How did a scandalous 19th-century countess help create the modern era of computing?

Ada Lovelace was a most unlikely computer pioneer.

Born in the early 19th century, this daughter of romantic poet Lord Byron was a scandalous socialite who became known as the ‘enchantress of numbers’.

In this Ada Lovelace documentary Dr Hannah Fry tells the enthralling tale of a life infused with brilliance, but blighted by illness and gambling addiction.

How did this aristocratic countess become a prophet of the digital age?