It will be directed by Nicholas Hytner, in his final production as director of the National Theatre. It will be broadcast to cinemas as part of NT Live April 16.

In the play, Hilary, a young psychology researcher at a brain science institute, is nursing a private sorrow and a troubling question at work, where psychology and biology meet. If there is nothing but matter, what is consciousness? This is "the hard problem" which puts Hilary at odds with her colleagues who include her first mentor Spike, her boss Leo and the billionaire founder of the institute, Jerry. Is the day coming when the computer and the fMRI scanner will answer all the questions psychology can ask? Meanwhile Hilary needs a miracle, and she is prepared to pray for one.

Hilary will be played by Olivia Vinall, who recently played Cordelia in King Lear and Desdemona in Othello at the National. The cast also features Vera Chok, Jonathan Coy, Damien Molony, Lucy Robinson and Parth Thakerar.

The production will be designed by Bob Crowley, with lighting by Mark Henderson and sound by Paul Arditti.

The Hard Problem is Stoppard's first play for the stage since Rock 'n' Roll (premiered at the Royal Court in 2006, before West End and Broadway runs). The National has previously presented Stoppard's Rosencrantz and Guildenstern are Dead, Jumpers, On the Razzle, Rough Crossing, The Real Inspector Hound, Arcadia, The Invention of Love, The Coast of Utopia and Every Good Boy Deserves Favour (written with André Previn). Other plays include Travesties and The Real Thing (which is being revived on Broadway this season). Public booking for The Hard Problem opens Oct. 23. To book tickets, contact the box office on 020 7452 3000, or visit nationaltheatre.org.uk.