Ever ask a mathematician for a proof any philosophy of value for his work exists? Or that precise definitions actually apply to premises derived solely on the basis of theory without regard to such qualitative determination? For if the process of determining a chess combination having 12 moves is incalculable because no such formula can be fed to a chess program, how can there be people that do this purely in their head?

This IS the spirit of the depth of this wonderful movie, David Auburn adopted from his own play, Proof. The accomplished Anthony Hopkins carries his role with spectacular success as a declining theoretic mathematician, tragically spending the last of his life trying to recapture his former brilliance. Gwyneth Paltrow is his beautiful devoted daughter, Catherine, plagued by an ironic parallel she is brought to anticipate as her own brilliance begins to eclipse even that her father had reached. Working on his doctorate, Hal (a part casted well for Jake Gyllenhaal,) wins the confidence of Catherine and begins to study the papers left behind by her father shortly after his death.

Little is obtained until, after Hal and Catherine become endeared, she trusts him with a key to find one last booklet. The discovery will turn everything on its head, challenging not only to offer a new mathematical proof, but the mindsets most entertain about such things as, “lightening doesn’t strike twice in the same place” and that women are any less than men in mathematics…even among the most brilliant of mathematicians. From the interplay with her presumptuous sister, Claire (the lovely Hope Davis) to the astonished and incredulous Hal, what follows is a supreme test of character and love in winning the ultimate confidence that can exist between two people. With stunning dramatic intensity. The story and how this wonderful movie represents it is on the highest level of grand. Very hard to do when there are essentially no villains.

It is hard to envision, once you’ve seen this movie, it succeeding nearly as well as a play. Director John Madden adds that much to it. A great deal of the story is told in flashback, almost a run-on of them. However, this piecing of these breaks in chronology are not difficult to contextualize and give the viewer little confusion. The economy of this achieves both a compacting of storyline and the dramatic effects of allowing emphasis to be carefully and artistically placed.

There is much more, the movie offers levels of meaning almost paralleling the various actual ways mathematicians strive for proofs. “Well if one can’t prove it, we’ll approach if we can disprove it.” What a metaphor for so many would-be scientists today that might reintroduce probability to their work!

Clearly a movie for Everyman, and child, and prospect of thought…even Republicans.