A good half of the portraits in Russia and the Arts are of figures without whom any conception of 19th century European culture would be incomplete. A felicitous subtitle, “The Age of Tolstoy and Tchaikovsky”, provides a natural, even easy point of orientation for those approaching Russian culture, and with it the country’s history and character, without particular advance knowledge.

Once you’ve seen him, you can’t forget him. Taken in 1951, Paul Strand’s black and white portrait of a French teenager sears itself onto your retina. He stares unflinchingly back, and looking into his eyes, you feel almost scalded by his exceptional beauty and the piercing intensity of his gaze. With his chiselled features, Roman nose, curled lips and leonine shock of hair, he could be a classical Greek sculpture; and as though to affirm this association, his skin has the sheen of burnished bronze. 

The dazzling, controversial, fascinating exhibition In the Age of Giorgione at the Royal Academy inadvertently provides a striking example of an unavoidable and perhaps insoluble problem common to almost all exhibitions of painting – especially those with a high proportion of loans – in public museums and galleries.

Much is made of the mystery surrounding Giorgione, a painter of pivotal influence, about whom, paradoxically, we know almost nothing beyond the manner of his death. He died in a Venetian plague colony in 1510 aged about 33, and was as elusive in the 16th century as he is today, his paintings highly sought after but hard to come by, and by the time of his death already invested with mythic status.

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A gallery chock-full of Botticellian lips and tits is no place to start disputing the central premise of this show, that the Florentine artist’s paintings are woven into the fabric of our collective visual consciousness. From tuppenny ha’penny statuettes to a Dolce & Gabbana trouser suit printed with fragments of the Birth of Venus, Botticelli’s most famous paintings, whether in spirit, pastiche or frank reproduction, are everywhere.

Celebrating the four ages of man, eight huge, semi-abstract paintings create a carnival atmosphere in the Serpentine’s central gallery. The freshness of Childhood is characterised by flowers, petals and stamens floating on a blue ground. The passions of Youth warrant a ground of hot orange crammed with circles and spirals jostling for space like amoeba in a petrie dish. Adulthood is dominated by a large, yellow gourd-like shape on a lavender ground; dancing in attendance are looping letters and clover-leaf swirls.

Was Leonardo da Vinci (1452-1519), who straddled the arts and science in such a unique way, several hundred years before his time? Did the painter-inventor-engineer really draw the prototypes for, inter alia, the aeroplane, the motor car, the helicopter and the submarine, or were they doodles to which history has ascribed more genius than they are due? This small but interesting exhibition attempts to answer those questions as it places his mechanical works under scientific scrutiny.

It is an inspired pairing: iconic images by the American photographer Richard Avedon (1923-2004) and the painter, printmaker and filmmaker Andy Warhol (1928-1987), almost all of whose mature work was based on the photographic image. They are together in a large exhibition at Gagosian, Britannia Street, itself one of the largest and most elegant commercial art spaces in London, designed by that cultural architectural duo Caruso St John.

In Hell, the souls of the damned endure cruelly imaginative punishments for all eternity. Corrupt churchmen are buried headfirst in the ground with their feet set on fire, and soothsayers, who in life presumed to be able to see into the future, have their heads turned 180 degrees and are forced to walk around looking backwards. Drawn in metalpoint strengthened here and there with ink, Botticelli’s lines are as fine as spider’s silk. Sometimes barely there at all, their extraordinary refinement lends a strange, jarring intensity to the violence and terror they depict.