Ron Howard
A Beautiful Mind

Not a beautiful mind; a wonderful mind. There are no other words to describe the mind of one of the greatest mathematicians of the 20th century. Only five papers in his career, three of which were revolutionary in the three fields touched by his imagination: game theory, differential geometry, and the analysis of partial differential equations. Now, if you enter a certain field of mathematics and, in two years, turn it upside down from top to bottom, it only means two things: either you are an extraterrestrial with knowledge we lack, or nature was very generous with you when it created you.

But immortal glory always has a price. The tremendous efforts to reach such heights were, according to some psychologists, the origin of John Nash's mental degeneration into schizophrenia. Simply put, the unprecedented efforts in abstraction made by his mind led him to live constantly in a sort of higher dimension, different from the earthly one. In this higher dimension, there are some insights that allow you to write immortal pages in art and science, but there are also the so-called "delusional thoughts," that is, intuitions that, over time, turn out to be just nonsense, but at the moment they take over, they overwhelm you: thoughts of suicide, absurd fears of being killed, thoughts of being ridiculed by your peers, and so on. From this higher dimension, it is humanly impossible to return to the real one except with the help of psychotropic drugs. Nash's greatness is that he succeeded in combining the drugs with an even more extraordinary will of his mind. And that is what this sublime work by Ron Howard, with the equally sublime interpretation by Russell Crowe, is about.

The film opens in a room at Princeton University, the temple of world mathematics. It's the late 1940s, and the best mathematical minds in the world are arriving at Princeton. John Forbes Nash is one of them. Young John is hungry for difficult problems, intractable problems, to solve in order to show his intellectual superiority, in an attempt to hide his sense of social inferiority, due, according to some (unauthorized) biographies, to abuses he suffered as a child. Perhaps for Nash, as for Will Hunting from the film "Good Will Hunting," mathematics was the sweet refuge from thinking about the horrors he had the misfortune to encounter on his path.

Nash’s ambition is unrestrained, and his friend-enemy Martin (Josh Lucas) loves to provoke him:
“What you are doing is just trivial nonsense,” – says John.
“Okay, John. Maybe you’re right. But what are you doing? How would you react if you lost?” – Martin responds.

But in the beginning, John doesn’t lose. He overwhelmingly wins. With an extraordinary insight, he revolutionizes game theory. Even Martin congratulates him, and the two toast together.
After game theory, it's time for differential geometry, with the famous "embedding theorem of manifolds" (only slightly touched on in the film, although it concerns the resolution of a problem that even the great Bernhard Riemann – precisely the one with the famous conjecture on prime numbers – could not solve, and this gives you a good understanding of who mathematician John Nash was).

The first setback comes with the missed victory of the Fields Medal, the Nobel Prize for mathematics (also only hinted at in the film).
In the meantime, John has become a professor. Eccentric, excessive, indifferent, with attitudes of superiority. He is incapable of empathy, but Alicia (Jennifer Connelly), a young and beautiful student, finds the courage to talk to him. She shows him the solution to a problem he posed on the blackboard. John Nash takes a look and tells her it's wrong; elegant but wrong. He has just glanced at it. He knows everything about mathematics; about how to treat women, nothing at all.
The two get married. For Alicia, it will be a hell she endures with heroic constancy. At the end of the film, the true praises will all be for her.

In painful silence, the devoted partner watches her man fall into schizophrenia. John's mind becomes a volcano in eruption: paranoid conspiracism, search for absurd coincidences, and not very reputable imaginary friends (Steve Harris).
He goes from electroshock (a criminal practice that definitively devastates him) to more reasonable psychotropic drugs that manage to calm his unrestrained mind. One day, calmed by the drugs, John asks Alicia a question that testifies to his inability to acknowledge reality and live it without too much reasoning: “What do people do?” Alicia, with her common sense, replies: “That’s life, John.” There are things understood, in their beauty, only if they live. First live, and then understand; not the other way around.

The psychotropic drugs help calm him but prevent him from soaring in the meadows of mathematical abstraction and "responding to the love" of his Alicia. John secretly stops taking them, and then the hallucinations return. But this time, something changes. One day John's mind comprehends the impossible: a hallucination that has been keeping him company for a long time (a little girl) can't be real. Only a mind like his can have an intuition (truly supreme) like this, the most important of his entire life.
John is happy, but his doctor—a good man who sincerely cares for him—tells him that these illuminations are miraculous and may never happen again:

“Why not? Why not?!” – John shouts.
“Because the problem is in your head” – his doctor replies.

A (brilliant) mind but blinded is only a blinded mind with flashes of genius. And unfortunately, flashes of genius are just flashes: intermittent and out of our control. Without the psychotropic drugs, there will be no peace for him. John then decides to be reasonable and returns to taking the medication but will combine it with a sincere effort not to indulge in delusional thoughts anymore. He will not be a lazy user of psychotropic drugs. In this synergy of chemistry and will lies the secret of his miraculous awakening.

With his will functioning again, our hero returns to his friend Martin, who welcomes him with fear. It is the mid-1980s (even if it is not mentioned in the film). Decades have passed since John transformed into gold everything he touched in mathematics. Now the rumors reaching Martin's ears say John is just a raging madman. What will he do?

Instead, John's words seem those of a wise man:

“In the end, it looks like you’ve won, Martin”.

Martin immediately recalls the conversation from thirty years earlier and responds:

“No. No one wins, John. We have always been friends”.

John has a sudden hallucination, but Martin, like a true friend, doesn’t pay attention and, like a true friend, gives John the opportunity to attend the Princeton University library.

One day a student braver than the others, knowing that strange man who writes on windows is a living legend, approaches him. He thinks he is dealing with a lunatic, and instead, that man is much saner than many of his professors. Nash, after centuries, returns to speak with someone. Alicia has waited a long time, but her waiting has been rewarded.
Nash immediately reveals his talent as an animator and a charisma that fascinates many young students. To his young friends, John says something that only a few can understand: “Mathematics is a form of art.” It is indeed so. And he was a great artist.

If we know how to react to difficulties, divine justice or fate will do the rest. Justice must repair the injustice of the Fields Medal, a prize that John greatly deserved. At Princeton, one day, a man arrives and says to him: “I come on behalf of the Swedish Academy of Sciences. We would like to give you the Nobel Prize.” Nash looks at him with a gaze that says: “I am mad, but this one is downright crazy.” This man tells Nash that his insights in game theory (dating back to 1950) have become fundamental in antitrust problems, testifying to how his ideas were ahead of their time. But the ambassador of the Swedish Academy has come to see if Nash is crazy or not. John then removes any doubt from the ambassador:

“You are afraid I may jump on the stage of the Award, aren’t you? Well, yes, to tell the truth, I am crazy. I see and hear things that are not real. I take the most powerful medications. But I have learned to control my mind through a kind of thought diet. Just as people don't consume certain foods, I don't let certain annoying thoughts enter my mind. I have decided to ignore them.”

Exam passed. The prize will be his, and with the prize also comes recognition from his colleagues with the magnificent scene of the pens being placed.

On the Nobel stage, John doesn’t jump, but he leaves us with another pearl of wisdom, worthy of a great mystic:

“I always believed in numbers, in equations and logic and reasoning. After a lifetime of these pursuits, I ask: what truly is logic? Who decides reason? My quest led me through the physical, the metaphysical, the delusional, and back. And I have made the most important discovery of my career, the most important discovery of my life. It is only in the mysterious equations of love that any logical reason can be found. I am here because of you [Alicia]. You are the reason I exist. You are all my reasons.”

Schizophrenia allowed Nash to discover the greatest of all theorems, namely that love comes before reason.