As the plot of Wit progresses, Vivian Bearing becomes increasingly aware that, in regard to the experimental and desperate form of chemotherapy that she is receiving, the doctors are far more concerned with Vivian's value as a test subject than as a patient whose life they may save. She finds this humorously ironic in that, over the course of her life, she has often held the same mindset.

However, Vivian realizes that for all her wit and intellect, none of it has prepared her for the isolation and pain she now faces. In the climax of the play, her old teacher visits Vivian in her dying hours. She offers to read her a sonnet of John Donne, whom Vivian had always favored due to his wit. However, seeing the meaninglessness of intellect, she declines. Her teacher, Dr. Ashford, reads instead The Runaway Bunny, a story about the love of family. Shortly after, Vivian dies.

The climax of this tremendous play comes when Vivian Bearing is forced to concede that the treatment she is receiving is killing her, which is something she finds ironic given the way that the treatment was supposed to treat her cancer and heal her. However, as she physically deteriorates more and more, she finds that her wit, which remains undiminished, and her intelligence do not equip her to cope with the intense emotions that she experiences. It is only human kindness that is able to comfort her at this point. Note the following quote from Vivian Bearing that supports this point: 

Now is a time for, dare I say it, kindness. I thought being extremely smart would take care of it. But I see I have been found out.

The climax of the play comes in the last few moments of Vivian's life when she realises that life needs more than wit and intelligence, and she metaphorically finds her soul when she dispenses with her intelligence, language and Donne's poetry. Wit, which is what Vivian has based her entire life around, only goes so far, and it is this realisation that marks the climax of this play.