A story by the great Argentine writer Jorge Luis Borghes imagines a 20th century writer who plucks from the ether a word-for-word copy of Don Quixote written in 16th-century Spanish. Beauty and truth are eternal, after all, and exist beyond time – there is nothing new, really; only re-interpretations of the same vision. A remarkable example of this idea can currently be seen at the Atelier Brancusi, a small art gallery next to the Centre Pompidou in Paris: three sculptures by the Japanese artist Hiroshi Sugimoto displayed alongside Constantin Brancusi's elemental forms which comprise the Atalier’s permanent collection.

Sugimoto is well known for his photographs. They are beautiful creations, infinitely detailed images of the simplest of forms: sea and sky, for example, each occupying exactly half the frame, a million gradations of grey between water and air. In some of his earliest photographs, he visited art deco movie theatres in New York and simply left the shutter of his camera open for the entire length of a film. The screen shows us a square oblong of the purest light imaginable, surrounded by luminous empty seats.

A few years ago, Sugimoto discovered a series of plaster casts from the end of the nineteenth century in the basement of a Tokyo university. He realised that these casts represented a series of mathematical forms, created by German scholars as a pedagogical tools. Their curved surfaces were something seemingly created just for the creation of infinite gradations of grey if placed in just the right balance of light and shadow: it was easy to see why Man Ray had photographed them, and he thought he would too. Once again, Sugimoto’s photographs (two of which are displated in the Atalier) are striking in their purity of form: in fact, there is only form, against an inky black background.

But after creating these photographs, Sugimoto had a remarkable thought: why not try to re-create the forms themselves, using the most modern and accurate methods available today? He decided to employ precision computer-controlled electronic milling machines, accurate to a fraction of a millimetre. In the video accompanying the exhibition, he explains how the longest part of the work was actually the writing of the computer code to control the lathes.

Visitors to the exhibition are confronted with three sculptures. Two are long, thin, twisting forms; several metres tall and made of smooth steel surfaces, it is impossible to tell where they begin and end. In fact, they do neither such thing. In the description next to each, one can read the three dimensional equation from which the shapes derive and, sure enough, the culprit is a "plus or minus infinity": easy to write, impossible to realise. The third sculpture sits on a small mirrored ledge next to a window, a tapering asymptotic surface manifesting as an unsettling inverted cone disappearing off to infinity in both directions. All of these sculptures as well as the photographs of the original plaster casts occupy the space at the rear of the Atelier Brancusi in a very precise, calculated fashion. There is no tension between them: one almost thinks of a Zen garden.

That mathematical forms can be beautiful is not new; what is notable is the affinity between Sugimoto's shapes and the sculptures of Brancusi which occupy the same exhibition space. On his death, Brancusi left the entire contents of his atelier to the French government on the condition that everything be kept together. In 1997, a specially commissioned building opened on the square in front of the Centre Pompidou for this purpose. Natural light streams from skylights, and visitors can walk around three glass-fronted rooms filled with Brancusi's sculptures and all the tools he used to create them.

It's a curious universe. Each sculpture is a form reduced its purest elements, and then beautifully finished. This can produce some strange effects; in one celebrated story, customs officials insisted that import duty be paid to ship one of Brancusi's works because they were certain it was actually a machine part, a propeller blade or turbine rotor. Apparently the finish and form were too perfect.

In amongst the sculptures and tools are photographs. It was Man Ray who taught Brancusi to photograph (another echo here). In one image, resting on a small table in the recreated atelier, we see of two of Brancusi's colonnes sans fin (columns without end). They stand far back in the photograph against a cloud-filled Eastern European sky (I believe the location is somewhere well to the east of Paris, a monument that Brancusi had been commissioned to create). The resemblance between Brancusi's infinite elongated rhomboidal forms and Sugmoto's surfaces is striking, and when I noticed it I froze for an instant at the sudden illusion of a mirror where I thought there was a really a photograph.

We should not be really surprised, though. Sugimoto has written of the role of the artist as one of honka dori or "taking on the original poem". Science and mathematics are exactly that, a search for the truth (and yes, beauty) at the centre of things. It is not unusual that this path should intersect that of a great sculptor like Constantin Brancusi.

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“Mathematical Forms” runs until 12 February 2006 at the Atelier Brancusi in Paris (click here for more information). Admission is free.