Unemployed number theorist Max Cohen, who lives in a drab apartment in Chinatown, Manhattan, believes everything in nature can be understood through numbers. He suffers from cluster headaches, extreme paranoia, hallucinations, and schizoid personality disorder. His only social interactions are with his mathematics mentor, Sol Robeson (now disabled from a stroke), and those who live in his building: Jenna, a little girl fascinated by his ability to perform complex calculations, and Devi, a young woman living next door who sometimes speaks with him.
Max tries to program his computer, Euclid, to make stock predictions. Euclid malfunctions, printing out a seemingly random 216-digit number, as well as a single stock pick at one-tenth its current value, then crashes. Disgusted, Max throws away the printout. The next morning, he learns that Euclid's pick was accurate but cannot find the printout. When Max mentions the number, Sol becomes unnerved and asks if it contained 216 digits, revealing that he came across the same number years ago. He urges Max to take a break from his work.
Max meets Lenny Meyer, a Hasidic Jew who does mathematical research on the Torah. Lenny demonstrates some simple Gematria, the correspondence of the Hebrew alphabet to numbers, and explains that some people believe the Torah is a string of numbers forming a code sent by God. Intrigued, Max notes some of the concepts parallel other mathematical concepts, such as the Fibonacci sequence. Agents of a Wall Street firm approach Max. One of them, Marcy Dawson, offers him a classified computer chip called "Ming Mecca" in exchange for the results of his work.
Using the chip, Max has Euclid analyze mathematical patterns in the Torah. Once again, Euclid displays the 216-digit number before crashing. As Max writes down the number, he realizes that he knows the pattern, undergoes an epiphany, and loses consciousness. After waking up, Max appears to become clairvoyant and visualizes the stock market patterns he sought. His headaches intensify, and he discovers a vein-like bulge protruding from his right temple. Max has a falling out with Sol after Sol urges him to quit his work.
Dawson and her agents grab Max on the street and try to force him to explain the number, having found the printout Max threw away. Attempting to use the number to manipulate the stock market, the firm instead caused the market to crash. Driving by, Lenny rescues Max, but takes him to his companions at a nearby synagogue. They ask Max to give them the 216-digit number, believing it was meant for them to bring about the messianic age, as the number represents the unspeakable name of God. Max refuses, insisting the number has been revealed to him alone.
Max flees and visits Sol, only to learn from his daughter, Jenny, that he died from another stroke. He finds a piece of paper with the number in his study. At his own apartment, Max experiences another headache but does not take his painkillers. Driven mad, he destroys part of Euclid. Believing the number and the headaches are linked, Max tries to concentrate on the number through his pain. After passing out, Max has a vision of himself standing in a white void and repeating the digits of the number. The vision ends with Max hugging Devi, who is revealed to be a hallucination. Standing alone in his trashed apartment, Max burns the paper with the number and begins to use a drill on his head in a trepanning procedure.
Sometime later, Jenna approaches Max in a park and asks him to do several calculations, including 748 ÷ 238 (an approximation for pi). Max smiles and says that he does not know the answer. He sits on the bench and watches the trees blowing in the breeze, seemingly at peace.
