Essentially, topologists study the qualitative continuation of geometric space and shapes. Thurston’s 1970s conjuncture proposes that “compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures,” according to scientificlib.com.  Dai Fujiwara and his creative team were so immersed in topology that Thurston and his colleagues housed them in seminars at Cornell University, where he instructed. 

“Mathematics and design are both expressions of human creative spirit,” expressed Thurston during an interview at the launch of the collection in Paris. Miyake’s implementation of topology principles and mathematical anomalies are manifested through the robust curvatures and vigorous cyclical formations that characterize the majority of his garments, dating back to even his earliest creations. 

Topology wasn’t Issey Miyake’s first jab at implanting mathematics on the runway. Experimentation with origami was also heavily instituted in the brand’s core aesthetic. The symmetrical and geometrical nature of the art expression was replicated in the label’s “132 5” collection from the Autumn of 2010 season.

The collection was led by the brand’s subsidiary, “Reality Lab”, which is “a space devoted to nurturing the work of designers and engineers dedicated to interrogating the link between mathematics and fashion design,” defined bubblegum.com. The collection’s name is a play on numbers– 1 referring to the “one piece of cloth” concept, 3 referring to the garment’s three-dimensional shape, 2 identifying Miyake’s process of folding that 3D shape into a two-dimensional one, and 5 signifying the fifth dimension– when the garment is personified by the wear of it. This collection eradicated the cutting and sewing process of Miyake’s designs altogether and replaced it with the folding and molding practiced within origami. Another testament to his sustainable, conservative, and green design ethos.