As an art student in the late 1990s, Conrad Shawcross stuck a “superstructure” of fishing rods, chairs and a kite on top of his blue Ford Capri and named the car the “Investigation Bureau into the Location of the Soul”. From here, you could “fish upwards into the clouds, fishing for your own soul”.

It sounds like a privileged public schoolboy joke, and it was. Educated at Westminster School, the University of Oxford and Slade School of Fine Art — plus training as a trapeze artist — Shawcross, 38, is the son of writers Marina Warner and William Shawcross and stepson of painter Johnny Dewe Mathews, who taught him to draw. In north London he had, he admits, “an enriched upbringing, an augmented childhood”.

Descending at the Clapton Pond terminus of the 38 bus in east London, I meet him at his home, the former stables for the horses that pulled the bus a century ago. Today, a concrete mixer churns outside; across a building site, rickety steps over mud puddles lead to a half-finished glassy studio, nine metres high, and a vaulted kitchen-living room where everything is wonderland-enlarged: cauldrons not saucepans, a jeroboam of Rioja, a giant box of PG Tips tea. Alongside a wooden rocking chair, skateboard and baby walker are soaring models of geometric shapes, diagrams of what could be ice crystals, a computer flashing circles of light: 21st-century Bohemia.

Unshaven, harassed, lithe, Shawcross darts in from the roof. Dressed for construction — jeans, trainers, smudged red T-shirt — he is dark-haired, dark-eyed, intense. He offers tea, poured from a big tin pot into wine glasses, and reminisces about the philosophical car — “It was very playful, a surreal reversal, a cross between Moby-Dick and Jaws” — as he shows me plans for what is surely its monumental successor, “The Dappled Light of the Sun”, opening at the Royal Academy next month.

The ice crystals turn out to belong to this sculpture of enormous welded steel clouds, or trees, or neural pathways — “I’m trying to refer to them by different nouns, I don’t want them to be one thing” — raised on rusty poles. Composed of 8,000 tetrahedrons which “keep radiantly going outwards”, this will form a canopy over the Annenberg courtyard for the Summer Exhibition.

Expect material shock — “as if scrap metal had been emptied into the courtyard, or a car wreck” — but also, Shawcross hopes, “beauty, subtlety, chaotic nature”. This installation referencing landscape will be complemented by one about structure: tetrahedrons — “The Greeks considered the tetrahedron to represent the very essence of matter” — stacked into erect forms in Inverted Spires and Descendent Folds at Victoria Miro gallery.

Molecules and metaphysics, geometry and the Greeks, mechanics and poetry: in the past decade Shawcross has had the most meteoric career in contemporary British sculpture. The youngest living Royal Academician, he is now at work on his largest commission, “Paradigm”, a 14-metre weathered steel sculpture that will stand outside London’s Francis Crick Institute, opening in October.

‘The Dappled Light of the Sun’ in production
‘The Dappled Light of the Sun’ in production © Marc Wilmot/Victoria Miro gallery

In the model before us, further tetrahedrons rise in a tower of magnificent instability. “It will be mammoth but very slender, just over a metre at the base but the top is wider than a double decker bus. The tetrahedron shapes get 10 per cent bigger as you go up. If you added another it would collapse,” Shawcross explains. “It’s called Paradigm after Thomas Kuhn and his idea that science advances by toppling the paradigm. There’s a sense of mightiness but also precariousness. Science builds upon itself but there’s also the moment when it topples itself. Collapse is part of progress, any life cycle needs collapse, decay, death. The Crick doesn’t like it, though, when I use the word collapse.”

For an institute of medical research, this is hardly surprising: perhaps the institute got more than it bargained for. “It’s not an arrogant sculpture,” Shawcross adds hastily. “It has totemic presence, but it’s about fallibility.”

From “Palindrome” (2008), a symmetrical machine inspired by quantum mechanics, with moving points of light drawing a diagram of a hole, to “Timepiece” (2013), where he reoriented Camden Roundhouse around a puzzle of revolving steel arms, Shawcross has sought to express abstract phenomena — time, black holes — in sculptural form. But I think his work really resonates because it distils our mix of awe and ambivalence about technological development — most perfectly in the shiny, steely robot he created in response to Titian’s “Diana and Actaeon” for the 2012 Cultural Olympiad: a vision of science, like the goddess Diana, as seductive, powerful, ruthless, and without human empathy.

‘Three Perpetual Chords’, in Dulwich Park
‘Three Perpetual Chords’, in Dulwich Park © Philip Vile/Victoria Miro gallery

Where do his ideas come from? “Sculpture and philosophy have so much in common; both rely on metaphor. Sculpture actualises metaphor. I dip into things, I read. I’m not an academic, I wish I was more of one. I’m a jack of all trades. I feel I’m tapping into eternal truths, ancient absolutes, harmonics, discoveries not inventions — the innate properties of the natural world and mathematics itself.”

A recent public commission — “Three Perpetual Chords”, looping forms representing the octave, fifth and fourth on the harmonic scale, inaugurated in Dulwich Park last month to replace a stolen Barbara Hepworth work — is “a visual realisation of a particular harmonic ratio”, he says. “In music your brain finds that incredibly pleasurable, I’m trying to reinvent that visually.” He is not a musician (“I’m uniquely bad, I’ve tried to play all kinds of different things”) but music is increasingly a reference point. For his “Manifold” series, in an exhibition opening in Salisbury, Wiltshire, next week, he shows a computer-designed sculpture based on an algorithm of a 9:8 ratio: the spiralling, blacked bronze piece “moves downward, entropy happens, it’s a picture of a chord falling into silence”.

I see such tough/tender pieces as continuing the lyrical abstract language of modernism — Brancusi, Anish Kapoor. Shawcross says: “I never tried to define myself within an art historical movement, but in terms of influence, it’s the rule-based artists: Sol LeWitt, Carl Andre. And Monet, the lily pads, going beyond the visible, creating a series of constraints. Monet’s lilies and Andre’s bricks should be in a show together.”

‘Manifold (9:8)’ at New Art Centre in Salisbury
‘Manifold (9:8)’ at New Art Centre in Salisbury © New Art Centre

Shawcross himself “would have been a terrible painter”, he says. “I don’t like the blank canvas, but when I imagined being an artist, I imagined a solitary life, me myself and I. Instead, I’m a director, overseeing many different specialisms and people.” He considered architecture as a profession but says: “I didn’t have the patience, and designing this place [his home and studio] reminds me how glad I am not to be an architect.” Yet, as for all prominent sculptors, colossal projects such as “Paradigm”, designed with structural engineers, verge increasingly towards architecture.

“In architectural work,” he says, “you surrender your ego and try to solve problems. It’s not me doing what I need to do, it’s about what a building needs, something people will love, that will have the wow factor, that people see everyday and have a relationship with.” Then, surveying his nearly toppling “Paradigm”, he looks light-headed: “There are no rules in sculpture, you can do what the hell you like, there are no building regulations, it’s completely wonderful that you can just get on with it.”

‘Conrad Shawcross: Manifold’, New Art Centre, Salisbury May 23-July 26; ‘The Dappled Light of the Sun’, Royal Academy, London June 8-August 16; ‘Conrad Shawcross’, Victoria Miro, London June 10-July 31; ‘Paradigm’, The Francis Crick Institute, London, from October; ‘Three Perpetual Chords’, Dulwich Park, London, permanent installation

Photographs: Anna Huix; Marc Wilmot/Victoria Miro gallery; Philip Vile/Victoria Miro gallery; Stuart Leech/Dulwich Picture Gallery; New Art Centre

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