What is a major theme in David Auburn's play Proof?

The two major themes in Proof by David Auburn are genius & madness and love & trust. The first, madness & genius, revolves around the comparison of Catherine and her father Robert with Hal and Claire. Through Catherine and Robert, Auburn depicts genius as being unconducive to emotional stability in a complex world built upon mundane, day-to-day tasks and understanding. Auburn suggests that the fine edge of genius is not suited to survival in a practical world in which concern for food and housing and careers must come before the luxury of extraordinary achievement built from abstractions.

Hal and Claire are representatives of intelligent people--not geniuses--who have adapted to the everyday world of accomplishment. Hal understands genius and covets it for himself, knowing that, on his own, the stroke of genius will always allude him. Claire sees the presence of genius in her father but doesn't understand its nature or even its worth. Her view of Catherine is that she is simply emotionally unstable and in need of looking after; she doesn't see genius at all.

What is the thesis of the play Proof by David Auburn?

The three dominant themes of Proof are that (1) genius is not suited to the mundane day-to-day world and may turn to madness under the pressures and performance of life. (2) Mathematics is provable but trust is unprovable and must be engaged in as an act of faith whether there are irrefutable grounds for trust or not. (3) The third is the contemplation of the inheritability of genius and/or of madness: Catherine's writing looks very much like her father's; her proof is elegant and full of genius also like her father's

Based on these three themes in Proof, it seems the suggested thesis is that trust in people is like trust in mathematical proofs, which may both have emotional instability at their core. Specifically, if a mathematical problem is proved by a series of elegant calculations, it must be trusted; similarly, if individuals prove their integrity and character by a series of elegant actions, then they must be trusted. The difficulty, as illustrated by Catherine's relationships with Claire and Hal, is in the ambiguous nature of proofs of the human abstractions of integrity and other inner qualities.