Actors clothed in chunky mirrored circles and triangles from Josiah McElheny’s “Interactive Abstract Body” sculptures (2012) were darting between visitors, reflecting the ever-moving crowds, at the launch this week of Adventures of the Black Square, the Whitechapel’s ambitious exhibition marking the centenary of Kasimir Malevich’s famous painting. Abstracted interpretations of the human form, McElheny’s glassy performative creations on one hand look straight back to Malevich’s grappling with the limits of representation. On the other, they joke that modernism has become just another fashion statement.

Can radical art maintain momentum as it is co-opted by history and the market? That is the question the Whitechapel poses in its elegant account of how geometric abstraction became a language of social and political resistance across the world.

Rich and unexpected, the show winds a curious path through international minimalism, taking in works as diverse as Fernand Léger’s parody of the mechanisation of daily life, “Ballet Mécanique” (1924), Dan Flavin’s soaring fluorescent tubes in homage to Russian Utopianism “ ‘Monument’ for V Tatlin” (1966-69), Nasreen Mohamedi’s 1970s taut, intricate abstract drawings strung through fine parallel lines and constructivist-inspired photographs of Indian buildings, and Liu Wei’s neon grid canvas “Purple Air” (2014) evoking changing 21st-century Chinese urban landscapes.

In this company, how affectingly small and fragile are the paintings by Malevich that open the show: “Black Quadrilateral”, “Red Quadrilateral” and “Black and White. Suprematist Composition”, with their wobbly, uneven, hand-drawn borders and now cracked surfaces. First displayed at 0.10 The Last Futurist Exhibition in Petrograd (now St Petersburg) in 1915, they resound with a century of myth and conceptual mystique, but close up it is their simplicity and restraint which astonish.

Although Malevich declared they marked the end of painting, they are beautifully made, the uncompromising monochrome intensity offset by subtle alterations of texture and impressions of weightlessness and space: idealism packed within cosmic dreams about flight into new worlds.

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