"A Beautiful Mind" is about great mathematician John Nash, Jr., a victim of schizophrenia. His theories impact us every day, but he believed for years that Russians were sending him code in the New York Times. Crowe is Nash, and Connelly, his wife, Alicia, who's pregnant when John's symptoms first appear. His mind, once so great, betrays him with frightening delusions.

Nash is a quiet, cocky young man who slowly becomes a tortured, secretive paranoid, believing he's a spy trailed by federal agents. Losing a game of Go, at Princeton in the late 1940s, Nash says, "My play was perfect. The game is flawed." Recalling his first teacher saying he was "born with two helpings of brain and a half-helping of heart," he adds, "I don't much like people, and they don't much like me."

Alicia helps find his heart. A grad student when they meet, she's touched by his loneliness. To the extent he can be touched, she touches him. Looking at the night sky, he asks her to name any object, then he connects stars to draw it. But when she finds his office papered with news clippings, connected by frantic lines into imaginary patterns, it's a lot less romantic.

Once compared to Newton, Mendel, and Darwin, Nash silently wanders the campus, paging through newspapers and magazines. Alicia stands by him, and medication helps - when he takes it. Nash has a gentle psychiatrist (Plummer) and agonizing insulin shock therapy. New drugs help; one day, he pays a colleague's daughter a compliment, and people notice that he seems better.

A man from the Nobel committee (Pendleton) visits, because Nash is "being considered." Nash says people are usually informed they've won, not that they're being considered: "You came here to find out if I'm crazy and would screw up if I won." He did win, and didn't screw things up.

Movies tend to show mental illness as grotesque, sensational, funny, tragic, or perverse. Here it's just a disease that makes life almost impossible. Asked to write about it, Nash honestly said his recovery "isn't entirely a matter of joy. Without 'madness,' Zarathustra would have been only another of millions of human individuals who have lived and been forgotten." Without madness, would Nash have been forgotten? Did his ability to penetrate the most difficult reaches of mathematical thought somehow come with a price tag? The movie doesn't know, and can't say.