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.