Architectural production relies on form that can be drawn, quantified, and analysed through geometry. The incorporation of calculus-based form in the 1990s and the more recent incorporation of physics simulation has pushed the edge of formal and mathematical analysis, as well as of architectural production. Yet, mathematics remains largely invisible in the current landscape – rarely addressed in discourse and hidden behind software interfaces in daily practice. As Antoine Picon has noted, architecture has unprecedented access to mathematical objects, while at the same time remaining indifferent to its relation to mathematics.

On 11 October 1935, the inauguration of the Slussen urban cloverleaf took place in front of the excited citizens of Stockholm. It had the attributes of a pure traffic machine taken from the most advanced traffic engineering publications, and it expressed the optimistic cultural modernism that five years ago the Stockholm International Exhibition had promoted.1 This urban cloverleaf was made of translucent glass, reinforced concrete, metallic handrails, and reflective tiles and was meant to solve, in one single gesture, the complex urban link between the Lake Mälaren and the Baltic Sea, between Gamla Stan – the historic city centre – and Södermalm – the southern district built on top of the 35-metre-high plateau [1]. The solution made difficult urban compromises between the foothills of the Brunkeberg topography, the smooth water surfaces of the Stockholm archipelago, the architecture of the historic urban tissue, and the demands of a complex articulated mobility. Boats, goods, suburban trains, subways, trams – later buses – pedestrians, cyclists, and automobiles finally converged on this place at different levels, completing the intricacies of a threedimensional geometry which, for the first time in history, was inserted into a compact city.

This article examines the work of Antonin Raguenet (1839–1920), who directed from his studio in Paris between 1872 and 1914 a vast project of architectural taxonomy, the Matériaux et documents d’architecture et de sculpture. Though unique in its vast geographic scope and empiricist approach, Raguenet’s project remains relatively obscure in the current scholarship of art and architectural history. Published monthly in eight-page pamphlets totaling over five hundred serialised issues, the Matériaux et documents ultimately contained over fourteen thousand illustrations of ornaments collected from buildings, plazas, monuments, and cemeteries across the European continent.

Raguenet’s ornamental gaze moves seamlessly from Haussmann-era apartment buildings, to universal expositions in Paris and abroad, to the façades of Lavirotte, Schoellkopf, and Guimard, reflecting the production and reproduction of ornament literature during the period of the Belle Époque. The collecting and cataloguing of architecture elements into categories – windows, cartouche, doors, capitals, balconies, etc. – is aided by the maturation of print media, the passenger railroad industry, and the rise of photographic reproduction in the late nineteenth century. This reading of the Matériaux et documents will introduce its context, contents, and methodology, as well as the role of ornament in imagining and observing the emergence of a new ‘modern style’ at the end of the nineteenth century.

Pruitt-Igoe, in St Louis, Missouri, United States, was one of the most notorious social housing projects of the twentieth century. Charles Jencks argued opening his book The Language of Post-Modern Architecture, ‘Modern Architecture died in St Louis, Missouri on July 15, 1972 at 3.32 pm (or thereabouts) when the infamous Pruitt-Igoe scheme, or rather several of its slab blocks, were given the final coup de grâce by dynamite.’ However, the magazine Architectural Forum had heralded the project as ‘the best high apartment’ of the year in 1951. Indeed, one of its first residents in 1957 described Pruitt-Igoe as ‘like an oasis in a desert, all of this newness’. But a later resident derided the housing project as ‘Hell on Earth’ in 1967. Only eighteen years after opening, the St Louis Public Housing Authority (PHA) began demolishing Pruitt-Igoe in 1972 [1]. It remains commonly cited for the failures of modernist design and planning.

The housing estate of Julino Brdo was built in the late 1960s in the Čukarica municipality of Belgrade, and housed the ‘middle class’ of Yugoslav selfmanagement socialism – managers, experts, and administrators, in an area that was also populated by the improvised homes of illegal settlers. Approaching the estate from the north, the observer first notices two clusters of homogeneous masses rising out of a plateau known as ‘Grujina Strana’. As the observer moves forward, the estate briefly disappears from sight, only to reappear as a single cluster merged with the steep sides of the plateau.

In This Is What We Do: A Muf Manual, the partners of the firm muf architecture/art wrote that ‘paradoxically, in order to make the thing the collaboration has to be about the making of the relationship rather than the object.’1 This article takes this assertion as its basis and examines the implications of treating the individual and collective relationships that structure an architectural project – which I will refer to as the project’s relational field – as a site that can be manipulated in order to affect both production and outcome. This is achieved through the transposition of concepts from Mikhail Bakhtin’s work on creative activity, art, literature, and language to design using a case study of muf’s Barking Town Square project in London (2004–10).

The article explores the interpretation of sustainability from the Japanese perspective. Drawing from four case studies, the article asks: how is sustainability interpreted in the context of urban regeneration in Japan? Two case studies (Musashi Kosugi and Kashiwanoha) are high-rise, high-density developments that use new building technology but have little or no attention to the context. UR Yokodai danchi renovation and Kamakura ‘regional capitalism’ are community-led projects that preserve the existing buildings and the local community. These four developments are analysed in relation to sustainability criteria that includes socioeconomic targets and conservation of the townscape. The findings suggest that although Musashi Kosugi and Kashiwanoha are prime examples of urban densification and the use of smart technology, challenges posed by the post-population peak society, oversupply of housing, and consequences of the pandemic question the flexibility and sustainability of these developments. Yokodai danchi demonstrates the potential of postwar housing stock to accommodate sustainable renovation and provide affordable housing. Kamakura ‘regional capitalism’, rooted in joint venture between the local governance, entrepreneurs, and old residents, middle-density and mixed-use urban fabric, can develop into flexible, idiosyncratic, and family-friendly environments. The research suggests that the Japanese government’s new policies such as Super Cities Program should not restrict the vision of sustainable cities to new build developments and that urban densification should not always be taken as a synonym to sustainable city developments.

In November 2004, the University of Cambridge announced its intention to close the Architecture Department,1 following a drop from a 5 to a 4 in the 2001 Research Assessment Exercise (RAE), which aimed to measure the quality of research activity across the Higher Education sector in the UK.2 Other departments in the University of Cambridge achieved a 5 or a 5* rating in the same exercise. In 2004 the University’s General Board, which oversees academic standards within the University, came to the conclusion that the Department of Architecture was making ‘insufficient progress towards meeting Cambridge standards in terms of research quality’ and advised that it should be shut down.3 While this remained a recommendation, with no official action having yet been made, the threat of closure sparked an outrage both within and outside Cambridge. After a campaign in the national press, the architecture department was saved [1, 2].

The Venice Architecture Biennale in 2010, curated by Japanese architect Kazuyo Sejima, co-founder of Tokyo-based practice SANAA, included a remarkable twenty-four-minute 3D film by the German director Wim Wenders depicting the practice’s Rolex Learning Centre in Switzerland. Entitled If Buildings Could Talk, the film ran in a continuous loop, without a tangible beginning or end, much like the building itself. Invited by SANAA to develop the film, Wenders found himself confronted with a new type of space that he had no prior experience of, and no vocabulary to describe: ‘The Rolex Learning Centre’, said Wenders during a talk given at the Biennale, ‘is more landscape than building.’