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What would your dream house look like? Think about it. And dream, baby, dream. Float down into the deepest sleep and stay there for a long while. You might begin to approximate the kind of dream that James Stewart had about 10 years ago, of a sumptuous house designed to liberate music and man.

This is a house that matters. Though it is still months from completion, the contribution of the Integral House to architecture here in Canada and places beyond promises to be immense. And so I bring this house to your attention now as a symphony of design, in which everything from the door handles to the windows has been contemplated and freshly cast.

Gimme shelter? Turns out there's more to a house than developers would have us believe. Look around at the carpet of sameness that has metastasized across North America. Radical departures from the norm are painfully rare; innovation and craft are regularly flattened by the steamrollers of convention. With the Integral House, however, we open ourselves to the dream of change.

This house -- designed by Shim-Sutcliffe Architects of Toronto -- is a singular treatise on the joys of the complex curve. Serpentine walls made of vertical glass separated by projecting fins of white oak form the gentle perimeter to the house, echoing the wisp of the creek in the valley below and the paths that wind from the back terrace through a forest of towering oaks, maple and beech. The architecture glorifies its ravine setting, with views of the majestic trees available from Rosedale's Roxborough Street clean through the house.

The client, James Stewart, is a mathematician and musical impresario who has gained a fortune by writing and selling around the world millions of calculus textbooks. In other words, he's done his math and decided that there's a compelling argument in favour of curves in architecture.

Years ago, Stewart took his idea for the house to Frank Gehry, the world's master of roiling form, and Gehry agreed to take on the project. Gehry's fees and the cost of building one of his bucking structures dissuaded Stewart, but he held onto his dream of commissioning an organic work of architecture. "Straight lines are really elementary," says Stewart. "They're boring. Curves are just more interesting."

But how to draw a curve without giving in to pornography of an excessively undulating line? Shim-Sutcliffe, admittedly, had never done much in the way of curves before Stewart's commission. But, one of the guiding lights for the practice has been the great Finnish modernist, Alvar Aalto, as much for his sensitivity to place as for his deft handling of scale, light, materials and, yes, designs that curve.

With confidence and restraint, architect Howard Sutcliffe has created architecture with the flow and energy of the 1936 Alvar Aalto design for the Karhula glassworks competition. Both are freely executed. And, just as the ravine has informed the Shim-Sutcliffe project, Aalto's organic designs were greatly inspired by the contour lines of hills and lakes so common to Finland.

Viljo Revell's design for Toronto's new City Hall had long inspired Stewart -- to be sure, an essay in curved restraint that blows apart the banality of the slab tower. And, as a junior fellow at Massey College, Stewart revelled in the craft and intimate magnificence of one of Canada's most exceptional modern works by Ron Thom. During the 1980s, he visited some of the works of Carlo Scarpa, the Italian architect who worked in visionary ways to revitalize historic buildings through articulated window frames and sculptural landscape interventions. At about that time, Scarpa's influence played importantly over the careers of Shim-Sutcliffe, heightening their interest in juxtaposing tough urban materials such as rusting steel against the lushness of wood.

That Stewart and Shim-Sutcliffe should have ended up together seems obvious -- a marriage meant to be. But it took years of patient searching before Stewart decided finally to hire them. Larry Richards, then dean of University of Toronto's School of Architecture, Landscape and Design, provided advice and guidance as Stewart's professional adviser. A list of 10 architects was established, with the idea of holding a competition among five finalists.

Once Stewart met Sutcliffe and Brigitte Shim, however, he abandoned the idea of the competition and hired them instead. Together with project architect Betsy Williamson, they have worked continuously on the house for 4½ years. The original commission on another Toronto ravine site was for two buildings, with New York architect Steven Holl designing a guest house on the property. But, after considerable study, the site was abandoned for a quieter location in Rosedale, and Shim-Sutcliffe was given full creative licence to create one house, one performance for Stewart.

Too often these days, architects give themselves body and soul to the monumental glass curtain wall. The results are blinding sheets of light and shades drawn against the harsh sun. But here the experience is one of transparency and near solidity -- it all depends on where you're standing in the house and from what angle the syncopated oak fins catch your eye.

From the street, the house presents as an L-shaped intervention that rises a discreet two storeys. The explosion of space occurs inside where the volume expands into five storeys. Stair, fireplace and elevator anchor the monumental space, extending from the lower pool level (where, by the way, 28-foot-wide -- 8.5-metre-wide -- windows can drop down into the floor by way of motorized controls, opening the swimming area entirely to the open air of the ravine) to the upper bedroom area on the fifth floor. The stairwell -- already a stunning volume of vertical space defined by finely poured concrete -- is to be covered on all four walls by a glass artwork cast in gradations of cerebral blue by Nova Scotia glass artist Mimi Gellman.

All door handles within the interior and the exterior have been custom-designed and modelled through computer-generated rapid prototyping, eventually to be cast in bronze. The front-door handle, says Stewart, resembles the letter S for a variety of reasons: "For simple figures like triangles and rectangles, you don't need an integral. You don't need calculus. But, as soon as you have curves, you need calculus and integrals. Volumes require double integrals, so the front-door handle will involve a double integral. The symbol for an integral is exactly the same shape as the sound hole of a violin. Historically, it's an elongated S for the word sum. S also stands for Stewart and Shim and Sutcliffe. There are many connections."

With the Integral House, Stewart establishes himself as a major arts patron in Canada. Like Phyllis Lambert, an architect who left her practice to found the Canadian Centre for Architecture in Montreal, Stewart has increasingly become a cultural impresario, after playing violin for many years with the Hamilton Philharmonic Orchestra and leading the McMaster Symphony Orchestra as concertmaster. In previous homes, Stewart and his musical buddies who were oftentimes also mathematicians would play together in impromptu concerts.

In May, 2008, in the Integral House's two-storey performance hall, the St. Lawrence String Quartet will play a composition by Vancouver-based Rodney Sharman, a work that Stewart has commissioned for the official opening of his house. The mathematician then plans to showcase promising young musicians in concerts for about 150 guests in his home. And he's also interested in having jazz concerts at home and maybe some cabaret..

"It's kind of the culmination of my life, really," says Stewart, who was the major naming donor to the James Stewart Centre for Mathematics at McMaster University and the library at the Fields Institute for math research in Toronto.

He plans to move into the lower section of the house this fall. "Having become this architectural buff, it'll give me great pleasure to walk down to my office to continue writing. Knowing what went into it, and knowing it's a very complex house to build will increase my pleasure."

The exhibition Integral House -- On Process continues at the Eric Arthur Gallery at the University of Toronto's Faculty of Architecture, Landscape, and Design, 230 College St., until April 28.