The old friends giggle as the photographer asks them to move ever closer. The RIBA HQ in central London is playing host to two of the foremost signature architects of the past 30 years, and they respond by embracing and mocking each other as they ham it up for the camera.

Toyo Ito and Massimiliano Fuksas have been pals for more than 20 years, despite the differences in their architecture - the Japanese designer defies pigeonholing, although many of his sculptural forms are inspired by mathematical grid systems, whereas the prolific Italian's work is identifiable by its rich colours and references to his predecessors. And in this photograph these sixtysomething legends of modern architecture are just minutes away from a gala dinner and two of the greatest prizes in the profession - for Ito, the Royal Gold Medal, for Fuksas, a RIBA international fellowship. Martin Spring spoke to Ito the morning of the ceremony, Vikki Miller interviewed Fuksas the following day, Eva Vermandel photographed them together on the night.

Toyo Ito and Massimiliano Fuksas

Toyo Ito and Massimiliano Fuksas

Credit: Eva Vermandel

The cerebral mathematician

It is 11am, and Toyo Ito cuts a very different figure to the kimono-wearing prankster that will be photographed eight hours later. Ahead of the gala dinner, the Royal Gold Medal winner is dressed in sober dark designer suit, and rarely breaks into a smile as he speaks in a composed and measured manner, albeit through an interpreter.

Royal Gold Medallists often have an architect-with-zimmer-frame image, retiring to bask in the glory of the supreme international accolade. Certainly he shows signs of his 65 years in the way he reminisces over how he met Fuksas - the Italian's wife, a writer, was enamoured by Ito's work and corresponded with him for an article, which eventually led to an invitation to speak at the University of Rome. In every other way, though, he comes across as an architect in the prime of his career.

A wiry, dapper man with a full head of black hair, an engaging manner and a ready laugh, he would easily pass for a man in his late 40s. Even more sprightly, Ito's 35-strong practice is not only still going strong, it's undergoing a radical transformation in style. "The practice is constantly contradicting itself," he says. "In the past, my architecture was light and transparent with a very pure geometry, like boxes. Now it's changing to a more organic architecture that expresses strength and nature."

His latest project is an opera house for Taichung, Taiwan's third city, for which he beat Zaha Hadid in an international design competition just before Christmas. It is a huge curvilinear honeycomb of a building containing cavernous spaces that flow into one another.

Ito’s 2002 Serpentine Gallery pavilion consisted of a mesh of angular columns and beams

Ito’s 2002 Serpentine Gallery pavilion consisted of a mesh of angular columns and beams

The practice's constant reinvention is acknowledged in the RIBA's gold medal citation: "We never know what he will discover or devise next, or how far he may push out the boundaries of architecture. In this way his activities seem to replicate those of the great Renaissance inventor-architects."

The fourth Japanese architect to win the Royal Gold Medal since the Second World War, Ito is less well known in Britain than fellow countrymen Tadao Ando, who won in 1997 and designed the retail crescent in Manchester's Piccadilly Gardens, Arata Isozaki or Kenzo Tange. In fact, Ito's only British project has been the temporary summer pavilion that is built every year at the Serpentine Gallery in Kensington Gardens. This seemingly random array of criss-crossing perimeter columns and roof beams was erected in 2002 and stood for just three months.

Ito belongs to the technophilic school of Japanese architects that spawned an extraordinary spate of space-age reimaginings of the city in the 1960s. Many were inspired by the Walking City fantasy of London's Archigram, whose leading light, Peter Cook, now serves on the Royal Gold Medal selection panel. Ito's particular fascination has always been structural grids. Right up until his latest projects, these have been based on polygonal geometry. The result was a series of extensively glazed, transparent buildings that were light in weight and bright in appearance.

Fuksas’ flagship Armani store in Hong Kong, completed in 2002

Fuksas’ flagship Armani store in Hong Kong, completed in 2002

Closely linked to his fondness for grids is a long-standing fascination with computer-aided design. "I founded my first office in 1971 with a friend who was a computer technologist. I designed architecture: he designed transport." Significantly, this first office went under the name URBOT, a portmanteau of urban robot.

He is very sophisticated and an intellectual

Fuksas on Ito

Four decades later, the same concerns influence his work. As he says: "Computer technology is a big influence on my architecture."

Paradoxically, it is precisely Ito's fascination with the highly artificial and rapidly advancing world of computer technology that has led him to his current love affair with natural forms. "Computer technology now allows architects to design very 3D, very organic forms," he says. "And it helps in structural design. That's a key change for architects."

Ito dismisses the idea that the green movement might be behind his rediscovery of nature. "These days I try to turn architecture into nature as a metaphor," he says.

Yet despite these poetic aspirations, Ito maintains his fascination for the practicalities and new potentials of building technology. "The quantity of glass in my buildings is being reduced," he says. "I am now using traditional materials such as concrete and steel but in quite a radical new way. For example, I designed a network structure using concrete. And last December, we completed a commercial building, the Tod's department store in Tokyo, where the external walls were made by pouring concrete between two plates, like a sandwich. The steel plates remained in position and just had a paint finish on the outside."

The Peres Peace Center, to be built from layers of concrete and glass

The Peres Peace Center, to be built from layers of concrete and glass

Ito's technological interests brought him together with Cecil Balmond, the London-based structural engineer and vice chairman of Arup. "Cecil is my best friend for developing ideas," he says. Balmond was behind the Serpentine Gallery project and joined in Ito's latest, most revolutionary project, the Taichung opera house, where Ito is attempting to reinvent the grid yet again. "The opera house is very complicated," says Ito. "The structure will be a combination of sprayed concrete and steel mesh to make it very thin." Balmond adds that this structural system is just an initial idea and might well transform into something quite different again, and no less revolutionary.

"I'm trying to invent a grid system with new rules," continues Ito. "In the 20th century, structural grids were just Cartesian geometry with straight lines. But I want to develop a 3D twisting grid. The idea is to create organic shapes that melt into nature. In nature, nothing is just straight lines, it's always wobbly and 3D. I call this the emerging grid."

Even with the Royal Gold Medal safely in the bag, Ito shows not the remotest sign of having an eye on retirement. The 65-year-old Ito can now concentrate on becoming one of the great emerging architects of the 21st century.

The creative force

Massimiliano Fuksas is relaxing in a pale blue armchair in the yellow haze that is Palm Court at the Ritz in London. It is the morning after the gala dinner at the RIBA and he passes on a titbit he has gleaned from his pal Ito the night before: "That's the first time he has ever worn a kimono."

Fuksas, on the other hand, doesn't seem keen to emphasise his national roots. "When I am in England, I am more English than an Englishman," he says, sipping tea from a bone china cup. He may be joking - it's difficult to tell - but it is this ability to mould his identity and take on a startling range of projects that has secured him a place in today's international architectural elite.

A regular at the Ritz, it is easy to get the impression that Fuksas, in a dark navy suit, embroidered grey cravat and expensive Italian shoes, is a jet-setting signature architect, who designs avant-garde buildings for high-profile clients. And that, in effect, is largely what he does. He is responsible for, among other schemes, Armani's flagship store in Hong Kong, Ferrari's research centre in Italy, and Vienna's Twin Towers.

Fuksas’ latest mixed-use scheme in Frankfurt

Fuksas’ latest mixed-use scheme in Frankfurt

But he is also responsible for the Peres Peace Centre in Jaffa, Israel, and has been commissioned to design the somewhat earthier delights of the new Hearts Football Club stadium in Edinburgh. Fuksas has sat on town-planning committees for Berlin and Salzburg and, last year, produced a critically acclaimed masterplan for the wholesale regeneration of Salford.

His work is very strong. He’s a strong person, too

Ito on Fuksas

Now Fuksas has his sights set on London. He has stated his intention to move to the UK capital for three years now, but won't come without a project - which, mysteriously given his credentials, remains elusive.

"The UK is in good shape," he says. "In the past 10 years, you have totally developed and changed the whole country. I love working in the UK - with your structural engineers like Arup and Buro Happold, and your contractors. My experience in the UK is perfect, actually."

In reality, his experience in the UK is limited to a framework for Central Salford Urban Regeneration Company. He has convincingly sold them a vision of a "secret garden city". The plan is to focus on the city's canals, green spaces and historical buildings and then throw in improved infrastructure and the odd modern architectural gem, thus discarding once and for all its reputation as Manchester's grubby sidekick.

Fuksas has attacked the scheme with all the gusto and conviction he can muster, but the internationally-renowned designer is not under the illusion that he has landed a plum job. "There are some dark spots," he says. "It's a challenging place - Urban Design for an area where there is a lost people. It's a difficult project and the end of the process is far away, but the process has at least been begun."

He is concerned that the proposed changes will gentrify the area beyond local residents' means and singles out developer Urban Splash, usually praised for its regeneration work and consultative methods, as a proponent of this.

Laughing uneasily, he criticises Urban Splash, aware that he is going against current opinion in the UK. He says: "It's a little bit strange. They have something that doesn't work and they have to be careful. The owners of land have become so important now it has become everything. This is weakening the community and it will suffer. I also think the quality of the building is ugly. We have to find a balance between the community and the developer."

Fuksas' wife and architectural partner Doriana, now settled in the adjacent blue armchair, is flicking through the paper and an Olympics article catches Fuksas' eye. "My proposal on the shortlist for the Aquatics Centre was my best project," he sighs. "But I feel fine that Zaha won."

He says he will definitely bid for other key projects in the Lower Lea Valley, but because the practice does not have a dedicated new business team - he is invited to do most of his schemes - he is unsure whether it will happen.

One project he is fully committed to is the Peres Peace Centre. Despite being commissioned more than 15 years ago, construction is yet to move much beyond the cornerstone. The £5.7m centre is entirely funded by donations and Fuksas insists it will serve as much more than just eye-candy.

He refuses to be drawn on whether he will join the potential boycott of construction companies working in the occupied territories, which has been begun by prominent British architects, but does admit that, in his mind, politics and architecture "live in the same world. Architects have to be critical - we play a critical role in society. The centre in Jaffa is a crazy dream but I want to see if it is possible. This could help people understand through architecture."

And Fuksas is determined to continue with this doctrine. He is currently waiting to hear if he has won a £200m scheme to design a campus for the African Institute of Science and Technology in Abuja, Nigeria. He is up against old friends Rem Koolhaas and Rafael Viñoly, as well as Olympics masterplanner Allies and Morrison.

This project has got Fuksas fired up because it challenges European architects to design a "genuine" African building. It also returns to a favourite theme of his - rescuing a forgotten population through architecture. "A lot of architects will work in Africa in the next few years," he says. "They have to, because we cannot have a lost continent." Whether it's the residents of Salford, Palestinians or the people of Nigeria, Fuksas will continue to use his ever-evolving identity to try to help people rediscover their own.

Head to head

What do you make of each other’s work?
Toyo Ito
 His work is very strong. He’s a very strong person too.
Massimiliano Fuksas Toyo’s work has lightness and kindness in it. He is very sophisticated and an intellectual. He’s a thinker and very intelligent. Toyo has been a friend for more than 20 years.

Which other architects do you most admire?
Will Alsop is a very old friend. I have known him for 25 years. He is a good architect and has always been a visionary. I am good friends with Wolf Prix and Renzo Piano. Richard Rogers is a very good friend of mine and Norman Foster is a nice person. He has had a very important life. Peter Cook is a very good friend.
I love him. He is so intelligent with a great sense of humour and irony.
Ito Rem Koolhaas. He's always fighting against society and breaking conventions.

What would be your ideal projects?
Fuksas I am very, very interested in the Serpentine Gallery pavilion because it is something that is a real experience. Architecture is an experience. Also, I would like to design a town for 300,000 people. I want to check if it is possible to create a critical mass where the quality of life is high and the people can be without fear but with pleasure and culture.
Ito My latest project is my dream project. We have just won an opera house competition in Taiwan with Cecil Balmond. We first worked together on the Serpentine Gallery pavilion.

How do you find working in Britain?
Ito Not so different from working in other European countries. But since I have not an office in Britain, the professional indemnity insurance is very high.
Fuksas I like the UK. You have creation in your economy and your economy can bring creation. It is one of the most exciting places for art, architecture and culture. The quality of building is exceptionally better than most other countries.