Proof, Donmar Warehouse, London <br></br>To You, The Birdie!, Riverside Studios, London <br></br>We Will Rock You, Dominion, London <br></br>Much Ado About Nothing, Royal Shakespeare Theatre, Stratford-upon-Avon

Superstar plus crazy old genius get the right result

External links

Donmar Warehouse online

Riverside studios online

We Will Rock You online

Royal Shakespeare Company online

The show's title is Proof and it couldn't be more appropriate. Ever since Nicole Kidman revealed her abilities in The Blue Room, treading the boards in London's Theatreland has been a popular test for Hollywood actresses, keen to demonstrate they are multi-talented thesps. Gwyneth Paltrow is the latest arrival. In this British premiere of David Auburn's Broadway hit, she plays a reclusive mathematics prodigy with understated skill and emotional conviction.

Paltrow's 25-year-old Catherine has to prove several additional matters. She has been stuck at home, caring for her mentally unstable father, a Chicago professor who used to be a genius specialising in prime numbers. After his death, she appears to be heading for a breakdown. Simultaneously, a post-grad called Hal (Richard Coyle) is enthusiastically combing through the numerous notebooks stashed in her father's study. Most are gibberish but one contains a theorem, a proof that (we're vaguely told) has defeated top brains for centuries. What Catherine then has trouble confirming is its true authorship. Her tentatively romantic bond with Hal is blighted by mutual distrust concerning plagiarism.

Meanwhile, her sister Claire (Sara Stewart) may be treacherously planning to have Catherine certified.

One might complain that this drama, which won a Pulitzer Prize last year, has nabbed some ideas from Arcadia and that Stoppard more illuminatingly drew parallels between scientific theories and human dynamics. Anyone wanting a maths lesson from Auburn will depart disappointed. However, his plot twists are neat, and he plays games with non-linear time, the remembered and the imaginary. There's suspense, too, as you try to gauge each character's reliability and Auburn clearly knows plenty about complex parent-child and sibling relationships. His combo of love, grief and social comedy is also a generally winning formula.

This production, directed by John 'Shakespeare In Love' Madden, for the Donmar's American Imports season, occasionally slips into sentimentality. Making the weathered porch (on which the whole play is set) revolve is a bit of a palaver too. But Madden's cast are a really fine ensemble, with no obtrusive star turn. As the lapsed genius, Ronald Pickup is warmly charismatic and sporadically crushing while Coyle – a superlative but never showy actor – is geeky and gentle.

Stewart's elder sister is frighteningly officious and Paltrow's Catherine – though glazed with despair – frequently flashes with wit, anger and competitive arrogance. Good stuff.

Far more experimental world-class fare is being presented by the London International Festival of Theatre. Mother-son relations have come to a pretty pass in To You, The Birdie!, the Wooster Group's characteristically wacky, post-modern and multimedia adaptation of Racine's Phèdre. In fact, the queen's illicit passion for her sporty (and here covertly gay) stepson, Hippolytos, keeps surreally transmogrifying into a badminton match.

This could be tiresomely pretentious and a couple of scenes do drag, but veteran director Elizabeth LeCompte ensures her company – including her off-stage partner, Willem Dafoe – create a wry and crazily fractured world that mocks the grand gestures of neo-classical tragedy and manages to be seriously disturbing.

Ancient Greece looks like a production line or recording studio: a steel cage rigged with mikes and video screens. A couple of dwarf palm trees jokingly hint at a more exotic location while an upturned hospital commode – where you might have expected a royal throne – suggests nightmarish dereliction.

Venus on vid (the disembodied head of Suzzy Roche) watches from on high as a merciless referee. Below, Kate Valk's riveting, lust-infected Phèdre judders around – corseted and with her crowned head proudly erect, only buckling at the knees. She's like some ceremonious Noh actress taken over by St Vitus's dance. And this is actually comparable with Racine's original alexandrines which are metrically strict while speaking of ruinous, burning desires.

Dafoe is extremely funny – and implicitly self-mocking – playing Phèdre's husband Theseus as a vain, ageing stud, grotesquely sucking in his withered six-pack until he looks like a vandalised Greek sculpture. Every step he takes is synchronised with thunderous reverberations – as much Monsieur Hulot as monolithic hero. Meanwhile, Phèdre's speeches are whispered by another actor and our protagonists appear split in two – standing behind low screens, half live, half on film. This is a playful but also haunting vision of divided personalities and of private fantasies versus public shows of propriety.

Back in the West End at We Will Rock You – the new mega-musical based round old Queen hits – you might just sing along to "Another One Bites The Dust" in the hope it proves prophetic. The songs themselves, from "Crazy Little Thing Called Love" to the anthem "Don't Stop Me Now", have stood the test of time pretty well. The sound quality is sharp, with Queen's Brian May and Roger Taylor joining Mike Dixon as musical supervisors. And Christopher Renshaw's cast includes some storming singers – not least Sharon D Clarke and young Hannah Jane Fox.

But Ben Elton's puerile, futuristic storyline – perhaps inspired by playing air-guitar in his bedroom – really ought to make this show die of chronic embarrassment. Imagine, man, it's the year 2302, right, and rock and roll has become just an occult legend. Instruments and live gigs have been banned on Planet Mall – that's, like, Earth, only ruled by an evil super-corporation called GlobalSoft which pumps out blandly manufactured music to totally docile citizens. Only one rebel kid, Galileo, can save mankind 'cos he is "The Dreamer" who's kind of mysteriously possessed and knows the long-lost lyrics of late 20th-century chart hits. Woah, how cool is that!

Mercifully, Elton is still capable of getting his tongue into his cheek, with some harking back to The Young Ones. Nigel Planer as a shambling wannabe-goth treats the nonsensical lyrics of "Bohemian Rhapsody" with clearly absurd reverence. Underneath the quips though, Elton is still palpably fawning. His predictions about the future are lazily myopic and this is also an ideologically fudged production. Oh behold, the wickedness of GlobalSoft's profiteering. Oh behold, the We Will Rock You merchandise on sale in the foyer. How hypocritical can you get?

Much Ado About Nothing in Stratford is miles more enjoyable, with a notably mature Beatrice and Benedick played by Harriet Walter and Nicholas le Prevost. Gregory Doran's RSC production is set in the courtyard of a peach-coloured Sicilian country villa in the Thirties. This romantic comedy does get off to an appallingly saccharine start – wheeling in a brass band, a cute school boy and the predictable jolly local on a bike. The dark central scenes could also more deeply change John Hopkins's jealous, arrogant Claudio and his reviled, innocent fiancée, Hero (Kirsten Parker). But overall this cast is buoyantly funny, with some priceless scurrying round hedges in the eavesdropping scenes. Clive Wood's camp Don Pedro is a charmingly silly prince, weeping with laughter at his own jokes.

Walter's verbal sparring with le Prevost touchingly masks old wounds and a tender heart. As Beatrice's warmth for Benedick blossoms, he proves an unexpectedly adorable, plummy old soldier.

k.bassett@independent.co.uk

'Proof': Donmar Warehouse, London WC2 (020 7369 1732), to 15 June; 'To You, The Birdie!': Riverside Studios, London W6 (020 8237 1111), to Thur; 'We Will Rock You': Dominion, London W1 (020 7416 6060), booking to 17 Aug; 'Much Ado About Nothing': RST, Stratford-upon-Avon (01789 403403), to 13 July