Autistic savant teenager Nathan (Asa Butterfield) struggles to connect emotionally with the people around him including his caring and patient mother, Julie (Sally Hawkins).

He cannot process love or affection, and when the real world threatens to gate-crash his confusing existence, Nathan finds comfort in mathematics.

The lad's unconventional teacher Mr Humphreys (Rafe Spall) recognises Nathan's gift for numbers and he suggests that the teenager might be good enough to earn a place on a British team who will compete at the forthcoming International Mathematics Olympiad.

The camaraderie of the Olympiad could change Nathan's life forever, but first he must travel to Taiwan to train, taking him far away from familiar surroundings and home comforts.

In this alien environment, he encounters powerful feelings for a Chinese competitor, Zhang Mei (Jo Yang), and must try to compute the illogical joy of first love.