Mathematicians will tell anyone that’s listening that mathematics is a language, that once mastered opens the mind to infinite possibilities. That’s as maybe but like many this writer had immense difficulties with it. Much easier to appreciate are lines or more technically, geometry, a branch of maths concerned with the use space and size. Geometry, at its most basic interpretation, is at the core of Columbus with its dazzling architecture an odd though intrinsic part of this touching story.

Casey (Haley Lu Richardson) is a very bright student in Columbus who works in the local library and is generally content to stay in the town, with its remarkable architecture and at some point in the future become a guide. Others aren’t so enamoured with the small-town life as her friend Emma (Erin Allegretti) back from Holland sees no future there.

Into Casey’s life comes Jin (John Cho) who has arrived from South Korea to see his estranged father at the behest of Casey’s mother. Casey and Jin meet over a cigarette and become friends and confidants. As Casey takes Jin around the sights of Columbus, so they unravel to each other their lives and secrets. Jin has no love for his father while Casey seems wedded to a town and future that are not bleak but unambitious and wasteful of her talent.

In some senses this is a coming of age film as Casey has to make decisions and others around her have to accept their part in it. There’re long scenes between Jin and Casey – almost too long – where they discuss past and future. These are fascinating, subtle performances from Cho and Richardson that require some investment from the viewer.

This is all very calculated by writer/director Kogonada. There is very little camera movement and almost everything takes place within the frame. That set-up may initially appear dispassionate but as the film progresses the heart starts to beat and a warmth begins to radiate.

There is such elegance in the way that the seemingly incongruous spaces, structures and characters are observed and balanced. It is a stunningly beautiful film.