Camille Silvy may be the least recognised of all the great photographic innovators of the 19th century. After a decade of almost ceaseless technical innovation, and astonishing output as the society portrait-photographer of the 1860s, he abruptly closed his London studio, aged only 34, returned to France, and, after a brief stint in the garde mobile in the Franco-Prussian War, spent much of the rest of his life in and out of asylums.

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.

I must admit that I enjoy killing things and, since the target of my murderous instincts are clothes moths, fruit flies and, occasionally, rats or mice, society condones my bloodthirsty instincts. But while I get some satisfaction from my exploits, the women in Paula Rego’s drawings and prints appear to go about their murderous business with a mixture of resignation and detachment. These things have to be done, their world-weary faces seem to say, let’s expedite them with as little fuss as possible.

It’s not often you find yourself in an art gallery with the business end of a bullwhip whizzing inches from your nose. Wielded by a disconcertingly slight, black-haired woman who can barely be half its length, the terrifying instrument defines the dimly lit space with its whirling undulations and earsplitting crack, sending the gaggle of spectators cowering into adjacent rooms. Why there is also a grand piano present is probably only entirely known to the unnamed artist who brought this trickily titled exhibition into being.

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.

It takes a lot of work to make a show look as unconsidered and chaotic as this one: thought and care and time and attention all have to be paid before something so random can be achieved. But as so often with Tillmans, the nagging questions persist: is randomness, are the offhand and the casual, valid as ends in themselves? Because Tillman’s über-hip affectless cool has become very tiresome indeed. Even worse, it’s becoming predictable and dull. Tillman's eye, as ever, remains wonderful, but I remain doubtful about the form in which he chooses to convey his ideas.

It took Picasso four years to learn to paint like Raphael, but it took him a lifetime to paint like a child, or so he said. For Brancusi it wasn‘t a case of relearning childhood, but of being careful not to lose it in the first place. “When we are no longer children we are already dead,” he said.