Auburn tells the story out of sequence, so that we move back and forth in time, seeing Robert both sick and well, watching Catherine spar with Hal, then warm to him. Along the way, Keeley offers a Catherine who evolves from numb and wasted — passively allowing Claire to set the course — to tentative and then increasingly willing to leave the safety of her comfort zone. Her winning mix of quirky and funny makes us root for Catherine as she struggles to emerge from her role as caretaker. Auburn’s delight in mathematical discovery — which the play’s practitioners describe as a lot of hard work, often frustrating, sometimes exhilarating — serves as an apt metaphor for the effort required of a young woman stepping out of her father’s shadow and into her own life.
The parallels between the real life of Nash and the fictional life of Robert in Proof are many, and they prompt questions of whether genius and insanity are linked and whether both are inherited. Robert is clearly a Nash-like figure. Hal reminds Catherine in act 1, scene 1 that when Robert was in his early twenties he had made major contributions to three fields: game theory, algebraic geometry, and nonlinear operator theory. These are exactly the same fields, according to Nasar, in which the young Nash made his impact. Nasar also points out that in the early days of his illness, Nash seemed to have a heightened awareness of life:
"And very close to that time — a few weeks later — I saw a little show on Channel 2, the educational channel in Boston, called What's Happening Mr. Silver?, the David Silver show. And all it was was an interview with Mel. The technique was poor, the camera work wasn't good, nothing was. And this little show moved me so deeply, just Mel's presence on TV was so strong and so alive, that I realized everything I was doing was a waste of time. What I really ought to be doing was helping to get Mel more opportunities to be on TV and to have his writing and his music and whatever he created out to the public.