A fascinating play that bears many similarities to Stoppard's Arcadia is David Auburn's Proof, which likewise looks at the topic of mathematical genius in a literary form and debates the nature of genius. What is interesting about the way in which these two plays present genius is that there is a marked divergence. In Proof, for example, the issue of genius is strongly associated with mental health, as the two characters who are presented as being geniuses, Robert and his daughter Catherine, are actually shown to be rather unsuited to live and participate in modern life. Catherine for example is shown to be almost crippled by her depression and perspective of life. Note what her father says to her about how she is living her life:
You sleep till noon, you eat junk, you don't work, the dishes pile up in the sink. If you go out, it's to buy magazines. You come back with a stack of magazines this high. I don't know how you read that crap. And those are the good days. Some days you don't get up, you don't get out of bed.
Genius might allow you to achieve wonderful and incredible feats, as indeed it does for both Robert and Catherine, however this play presents genius as coming at a cost, and therefore explores the peculiar fragility that is associated with being a genius. It is clear that the genius of Robert and Catherine is contrasted with the character of Claire and Hal, who are far more able to participate in life precisely because they lack the extreme intellect of Catherine and Robert.
By contrast, there is little of the fragility in the two characters in Arcadia who are presented as being geniuses. Yes, Gus Coverly chooses to be silent, as if he is unwilling to share his insights and knowledge with those around him like a Greek prophet. However, both he and Thomasina are presented as being happy in themselves. Thomasina's genius, in particular, is presented in a very healthy way as she seeks to take the scientific knowledge of her day and stretch it and expand it to encompass real life:
Each week I plot your equations dot for dot, xs against ys in all manner of algebraical relation, and every week they draw themselves as commonplace geometry, as if the world of forms were nothing but arcs and angles. God's truth, Septimus, if there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose?
Here Thomasina shows she is not happy sticking to the way that science and mathematics can be used to reflect abstract systems of thought and wants to extend it to explore the meaning behind reality. If genius in Proof is presented as a very fragile state, genius in Arcadia is all about the pursuit of knowledge and is what defines us as human. Both plays therefore explore similar themes in very different ways, making them suitable for comparison.