A feminist Pirelli calendar and the rise of Donald Dump – the week in art

Pirelli has a bit of a gear change with Annie Leibovitz’s portraits. Plus a high-speed tour of Art Basel Miami Beach, and how Donald Trump the pottymouth sparked an art movement – all in your weekly art dispatch

Are the most expensive paintings ever worth their prices? A definitive ranking

On Monday, Modigliani’s Reclining Nude joined an elite band of artworks that have commanded over $150m at auction or private sale – but are they worth it?

Sex sells: why Modigliani’s 98-year-old hymn to lust is worth $170m

Painted through an absinthe haze as the first world war raged, Amedeo Modigliani’s Nu couché mixes modernist thrills with age-old hedonism. No wonder it still seduces

Ai Weiwei, Julian Assange and graffiti grannies – the week in art

Ai Weiwei and the Celts conquer London. Plus extraordinary outsider artists, endangered buildings and the real Alice in Wonderland – in your weekly dispatch

The Vatican’s new philanthropy app could ruin everything

The last time wealthy art fans did a Vatican restoration, they nearly destroyed the Sistine Chapel. The new Vatican app is elitism 2.0 – and will only endanger more masterpieces

The more time we spend glued to our iPhone cameras, the less we see

Apple’s iPhone 6 campaign is keen to remind us that we can all take beautiful photos. But while we stare into our screens we miss out on the richness of the world around us