In chapter twelve, we see the growing relationship between Colin and Lindsey. I believe that John Green did this to show growth throughout the plot of the book. Green reveals how far people can come throughout the course of a novel. He shows how the opposite can come together to accomplish a goal. In their case, the goal was the theorem. Lindsey helped Colin and Colin helped Lindsey. They have come together as great friends, or maybe even more than friends, starting out as the know- it- all who couldn't make friends and the popular, oblivious teenager. Since the beginning, they have both come very far.