Eduardo Souto de Moura at the Royal Academy

Eduardo Souto de Moura appears to be playing a game of peek-a-boo with photographers at the Royal Academy in London – the gag being that his bulky frame can’t really be concealed by the slender outline of an arch he has built there.

It is, in a way, the perfect introduction. Souto de Moura, one of Portugal’s greatest architects and, I’d argue, one of the few true greats of the modern age, has designed a pair of slim concrete casts of the inside of two of the RA’s huge doors, which stand like elegantly emaciated triumphal arches.

Most of the other architects in Sensing Spaces, which hosts large-scale installations from seven practices, have filled their spaces with massive pieces of work. Only Souto de Moura’s mentor, Álvaro Siza (with whom he shares a Porto office building) has done anything as thoughtfully sparse, inserting a few slight, yellow-painted, abstracted column fragments into the RA’s courtyard.

Why, when presented with these huge galleries, has Souto de Moura’s response been so minimal? “In his lectures [published as Six Memos for the Next Millennium] Italo Calvino said the future should be simpler and lighter,” he replies. “The story of architecture is just this, a progressive reduction in material. Houses used to be built with 2m thick walls, now this has been reduced to 4mm of double glazing. I thought I’d do these forms with carbon fibre, as thin as it gets, but it was too expensive so instead we cast it very thin in concrete.”

Souto de Moura has won architecture’s biggest prize, the Pritzker (in 2011, presented by Barack Obama) yet, unlike other recipients such as Norman Foster, Zaha Hadid, Frank Gehry and Rem Koolhaas, he remains far from a household name. Even within architecture he is more cult than star. He has eschewed the blockbuster museums, airports and offices that have become the currency of global architecture and, instead, developed an oeuvre based in his native Portugal that is careful, thoughtful and, on occasion, magically moving. From the smallest municipal market hall to the football stadium at Braga – perhaps the best amphitheatre built since the Romans – his buildings need to be experienced to be understood. Their simplicity and reductivism are not designed for the glancing culture of the internet or the photoshoot.

Souto de Moura, 61, is a bear of a man. Dark, bushy eyebrows surmount soulful eyes; glasses perched on top of his head hold back thick, greying hair while a short salt-and-pepper beard sprouts over his jowls. But his appearance is in contrast to the ethereality of his architecture on display here. The grey arches, one with a rounded head, another with a square, appear just apart from the doors, as if they had simply opened out from the frames. Their stony tone is reminiscent of Michelangelo’s slate-grey mannerist door surrounds in the Laurentian Library in Florence, devices to explain the meaning of a door.

But don’t talk to Souto de Moura about meaning. He is, determinedly, a modernist materials man. “Architects went wrong because they spent too much time talking about the meaning of things and not about the things themselves,” he says. “From Nietzsche and Heidegger and on into existentialism we see that the importance is in the existence of things and not in the deduction of things. Just as Wittgenstein says, ‘Whereof one cannot speak, thereof one must remain silent.’”

The thing Souto de Moura is most silent about is, almost heretically for an architect, space. “I don’t know what space is,” he says, becoming animated. “How can I design it? But I do know what a stone is, what it feels like. And I know that with it I can build a wall. That wall will change the space. With that wall I can solve a problem. And this is what architecture can do.

“I build to solve problems – not to provoke emotions or sensations.” Surely architecture, with its history, its language, its associations, its embodied memories, must be more than problem-solving? He does add: “If that wall causes emotions, then that gives me pleasure.”

Sensing Spaces is an immersive show in which the visitor is plunged into real architectural spaces, clearly designed to escape the conventions of an exhibition confined to second-hand renderings, models, drawings and films. Japanese architect Kengo Kuma has created an installation from bamboo filaments woven into a complex web of waves and curves. Diébédo Francis Kéré from Burkina Faso has built an archway of cheap honeycomb plastic panels (which visually work with Souto de Moura’s own arches). Chinese architect Li Xiaodong has constructed a labyrinth of sticks and mirrors leading the visitor around an illuminated floor, which gives the impression of early evening in an expensive Bali nightclub.

Chileans Mauricio Pezo and Sofia von Ellrichshausen have built what looks a little like a swollen oil platform in timber, an overscaled structure that lurks in a corner of one of the biggest galleries. Grafton Architects from Ireland has made a misjudged simulacrum of concrete brutalism, a heavy series of film-set fake concrete interventions deliberately destroying the delicate gallery spaces.

There are some real problems on display here. These may be spaces conceived by architects but they are somehow inauthentic as architecture – even less so than the temporary pavilions that have become the global language of contemporary architecture installation and that are, at least, usually freestanding and weather resistant. There is also, as ever with architecture shows in museums, a difficulty of confusing architecture with art, as the context transforms the content. Souto de Moura’s arches stand very much as objects in the gallery. Were they conceived, I ask, as art?

“It is an old debate, whether architecture can be art,” he replies. “I think it is not. When an architect sets out to make art it is always ridiculous. But because I am selfish I want to use projects to resolve my problems. I play with scale, with the forms. To me, this is a testing ground for ideas.”

And those ideas are simple, the stripping back of form and material. “If you take things back, always reduce, it can become something else. The same as the old. But less.

“I’ll show you.” Taking a piece of paper, he begins to sketch a section through the football stadium at Braga. The stadium is carved into the slopes of an old stone quarry so that when a match is on, poorer spectators can simply sit on the hillside and watch for free (Obama commented on the generous democracy of that).

“When I designed this,” he says, “I thought we could do it with no roof. Just air. Look …” he draws lines indicating wind blown from a machine. “The wind throws off any rain and we don’t need a roof. It’s quite easy. Then he draws a supporter on each stand, each with a banner: one for Portugal, one for England.

Then he adds numbers: “Portugal 2. England 1,” looking up from the paper with a cheeky grin. It’s just about what I feel when I think of Souto de Moura’s wise, worldly, sophisticated architecture and London’s increasingly clunky commercialism. Portugal 2, England 1.

‘Sensing Spaces’, Royal Academy, London, to April 6

royalacademy.org.uk