Catherine thinks that her father’s notebooks are worthless and that nothing of value can be found within them. They're full of rambling, incoherent nonsense, the product of a once brilliant mind ravaged by years of mental illness. But Hal, a former student of Robert, disagrees with Catherine; he regards the notebooks as full of very valuable information. He’s been working on them, and as well as the mathematical knowledge they contain, they’re also valuable for an appreciative comment that Robert made about Catherine.

That’s why Hal was planning to take the notebook home with him, wrap it up, and give it to Catherine as a gift. In this deeply heartfelt, romantic gesture, the notebook can be seen as a symbol of Hal’s desire to establish a connection with Catherine and, by extension, with her father.

It can also be said to symbolize the way in which Catherine has suppressed her own skills and knowledge as a mathematician for years in order to take care of her mentally ill father. The notebooks contain complicated mathematical theorems that Catherine herself had devised. When Hal hears about this, he’s notably skeptical. This demonstrates just how effective Catherine has been in effacing the extent of her own knowledge.