional and technical breakthroughs in their sixties and seventies, at an age when the received wisdom about a dramatist's career-span would have written them off.

A host of intriguing points emerged from chatting to Evans, David Grindley (director of the new production of Copenhagen), Henry Goodman (who is playing Niels Bohr in it) and Paul Miller (who is directing Democracy). Our perception of a play inevitably shifts with time and a changing context. It's amusing that Democracy, a play that is mordant about the ignominious alliances of coalition government in Sixties West Germany, is now revived in the throes of a wholly unforeseen British experiment in coalition governance. Moreover, it will be presented in a theatre smack in the heart of Nick Clegg's constituency. All were agreed that whereas the original audiences were dazzled, delighted and daunted by the rarefied cerebral pyrotechnics and the intellectual wit of these plays, the emotional undercurrents are likely to be more strongly felt this time round.

Copenhagen famously worries away at the question of what actually happened when Werner Heisenberg, the scientist who formulated the Uncertainty Principle and was the head of Nazi Germany's atomic bomb research, visited his Danish, half-Jewish mentor, Niels Bohr, in occupied Copenhagen in 1941. Why did the latter abruptly terminate their walk? Frayn could have set the play in 1947 when there was an uneasy re-encounter. Instead, in a stroke of genius that gives the play a haunting poetic dimension, he brought the two men, and Bohr's wife, Margrethe, back together in an afterlife of never-ending speculation and recrimination, where the question will nag on for all eternity.

It provides the perfect indeterminate context for Frayn's application of the Uncertainty Principle to Heisenberg's own hidden purposes. Why did he make the 1941 trip? Did he want to warn Bohr and the allies of Germany's atomic bomb project? Did he remain working for the Nazis in order, as he claimed, to be there to rescue German science after Hitler's defeat? Or does his refusal to emigrate leave him inescapably compromised with self-interest?

And don't jump to the conclusion that the ideas are drying up. Frayn just happens to be busy working on a novel. As he approaches 80, this magnificent writer would seem to be as fertile – and various – as ever.

'Copenhagen', Lyceum Theatre, Sheffield (0114 249 6000) 29 February to 10 March; 'Democracy', Crucible Theatre, Sheffield, 8 to 31 March; 'Benefactors', Studio Theatre, Sheffield, 1 to 24 March; 'Noises Off', Novello Theatre, London WC2 (0207 400 157) 24 March to 30 June; 'Here', Rose Theatre, Kingston (08444 821 556) 19 April to 12 May