Treasures from Budapest: European Masterpieces from Leonardo to Schiele, Royal Academy

'Sleeping Girl': 'A smile plays on her lips as if she is dreaming of a lover, whose scent, perhaps, she can still smell'

A rich goulash: an exhibition that will exhaust and delight

Treasures from Budapest – phew! It’s overwhelming. One staggers out quite cross-eyed and wobbly-kneed. There are over 200 works, for heaven’s sake. And so many Virgins: sweet-faced Italian Madonnas, austere Eastern European Madonnas, pallid German ones. There’s a tiny, exquisite yet unfinished Raphael Madonna, known as The Esterházy Madonna, since much of the collection of Old Masters shown here was amassed by Prince Nikolaus II Esterházy. Oh, and there’s the stubby-nosed, chinless Viennese one by an unknown altar-piece painter (such an arrestingly odd face; are her eyes actually going in the same direction?). She can’t compete in the beauty stakes, but you’re spoiled for choice in the line-up.

Art Gallery: Pordenone Montanari, An Italian Discovery

Pordenone Montenari: 'Il Pittore a la modella' (1978)

A reclusive painter comes out into the light. Is he a lost genius?

Our culture is hungry for stories of buried treasure, for the lost archive. So when something of startling value is brought blinking into the light after many years, it answers a romantic urge. Of course it doesn’t happen much any more, not in a digitised e-culture in which, like Puck in A Midsummer Night’s Dream, you really can put a girdle round the Earth in no time at all. Something interesting has just cropped up in Italy, mind.

Sargent and the Sea, Royal Academy

The great portraitist honed his craft on sea paintings

There’s a little-known side to the 19th-century American artist John Singer Sargent, and it is as far removed from the razzle-dazzle of his glittering career as a high-society portraitist as you can imagine. The artist who was famously described by Rodin as “the Van Dyck of our times” started his career emulating that great master of the seas, J M W Turner. He diligently honed his craft by painting dramatic seascapes, gentle coastlines and noble fishing folk. And if the 20-year-old Sargent couldn’t quite manage the roiling waves and lowering skies with quite the same level of brilliance as the English painter, he nonetheless possessed a quite remarkable artistic maturity. Turner, by contrast, couldn’t paint a convincing human figure for love nor money.

Alice Neel: Painted Truths, Whitechapel Gallery

Neel wanted to get under the skin of her sitters. Her unflinching gaze served her well

What a troubled life Alice Neel led. The death of her first child, a daughter, who died of diphtheria in 1928  just before her first birthday; another daughter lost to her estranged husband’s family in Cuba two years later (as an adult and a mother herself, the daughter, Isabetta, committed suicide); life as a single mother raising two later sons on welfare in the slum district of New York's Spanish Harlem; and a neglected but always diligent artist for much of the rest of it, only achieving fame and acclaim towards the end.

Tim Marlow Meets Terry Jones, Sky Arts

Terry Jones and Tim Marlow engage in a polite conversation about art

The former Python and medieval scholar chats about his favourite paintings

He may be a writer, a director, an actor, a historian, and, of course, a former member of Monty Python, yet rather than being a Renaissance man, Terry Jones is clearly a mediaevalist at heart. We know this not only because he has written well-received books on Chaucer and medieval history, but an amiable half hour spent in his company at the National Gallery shows us just where his sensibilities lie. He was the first guest in a series inviting celebs to talk about their favourite artworks and Tim Marlow, whose televisual style is so effortlessly smooth and mellow that you might mistake him for a brand of instant (decaff) coffee were it not for his serious, but never heavily worn erudition, proved to be the perfect host: unlike more excitable presenters in the genre of television arts, he never upstages his guests.

Close Examination: Fakes, Mistakes and Discoveries, National Gallery

'Dead Soldier' by an unknown 17th century artist was once thought to be a Velázquez

A genuine Rembrandt or a fake? The painting detectives lay out the secrets of their trade

When is a fake a forgery? When is it a mistake? And when is it simply not what it appears? The National Gallery’s second summer exhibition to focus on its own collection here examines the questions of attribution, using the latest scientific resources to back up – or contradict – tradition, connoisseurship and curatorial decisions, good and bad. The gallery is putting its own mistakes on show, and over the 170-plus years of its existence, there have been more than a few.

BP Portrait Award 2010, National Portrait Gallery

'Lila Pearl' by Thea Penna: 'a disarming and entirely empathetic portrait'

What are portraits for? You might find the answer right here

Last month, the National Portrait Gallery unveiled a huge, new portrait of Anna Wintour. Painted by Alex Katz, the celebrated New York Pop portraitist, American Vogue’s scary editor-in-chief is shown with famous helmet bob intact, but minus her trademark dark glasses. The picture depicts Wintour, whose icy blue stare could run a chill through you (she's known as Nuclear Wintour), against a sunny yellow backdrop –  which looks like an attempt to raise the temperature of that icicle glare. You pass it as you enter this year’s BP Portrait Award.

Art Gallery: Terry Setch - Lavernock

Terry Setch: The most underrated artist in Britain? Pictured: 'Viewing Lavernock Point', 2009

Sumptuous paintings of the post-industrial Welsh coastline from an underrated master

Terry Setch can lay claim to being the most underrated artist in Britain. Not that the Cardiff-based Londoner has been entirely neglected: acclaimed as one of Britain’s most powerful painters by his contemporary John Hoyland, he’s been garlanded with awards, granted a retrospective at The Serpentine and was recently made an RA. Yet Setch (born 1936) has still had nothing like the recognition he deserves as one of Britain’s most intelligent and inventive painters. And the crime for which he’s been sentenced to this relative obscurity: simply, not being based in London, but in Wales.

Art Gallery: Howard Hodgkin - Time and Place

Howard Hodgkin: 'The grand figure of British non-figurative painting'. Pictured: 'Dirty Weather' (2001)

Enter the colour-saturated world of an artist often compared to Matisse

Howard Hodgkin is unquestionably the grand figure of British non-figurative painting. Often compared to Matisse in his use of intense colour, he has always insisted that his paintings are not abstract. They allude, he says, to memories of people and places and states of being, so that his titles are what you would expect from a landscape artist or even, occasionally, a chronicler of modern manners: Dirty Weather, Spring Rain, Privacy and Self Expression in the Bedroom. And he often paints on unconventional surfaces, favouring wood rather than canvas, painting the frame so that we see the paintings more as objects than as two-dimensional surfaces. Tate Britain’s major 2006 retrospective surveyed his work over six decades, but a new exhibition, at Modern Art Oxford, is a tightly focused affair: paintings executed by the 77-year-old artist over the last decade, including a body of new work. They offer a window on to a brilliant, colour-saturated world.

Doctor Who: Vincent and the Doctor, BBC One

The Doctor tries to rescue Van Gogh from his demons, real or imagined

The Doctor Who crew are fond of their encounters with historical characters. In his time, and let's face it he has infinite supplies of it, the Doc has rubbed shoulders with Shakespeare, Charles Dickens and Agatha Christie, and recently weathered the Blitz with Winston Churchill. For this one, "Vincent and the Doctor", le Docteur voyaged back to 19th-century Provence to straighten out a puzzling temporal kink.