An unnamed extraterrestrial from a highly advanced, ultra-rational society who is sent to Earth on a mission. He occupies the body of Cambridge University mathematics professor Andrew Martin to erase evidence of a recent mathematical breakthrough. Initially repulsed by human physical forms, customs, and irrational emotions, he operates with strict logic but soon finds himself curious about human experiences like music and tasting peanut butter.

Isobel is a historian, an aspiring fiction writer, and the wife of Professor Andrew Martin. She bears the emotional weight of a highly strained marriage and acts as the primary stabilizing force in her household. Her interactions with her husband reveal years of neglect, yet she tries to support him through what she believes is a severe mental health crisis brought on by intense academic pressure.

Gulliver is the teenage son of Isobel and Andrew Martin. He struggles with severe depression, social alienation, and bullying at school. Harboring deep resentment toward his father for years of neglect and self-absorption, Gulliver reacts defensively to the sudden, erratic attempts at communication from the new version of Andrew.

A prolific mathematics professor at Cambridge University who recently solved the Riemann hypothesis. His intellectual ambition and obsession with his work led him to neglect his wife and son for years. His mathematical discovery inadvertently threatens the universal order, prompting the extraterrestrial intervention on Earth.

The Martin family's pet dog. Uncomplicated and expressive, Newton becomes one of the first Earth creatures the alien narrator successfully communicates with. The two share an unexpected affinity, bonding over walks and crunchy peanut butter.

A young woman with pink hair who is a fellow patient at the hospital where Andrew is temporarily held. Having been driven to mental instability by her intense reading of Schopenhauer's philosophy, she provides the narrator with early insights into human existential dread.

The Lucasian Professor of Mathematics at Cambridge University and a colleague of the real Andrew Martin. He is aware of Andrew's recent work on the Riemann hypothesis and serves as both an academic peer and a target of the extraterrestrial's mission to erase evidence of the discovery.

The wife of Daniel Russell. She is fiercely devoted to her husband and deeply concerned about his fragile health, demonstrating a raw emotional vulnerability that surprises the alien narrator.

A friend of the real Andrew Martin who invites the narrator to a Cambridge United football match. He assumes the new Andrew is fully aware of their shared history and past indiscretions, inadvertently complicating the alien's attempt to blend in.

A young university student who attends Andrew's mathematics lectures. She shares a prior, hidden connection with the human Andrew Martin and approaches the new Andrew with an intimacy that thoroughly confuses his alien sensibilities.

A teenager from Gulliver's school who actively bullies him. He represents the physical and social threats Gulliver faces in his daily life outside the home.