I chose to focus my post on Lieutenant Jimmy Cross' infatuation with a college girl, Martha. As the book starts out, we are immediately informed that Martha and Cross are not "an item", because of certain key phrases O'Brien used. ("They were not love letters, but Lieutenant Cross was hoping...") Reading those words made me pity Cross, because his feelings for her are clearly stronger than her feelings for him, if she possesses any at all. He seems like a love sick puppy in the ways he acts, licking the envelope flap in hopes of any of Martha's tongue remnants still remaining. He appreciates her writing abilities, and notices how smoothly her words flow on the page. It's clear that this young woman has left a lasting impression on Jimmy Cross.
Cross then revisits a "date" that he and Martha went on. The way that Martha indifferently looked at Cross when he put his hand on her knee indicated that she had no feelings for him whatsoever. This tells me that Cross is lingering onto Martha's every word in her letters in hopes of having his feelings reciprocated.
If Martha has no feelings for Cross, it seems as if she is almost taunting him by sending him pictures of herself, knowing how he feels about her but not willing to return her love. I suppose all women have that manipulative streak, myself included. In every picture, as described, her gray eyes are simple, indifferent.
Fast forward to page 16 in the book, after Ted Lavender died, supposedly due to Cross' negligence. Feeling guilty and grief-stricken, Cross came to the realization that although Martha was a real person, he subconsciously turned her into an angel who loved him unconditionally; in reality, she was indifferent, uninvolved, and would never love him. He was then determined to focus on the war, and not let a somewhat fictional woman cause the death of another soldier. So to help heal his broken heart, he burned all of Martha's letters and pictures she sent him.