The weird, contrary, poignantly brief career of Alighiero Boetti, as introduced by Tate Modern’s new retrospective, is bookended by two absurdist self-portraits. The Italian artist was still in his twenties when he made “Me sunbathing in Turin 19 January 1969”: 111 clumps of concrete denoting the human form lying face down, featureless, adorned by a yellow butterfly, an image evoking the clash between a deadened industrial society and art’s potential for freedom and beauty.

Less than 25 years later, “Self-portrait” (1993), created shortly before Boetti died of pancreatic cancer, is a bronze depiction of a pitiful straggler in a baggy suit, holding a hosepipe sprinkling a jet of water on his head. A heating mechanism turns the water into steam, wafted from Tate’s balcony across the Thames.

Defeat and futility, or the glory of thinking and of idleness? With Marcel Duchamp as his model – that final jet of water pays homage to “Fountain” – restlessness, frustration, inefficiency, disorder are the leitmotifs of his oeuvre. “Annual Lamp” is a light bulb in a wooden box that turns on for 11 seconds a year – a portrait of the artist awaiting inspiration. In photomontages he presents himself as a pair of identical twins, one introverted, the other extrovert: Alighiero and Boetti. Yet, despite all these self-depictions, Boetti was an artist who wanted not only his marks but even his intentions to vanish.

He came of age with the arte povera movement, but dispensed with its materiality early: Tate’s opening room emphasises his preference for the flimsy and expendable: a paper doily column, a corrugated cardboard tower. He saw life as a “kingdom of papers”, teasing out philosophical games in pencil, ink or biro. In “Bringing the world into the world in Rome in the spring of the year nineteen hundred and seventy-eight thinking in the round” a thick biro surface suggests a sky, with commas sprinkled like stars.

Scores of such minimalist works here are dry, visually dull, but just as you dismiss Boetti as a cerebral joker, you turn a corner – Tate’s labyrinthine installation, mimicking Boetti’s tail-chasing mentality, invites diverse routes – to be arrested by the crazy mastery of the “Aerei” series: huge biro drawings, composed with assistants, of fighter jets, passenger planes, cargo craft, two-seaters, propeller engines, flying in every direction, without hierarchy or perspective, made “because today everything seems to me to be simultaneous”.

Boetti spent a lot of his life in the air, fleeing Italy, searching for a place “devoid of the cacophony of capitalism”. He found it in Afghanistan, a second home in the 1970s. He set up the One Hotel in Kabul – “creativity also means opening a hotel” – and commissioned Afghan craftswomen to sew his tapestry maps of the world, “Mappa”, with each country coloured according to its flag. “The embroidered map couldn’t be more beautiful,” he said, because “I did nothing for this work, chose nothing, in the sense that: the world is shaped as it is, I did not draw it, the flags are what they are, I did not design them. I created absolutely nothing.”

The highlight of this show is Tate’s display of a dozen such maps, made between 1971 and 1991, unravelling recent world history as events change the appearance of continents and countries. The maps also tell the story of their making: one has rose-pink oceans because that colour thread was in plentiful supply. After the Soviet invasion of the country, several contain Arabic texts reflecting the thoughts of the workers in exile in Peshawar. “Muslim mujahidin have lost their lives like butterflies …they have embarked on jihad and will persist until the last drop of their blood” are examples. As they dreamed, the workers – Boetti estimated that he employed 500 – also created his over-saturated “Tutto” (“Everything”) embroideries, satires on the excesses of late capitalism, from designs Boetti assembled out of advertisement images, abstract shapes, silhouettes of the Three Graces, business logos.

The embroidered maps and abstractions, sold to collections worldwide including New York’s Museum of Modern Art, are Boetti’s signature pieces. Graceful, lyrical, they retain, despite their dizzying polychromic surfaces, something of the poetic simplicity of arte povera, yet belong inescapably to a fleeting, late 20th-century historical moment when an artist could be at once a nomadic late romantic and a global businessman.

‘Alighiero Boetti: Game Plan’, Tate Modern, London to May 27 www.tate.org.uk

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