What a gift to the biographers, what an inspiration to the innovators, is the life of mathematician and writer Ada Lovelace. A challenge to the playwrights, maybe, as programming and platonic love play such a part in her mythos. Fortunately, a play has been created that is as intelligent and tragic as its subject; and in where else but this city should action based on the thrilling currency of ideas (and the drudgery of slashed academic funding) receive its taut, moving European première? This is the second such première of Lauren Gunderson's work by ElevenOne Theatre, a company versatile enough to make manifest characters who are definitively 'not just one thing'.

This vivid, brief life (Lovelace died at 36) could've been realised in a one-person show like ElevenOne's Brief Lives, but it's from the tenuous relations between Lovelace and her co-characters that most of the heart-involvement is wrought, even though she's a woman who prefers numbers to people. It's an enigma that Chloe McKenzie is called on to play, from débutante ball to deathbed, but she acts as one full of life, animated by ideas (with the puppyishness of Doctor David Tennant or the 'pure imagination' of Ellen Page in Inception), a steely personality sure of her own mind, and intrigued by her absent father - Lord Byron. Her very mini-expression of curiosity, as her mother bewails the possibility of Ada inheriting his itinerant ways, shows how Ada would relish that chance to escape convention and find her own path. A star performance.

Gunderson is similarly inventive - with achievements unequal to her young years (yes, America's most-produced living playwright is 35. Permission to feel wholly unproductive), she has produced a script evocative of the period, alive to the era-less ripeness of Lovelace and her beloved co-dreamer Charles Babbage, and striking the balance between scientific correctness and emotion. Lovelace is sometimes awhirl with insight and calculation, sometimes ineluctably drawn to the much older Babbage in ways frowned upon by her mother and husband. Andrew Whiffin is at ease in a role combining diffidence, impotent fury, and a spectrum of love towards one by whom he is illuminated and almost eclipsed. Alistair Nunn is all punctured pomp as the undesired husband, channelling Miles Jupp but equally good when his grief transmutes into rage; Helen Taylor allows the mother to be restrictive but never monstrous, her inflexibility clearly resulting from wounds left by Byron. And Phil Weller brings a surprisingly quiet loucheness to this poetic titan, when he finally appears in Ada's imagination.

Lady Ada King, Countess of Lovelace is a character "made for storytelling" as Gunderson notes in our programme. It's brought to life in stagecraft and song. As the script transitions elegantly from the dramatic to the epistolary, we can tell that the characters are no longer sharing the same space. Annabella Byron encases her daughter in showy crinolines from the costumiers, and sends her to the 'marriage mart', which we only hear on tape. It was Lord B who coined that term, and whose licentiousness is used as a cautionary tale to make Ada conform. But in the end, his poetry and her prescient discovery commingle, entwined like DNA strands in a song which McKenzie, Whiffin and Weller voice very movingly - indelibly so, in fact. Sometimes drama earns the right to reach its emotional crescendi, and this is not only the mark of a faithfully realised script, but integral to the thesis. Poetry and science are not unacquainted; the head and the heart both deserve attention. Teaching us this is the woman who invented computer programming before computers had been built, thought them able to write music, and saw a future we're living in.

Ada & the Engine tells the story of the “towering idea” of the Analytical Engine, as nurtured through the collaboration between Ada Lovelace and Charles Babbage in the mid nineteenth century. Produced by the ElevenOne Theatre Company and directed by Ida Berglow Kenneway, the play opened this week at the Old Fire Station, and runs to the 23rd September. Its striking features are a meticulous sense of rhythm and tantalising theatrical chemistry, which is heightened by intimate staging. The set is compact, and carefully zoned: a sideboard with decanter and glasses, a garden bench, and two small desks (one of which is raised on a platform that looks, appropriately, like a segment of a cog) demarcate locations, all beneath a shining chandelier of perspex 1s and 0s. A gently steampunk vibe underpins the vision of this play. Elegantly simple lighting, and Jon Ouin’s airy yet mechanical soundscape, expand and shrink our sense of the stage as needed. Shifting between moments of realism and fantasy, the play is imbued throughout with a dream-like quality, despite being solidly rooted in history and science.

Playwright Lauren Gunderson is known for her work on the history of science, often focusing on the human drama and the story that narrates the uncovering of the principles of the universe. As she writes in the programme for this show, “a play is always about people not facts”. This is certainly true of this production, but Ada & the Engine is nonetheless meticulously researched. The play reproduces and riffs on real documents, including letters and most particularly Ada’s Notes on the Analytical Engine, which contain the first computing algorithm.

The play is woven through with documents and letters read aloud, delivered with lightness of touch and delicately precise timing. There are also moments of real humour, such as Alastair Nunn’s William King, later the Earl of Lovelace, whose excellent command of the comic potential of a pursed lip or raised brow provoked sharp, heady laughter from the audience. The relationship between the play’s central characters stands out in its vivacity. Charles Babbage was in reality 42 years old when Ada, only child of the marriage between Lord Byron and Lady Annabella Wentworth, met him in 1833, aged 18. The age difference is stretched further still by Andrew Whiffin’s presentation of him, which is admittedly just a little more twinkly than I had personally imagined the proud polymath. Yet the palpable, almost agonising, chemistry between Charles and Ada, is undeniable: they light each other up.

Ada, played by Chloe Mackenzie with stylised gestures and winningly earnest energy, presents herself as avian, fairy-like, and a little magical. She is received by both Babbage and Lovelace as an effervescent, sparkling presence. But Ada is also gauche, uninhibited, eager, almost tripping over her words in enthusiasm, and assertively, almost stridently, spoken: in short, full of complexity and substance. A “feminist before feminism”, Ada grapples too with the gendered expectations and restrictions placed on her, spending the entire play wearing a dress that she hates, and asking blunt questions such as, “why don’t men have to earn their freedom?” At the centre of this production is a hardwired fascination with the real woman that inspired it.

Ada & The Engine ultimately asks questions about how the language we use to record meaning can both conjure and preserve human presence, from poetry, to music, to mathematics. It traces the fascinating, changing interdependence between human codes and human lives. Far from a dry recapitulation of scientific history, this play is a sparkling and whimsical exploration of the passionate relationship between two visionaries and their shared dream of a machine that could think.