A mysterious host, going by the name Fermat Federico Luppi, invites a handful of the nation’s top mathematicians to a private gathering. Each participant must solve a puzzle to earn an alias drawn from famous mathematicians or philosophers, and they are strictly forbidden to reveal their true identities. They are instructed to arrive at a precise place and time, alone and without a cell phone, to wrestle with what is described as “the greatest enigma.”
At the appointed hour, four individuals converge at a riverbank: Galois [Alejo Sauras], an earnest young man; Hilbert [Lluís Homar], an older, calculating man; Pascal [Santi Millán], a modest, quick-witted youth; and Oliva [Elena Ballesteros], a stylish and perceptive woman. At dusk, a car on the far side of the river flashes its headlights, signaling the start of a strange journey. A PDA appears in the car, offering GPS coordinates and travel instructions that guide them to an abandoned warehouse. Inside, a back room has been transformed into an elegant parlor, with a large dining table set for five and shelves of books that give the space a timeless, academic air.
An elderly man enters and announces himself as Fermat. The group spends time mingling and discussing academia, mathematics, and the puzzles ahead. Fermat mentions a daughter and leaves in a rush after a troubling phone call he can’t fully interpret, forgetting his coat in the scramble. Fermat’s wallet falls from a pocket, and Pascal notices a photograph of a girl inside.
The PDA presents another puzzle with a one-minute timer. Hilbert, Oliva, and Galois struggle to meet the deadline, while Pascal breezes through the challenge, dismissing it as an old cliché. The walls of the room begin to close in as the time slips away, and the group realizes they are trapped. The device continues to flash new puzzles, and as they work, tensions surface: Oliva and Galois share a past, including Oliva’s betrayal of Galois with Hilbert.
They stack the furniture to block the moving walls, but the furniture breaks as the room tightens around them. Pascal discovers a sales order for four industrial presses, hinting that the pressure of the room is designed to crush them each time a puzzle is missed. The room feels like a trap with no escape, intensifying the sense that every action matters.
As the pressure mounts, the group learns that Oliva and Galois had a romantic history and that Oliva cheated on him with Hilbert. Their attempts to survive intensify, and the mystery surrounding Fermat deepens. There are moments where Pascal suspects Fermat of a ruinous revenge, especially after recognizing the girl in the wallet’s photo as someone he severely injured with his car. The revelation implies a broader vendetta at play, turning the other guests into collateral victims unless they uncover the truth.
Further clues emerge: an invitation addressed to Fermat with different instructions reveals that Fermat is not the true host but another pawn in a larger game. If this is revenge, the killer must be present in the room with them, unseen.
Galois finally confesses that his celebrated claim to have proven Goldbach was a lie, staged to win Oliva back. Hilbert then reveals his true role: the mastermind behind the entire scheme. He confesses a lifelong obsession with proving Goldbach and admits his jealousy toward Galois’s supposed breakthrough, which spurred him to orchestrate this deadly contest. Fermat, instead, was a decoy whose fate would be sealed by a silent poison gas released in his car.
Hilbert announces that he has indeed “proved” Goldbach, and he hands a folder containing his supposed proof to Galois. The tension peaks as Galois acknowledges the brilliance of Hilbert’s work, yet the revelation comes at a harrowing cost. The trio pieces together a chilling realization: the ages of the people named Oliva, Galois, Fermat, and Pascal match the ages of the current guests, while the real Hilbert died at 81. It becomes clear that Hilbert had an escape plan all along and did not intend to die with them. In a last act of defiance, they discover a hidden wall panel and escape, taking with them Hilbert’s supposed proof.
Returning to their cars, Galois grapples with the dilemma of publishing the solution under Hilbert’s name or under his own. Pascal seizes the folder and scatters the pages along the river, delivering a blunt verdict: the world remains the same with or without the proof, and the pursuit itself has proven more corrosive than any final vindication.
