We're obsessed by it. Each and every one of us in our own, small way thinks of ourself as a mini anthropologist, whether that's by picking up on the quirky little foibles of the people we encounter each day, snapping a picture of the city's (narrow, but admittedly, very beautiful) landscape, or by documenting our daily lives online. Here's one theory for you: we're all generally quite positive people that collectively have a bright and sunny outlook on things. We can look at a high-rise building, a bus stop, our lunch, and see some beauty in the mundane.

Photographer Saul Leiter was a champion of this predilection, known for his wallflower-like observations of the nuanced beauty of urban life. Born in Pittsburgh, Leiter was a rabbi's son who grew up thinking that he'd follow in his father's footsteps, but instead moved to New York in his early twenties to become a painter. There, he ended up working as a photographer for magazines like Harper's Bazaar, Elle, and Vogue. He was a pioneer of mainstream colour photography but his work wasn't taken seriously, and it was only in the last decade of his life (he died in 2013, at the age of 89) that his photography began to garner widespread artistic traction.

The Photographers' Gallery is currently exhibiting a retrospective on Leiter with more than a hundred images pulled from his work from the 1950s-1970s, plus sketchbooks and ephemera. The exhibition is the artist's first major public show in the UK.

It's absurd that, for the majority of Leiter's life, his images were overlooked for the work of other photographers. Leiter's early ambitions to become a painter reflect in the sensibility of his photographs: in the highly aestheticised depictions of reality, the deliberations on colour and texture, and the arrested energy of his subjects – a sort of meditation on stillness and motion. Documentary photography of the city – and all life within it – has never looked so good.

Saul Leiter is at The Photographers' Gallery until 3 April.