Pablo Picasso is the presiding genius of 20th century art, the most influential artist in the modern period, lauded for his protean inventiveness, originality, individuality and overwhelming productivity. In 1934 poet Geoffrey Grigson declared that he was all the history of modern art, in 1942 the artist Jankel Adler observed that “Picasso, the greatest innovator of the twentieth century, has knocked on the door of every painter’s studio in the world”. Too true: his ghost is still present amongst art’s practioners and its audience.

Yayoi Kusama, one of Japan’s best-known living artists, has spent the past 34 years as a voluntary in-patient in a psychiatric hospital in Tokyo. Now 82, she was part of the New York avant-garde art scene of the Sixties, making work that anticipated both Andy Warhol’s repeated-motif “Cow Wallpaper” and Claes Oldenburg’s soft sculptures. Her nude happenings included orgies and naked gay weddings, over which she presided fully clothed like a psychedelic high priestess.

The work of the photographer, theatrical designer, narcissist, snob, careerist, and exceptionally talented Cecil Beaton (1904-1980), including 18,000 vintage prints, negatives and transparencies, contact sheets and 45 books of cuttings are at the Victoria & Albert Museum. They have all been brilliantly culled for the alluring and significant exhibition of some of Beaton’s royal portraits, billed as A Diamond Jubilee Celebration. 

Sitting for Lucian Freud was quite a commitment. Unlike Hockney, whom he painted and who painted him, Freud was a very slow painter and he was methodical. Paying close attention to detail and absorbed by different textures, he was intent on building up surfaces meticulously, layer upon layer. This meant that sessions would usually go on for several months, sometimes years.

Billed as an exploration of the contribution made by immigrants to British art, Migrations is ridiculously ambitious. Starting with the sixteenth century, it hops and skips through to the present day, inevitably leaving out a lot of people on the way. Hans Holbein who settled here in 1532 and, as the King’s Painter, produced that splendidly iconic portrait of Henry VIII, which establishes the monarch’s authority by making him look as square and solid as a rock, is not included.

It has been nearly a century since modernism decreed that “art” is whatever is produced by an artist, and “an artist” is whoever claims to be one. Mostly I agree with this, and my eyeballs tend to roll back in my head when the conversation moves on to the “my three-year-old could do this” refrain. But I’ve got to say, with David Shrigley, a lot of me spent a lot of time in the Hayward thinking, “Um, is this art?”

Turner and the Elements is a visual joy and an intellectual pleasure. The backbone of the selection is Turner’s genuine engagement with the scientists of the day. The argument is that he amalgamated the traditional segregation of the elements – earth, air, fire and water – into a fusion of all four; that technically, instead of schematic compositions divided into discernable sections and monocular viewpoints, he painted, so to speak, from the centre out.

In one small room of the Freud Museum, which was once the home of Sigmund in the last year of his life, are the works Jane McAdam Freud made in the final months of her father’s life. Below an imposing photograph of Freud the elder, the progenitor of the clan, are two detailed, tender sketches of Lucian in profile. In the right sketch the dying artist stares resolutely ahead, his gaze, coupled with the firm set of his jaw, capturing a sense of absolute stillness. The left sketch shows the artist now more gaunt, eyes closed, in death, we imagine, or possibly just asleep.  

These are, we are told, David Hockney's landscape works, and in that they depict the outdoors - early Grand Canyons and LA scenes, Yorkshire from the Nineties to now - that is correct. As a description, however, it comes nowhere near encapsulating the mystical, profound, plain beautiful pictures presented at the Royal Academy.

It’s safe to say that the diary of Tryggve Gran does not capture the mood of this centenary exhibition. “This life is of little interest," he wrote; "one day is just as monotonous as the next.” Gran was the Norwegian hired by Captain Scott to teach his men to ski and was in the party which discovered the frozen bodies of Scott, Edward Wilson and "Birdie" Bowers. On the sledge which Scott and his exhausted men had hauled through nearly 1,000 miles, they found 30 pounds of geological specimens. Gran hazarded a sceptical note: “I think they might have saved themselves the weight.”