It's Catherine's birthday. She's 25, her father Robert (a languid Robert Pickup in flashback) has just died and she's worried she might be going crazy, not only with grief but through the cruelties of the gene pool. Robert, a mathematical genius who made all sorts of important discoveries in his early 20s, was more occupied in the twilight of his career with losing his mind and being waited on hand and foot by Catherine, sacrificing friendships, education and her misspent youth to do so.
Has Catherine inherited her father's sickness? His talent for numbers? Both? When, in one of the hundred-odd notebooks left behind in his study, the solution to a brilliant mathematical proof is found, Catherine claims that she, not Robert, wrote it. If so, she is a genius; if not, so Auburn's script suggests, it's to the asylum with her. But neither Catherine's sister Claire nor Robert's protégé Hal - nor, for a few tantalising scenes, the audience - are certain.
The proof of the title refers not just to the mathematical equation and to its disputed authorship, but also to the flipside of the need for proof - the importance of trust. Can you trust what you see? Can you trust what you're told or what you feel? How about the people around you or your own mind? These are nice meaty questions that Auburn raises, even if he does seek to answer them rather too patly for us.
More frustrating is the author's lost mathematical opportunity. Unlike in Michael Frayn's Copenhagen, set in the world of nuclear physics, the science is used more as convenient plot prop - and recurring joke at the expense of wild but still geeky mathematicians - than metaphor for mining any deeper meaning. And we certainly don't learn anything about this arcane field, except maybe that the last great female mathematician was born in the 18th century.
But none of the above detracted from my utter enjoyment at the Donmar, where 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 proof may not ultimately be here in the play, but it is in the production - all pudding.