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LONDON THEATRE GUIDE review by Darren Dalglish
”Proof”, already lauded by critics for its Broadway production, now makes its British premiere at the 250-seat Donmar Warehouse. It also reunites Gwyneth Paltrow with director John Madden after the success of the Oscar winning film “Shakespeare in Love”. Gwyneth Paltrow is perfect for the part of Catherine. She plays her character in a vulnerable child-like manner and is utterly convincing with excellent timing and delivery. I hope she will make many more West End appearances as she is a natural. Richard Coyle, who has recently finished playing in “The York Realist” for the Royal Court, has again produced a sound performance playing Hal, a former student of Catherine’s father, who wishes to go through the genius’ handwritten notebooks for any mathematical finds, but also finds himself attracted to Catherine. Ronald Pickup as Robert, the father, also produces a competent performance and Sara Stewart is excellent as Catherine’s older sister Claire, who feels guilty for leaving Catherine to care for their father alone and now tries to amend by offering to care for her. "

THE INDEPENDENT review by Kate Bassett
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. 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.

BRITISH THEATRE GUIDE review by Philip Fisher
He [Hal] is a combination of sensitive human being and shy, geeky mathematical bit player, who idolises Robert. Richard Coyle, straight from success in The York Realist, is perhaps a little too attractive as the unshaven, nerdy Hal. However his real enthusiasm both in Catherine's company and when he can spot a mathematical breakthrough strike a chord.

THE TELEGRAPH review by Charles Spencer
"There is outstanding support too from Ronald Pickup as her dad, who never seems more sane than when going quietly bonkers, from Sara Stewart, lethally comic as the patronising older sister, and from Richard Coyle as the delightfully awkward maths nerd. The show must surely have a life beyond the Donmar"

THE INDEPENDENT review by Paul Taylor
"Now as she tries to come to terms with his death, Catherine also has to contend with a visit from her estranged currency-analyst, sister Claire, all overweening "concern" in Sara Stewart's very funny performance, and with the attention Richard Coyle's Hal, a geeky protégé of her father who is hoping to discover some mathematical gold in the notebooks he left behind."

GUARDIAN review by Arthur Smith
"The great Ronald Pickup plays Robert, the maths genius, with an intensity charged with despair and hope. Sara Stewart as the stable, less gifted of his two daughters makes a great job of transforming from an irritating shrew into a sympathetic and complex woman. Richard Coyle is splendid as the ambitious protege."

THE TIMES review by Benedict Nightingale
"Still, I enjoyed the jokes about the antics of nerdish theoretical physicists and mathematics geeks (represented here by a shy, likeable Richard Coyle), a category of person apparently given to drugs, hotel orgies, rock music and 48-hour boozing sessions."

THE DAILY MAIL review by Michael Coveney
"Apart from the pellucid Paltrow, we can also savour the wonderful performances of Ronald Pickup, attaining Lear-like stature, as her father, and curly-headed Richard Coyle (of Coupling on television) as the clever student Hal who helps her through the night. "

THE GUARDIAN review by Michael Billington
"Her sister Claire, a hardheaded New York currency analyst, is sceptical about Catherine's claim. And Hal, a maths post-graduate, cannot quite accept that this moody, withdrawn girl has evolved a theory that will set the scientific world alight. Out of these doubts, Auburn spins his play." "Ronald Pickup as Catherine's deluded father, Sara Stewart as her chic, heartless sister, and Richard Coyle as the wildly excitable Hal also give fine supporting performances."

WHAT'S ON STAGE review by Terri Paddock
"...Auburn's play is elevated by some exquisite acting. As Catherine, Gwyneth Paltrow (pictured) is captivating and genuinely moving in her grumpy bitterness and self-doubt. And her performance is matched by her British co-stars, all sporting spot-on American accents and clamouring gamely on and off Rob Howell's raised and rotating backporch set. Brimming with geeky enthusiasm, Richard Coyle's Hal woos both father and daughter sweetly, while Sara Stewart provides superb, scene-stealing comic relief as the sparky self-satisfied sister.

THE OBSERVER review by Susannah Clapp
"Auburn has a lethal competence: you can see his play, which is already bound for celluloid, eating up the West End. He times his major plot surprise perfectly. He produces a scatter of droll lines, deadpan-handled by Paltrow and Richard Coyle (who gives a nicely judged performance as the geek whom Paltrow finds 'well - not totally boring')."

THE STAGE review by Peter Hepple
Guided by evidently helpful direction by John Madden, Paltrow gives a spellbinding performance of a young woman tortured by indecision. There are times when she appears to be on the point of beginning a loving relationship with Hal, played by the excellent Richard Coyle. But there are others when she seems on the point of a fresh existence in New York with her manipulative sister Claire, played by Sara Stewart.

CURTAINUP.COM review by Lizzie Loveridge
Richard Coyle, fresh from appearing in The York Realist, with his mop of curls and tiny moustache is the geeky doctorate student, mathematician and hobby rock musician who gets involved with Catherine. Coyle is maybe rather too affable and less ambiguous than the playwright intended. He comes back not for the girl, but for the manuscript.