From Scott Hudson's LAByrinth Theater weekend workshop (Hudson wrote a truly good play called Sweet Storm), he said, by way of discussing a scene from the play Proof , that Hal's failure to take the notebook was botchy:
Botched (my word) suggests that the gesture is un-charming, whereas botchy finds it endearing.
Of course a University of Chicago math professor who happens to also be a drummer and a runner perhaps receives the benefit of the botchy simply because he is so appealing.
Hal is certainly more likable than Catherine's sister, who either refuses to know Catherine or is incapable (tone-deafness? self-absorption? older-sister condescension complex?) of doing so. Personally I don't trust Hal until the very end of the play, when he wants to discuss Catherine's hip proof.