Two superb exhibitions at Tate Modern bring into public view the work of Japanese artist Yayoi Kusama and Italian conceptualist Alighiero Boetti; their work is not in any way connected except that, with their singular voices, each deserves much broader recognition.

A show about lines: my tiny minimalist heart goes pitter-patter. And with good cause. Lines can be a bit blah – a quick scribble, and you’re on to the next thing. But they can also by their very simplicity, their irreduceability, lay bare some fundamentals, can draw a line under (yes, lots of “line” jokes available: line right up!) what really matters.

A remarkably tidy parade of thousands upon thousands of objects, neatly grouped into their categories – soap, plastic bottles, cooking pots and utensils, empty cardboard boxes, shoes, flower pots, gloves, string, to name but a few – Waste Not is a deeply disturbing yet affecting display of the obsessive accumulation of sheer stuff. These are the household goods of Zhao Xiang Yuan, the mother of the Chinese conceptual artist Song Dong, collected over five decades of family life. 

In a year of centenary celebrations paying homage to Captain Scott and the men who accompanied him to Antarctica at the end of the Edwardian age, two exhibitions in London have assumed pride of place. The Natural History Museum places a spotlight on the scientific achievements of the Terra Nova expedition. At the Queen’s Gallery two photographic archives capture with remarkable immediacy the sheer splendour of the polar regions.

As he readily acknowledges himself, Jeremy Deller can’t paint and he can’t draw, so he never went to art school. For many artists of his generation (he’s 46), this lack of traditionally based skills seems not to have presented a problem. But Deller clearly isn’t one for trying to be good at things he’s so self-evidently bad at, so instead of going to art school he studied art history, and then began to follow his interests. Luckily for him, and us, all the stuff that interests him falls within the periphery of what one might call art.

Hajj: Journey to the Heart of Islam is an exhibition about faith that even an avowed atheist might find rather moving. The last of the British Museum’s series of in-depth exhibitions exploring aspects of the three great Abrahamic religions, the exhibition attempts to shed light on what is, to outsiders at least, the most mysterious of religious rituals.

Conversations between artists both verbal and visual are the flavour of the month: the big voice of Picasso is almost but not quite drowning out a septet of British artists over at Tate Britain. Now joining the chorus is a fascinating exploration of the 1930s, in which the Brit Ben Nicholson and his Dutch friend and colleague Piet Mondrian are described by that hotbed of art history, the Courtauld, as "leading forces of abstract art in Europe”. 

He was uncompromising, honest, personal. He didn't like doing what he was told. He never followed fashion. Is this an accurate picture of Lucian Freud, or is it a description of almost every great artist who ever lived? The intensely banal voiceover for Lucian Freud: Painted Life on BBC Two which contained these insights (at least in the rough cut I viewed) made it seem like a painter out on his own, stringent in his artistic pursuit, was something we had never seen before. Thankfully the talking heads, intimates of Freud, created a properly personal portrait.

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.