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"He has the tenacity of a pervert," says Rem Koolhaas of structural engineer Cecil Balmond. "He finds it unacceptable not to go to the limit." Koolhaas, looking weary, has just flown in from China to introduce his friend and long-time collaborator to a packed house at the RIBA, where Balmond is receiving the Jencks Award for his contribution to architecture. The award's patron, writer Charles Jencks, has just said how strange it is that it should be going to an engineer. But Balmond gets up, the lights dim, and for the next hour, he casually enthrals the audience with his structural solutions to some of the most inventive buildings of recent times, punctuating each one with the words "no sweat". Perhaps it's not so strange then.

If you saw Marsyas, Anish Kapoor's 140 m long sculpture in Tate Modern, or last year's Serpentine Pavilion in Hyde Park, designed with Japanese architect Toyo Ito, or if you've seen the designs for Daniel Libeskind's spiral extension to the Victorian & Albert Museum, to name just a few, then you'll be familiar with Balmond's work. This 35-year Arup veteran and chairman of the firm's Europe and building division constructed his reputation through close and long-standing collaborations with headline-making architects: first "Jim" Stirling, then Koolhaas and more recently "Danny" Libeskind. But Balmond's conspicuous presence in their, and others', designs has made him hungry for recognition. But does he deserve it, or has his ego got the better of him?

The day after the lecture, Balmond is in high spirits. "I should have worn my national costume," he says as he strikes a dignified pose for the photographer. The Sri Lankan-born engineer is relaxed; he knows his talk went down well. Even though he assaulted the audience with number theory, there was an awed silence and nobody walked out. Soaking up the camera's attention, he cuts a distinguished figure with his caramel dome of a head and white parabola of a beard as elegant as one of his structural systems. It takes some imagination to picture him as a young man playing in "high-life" bands (a sort of pop-reggae) in Nigerian clubs. Balmond considered a career as a classical guitarist and can talk at length about trying to master Bach's Chaconne, one of the most demanding pieces in the guitar repertoire. Music is a big influence in his designs, and he talks about his approach as one that "allows structure to be animated - it slips, it jumps, it's got staccato".

Last year, Balmond did something unusual for an engineer: he produced a book of his works. Informal sold well and is now being reprinted for Christmas. Did he just have energy to burn or was this another step towards establishing the Balmond brand?

"The buildings were iconic; the architects were publishing them and becoming famous, and I just thought I should write about our contribution. It's not easy to get recognition, because architectural machinery is so much more powerful and geared to publicity … but it was Rem and Danny who pushed me into it."

In fact, Informal is Balmond's second book. The first was a sort-of novel, Number 9, in which he tried to convey some of the mystery of numbers (hint: multiply any number by nine and add up its digits). There are two more books in the pipeline – another novel and a book on pattern structures.

Informal networking is the term Balmond has given to his approach to structural engineering, one that he explains with fluency. "Informal because I don't recognise fixed systems of order, closed symmetries or assumptions of hierarchy, and network because I see structure as a connective part through pattern. How do I start a project? I look and feel for patterns."

Balmond is not shy about the role he and his pattern-hunting have played in the work of his famous collaborators. "I'm always bringing out the conceptual move in the first phase E E of the design and that's what Libeskind likes, what Rem likes. I'm reminding everybody why it's important to keep the conceptual up front, because in time it will get diluted – pragmatism comes in, you can't keep that pure concept." This sounds like a reversal of the traditional view of the relationship between architect and engineer, in which the pragmatic engineer grounds concepts in reality. "Sadly," says Balmond, "the standard picture is that the architect thinks of something and the engineer will calculate it all out faithfully – that's not what happens with me or with any good engineer. We conceptualise together, it's a two-way thing, there's no hint of territorialism."

Balmond sounds slightly peeved that the public doesn't grasp the extent to which the structural engineer can control the overall aesthetic of a design. Marsyas comes up by way of illustration. As he explains how the sculpture evolved from being secured at the halfway point to stretching right across the Tate's turbine hall, Balmond instinctively starts sketching it out on paper. "I said why don't we go the whole distance, why don't we go all the way. That's what we do, we act as a catalyst, challenge the assumptions, provoke a new direction, and if the architect or artist is imaginative and fertile, they rise to the challenge immediately, they impose challenges back."

Last year's Serpentine pavilion, ostensibly the work of Toyo Ito, was even more under his control. The whole design revolved around an bit of maths that he fed into a computer, manipulated and ultimately tweaked into a structural frame that was the final building. "It was a perfect example of my work in a way – the diagram was the architecture in one go, and I was really proud of it." Would he like to design a Balmond building? "Yeah, but strangely, I feel I do that often, although the architect's name is there."

This public dedication to the work hasn't always been welcomed by Balmond's collaborators. His structural solution to Foreign Office Architects' much acclaimed Yokohama International Port Terminal significantly affected the shape of the building, but his appraisal of his contribution landed him a letter from FOA's lawyer. The practice's Alejandro Zaera-Polo sounds pained as he recalls the incident, but plays down the collaboration as "only very preliminary".

I do believe the tide is turning, that engineering will be seen more inventively; the more we see art and science overlapping, the better

Other engineers clearly welcome the fact that Balmond is forging a path for them into the public consciousness. Some, however, question whether he is the right man to be holding the torch. Chris Wise, formerly of Arup and now head of Expedition Engineering, says Balmond's reputation rests more on being a shrewd businessman and dismisses his number theory as quackery. "If you went around and asked engineers who the top 50 designers were in the last 20 years, I don't think Cecil would be on the list," says Wise.

At the previous night's lecture, those few members of the audience not wowed by Balmond's journey into Fibonacci series and Mandelbrot sets started to raise their hands. Isn't it a bit esoteric? What about a building's functional requirements? Balmond knows that numbers and patterns could, were he not careful, descend into trivia, but he uses them as catalysts for organising space: "My fundamental concern is with people moving in and out of buildings."

Balmond currently oversees 1700 staff and, in April next year, he will become deputy chairman of the whole firm. Don't his administrative duties impinge on his ivory-tower pursuits? "It's a balance," he replies, "but I decided long ago that to further ideas you also have to have influence and if I had stayed purely creative that wouldn't have happened. At Arup, the front people are good engineers, and those who get the work in get to grow groups."

One of Balmond's pet groups is the advanced geometry unit, which spends a third of its time on pure research – directed by him. It also works independently on projects, such as this year's British Pavilion at the Venice Biennale, with David Adjaye. "The whole idea is to put Arup at the forefront of this work."

But with Balmond's numerological interests and rigorous mentoring, might he not be stifling younger talent? "I'd like to think I encourage free thinking, which is all that good architecture is," he says, looking slightly hurt. He goes on to explain how he has groomed younger designers to take over his roles: "I've grown a whole generation of people. Now Rory does Rem. I put Hamish together with Oscar Niemeyer and now he's taking his expertise on a lecture tour of New Zealand.
I mean, that's great."

Mentoring aside, Balmond has plenty on his plate. He's designing his first bridge – and the first "Balmond" structure – for Coimbra in Portugal, and has been working on Toyo Ito's Selfridges store for Glasgow. Another project he's immersed in is China's CCTV headquarters in Beijing (pictured right), designed with Koolhaas. Balmond describes the 5 million ft2 building as an "Everest of analysis … the sheer size of it scares the hell out of everybody". With the structural model in his hands, he lovingly traces the lines of his curving bracing system. "That shouldn't be structure," he says, "structure's used to going straight." Balmond is prepared to fly to Beijing at the drop of a contract, and Arup has just won the city's airport, designed by Foster and Partners.