The Cigarette Case
As a late birthday present, Mimmi gives Salander "a beautiful cigarette case with a lid of blue and black enamel and some tiny Chinese characters as decoration" (9.43). We wish we could tell you what the characters translate to, but we don't know. When Salander asks Mimmi, she says, "How on earth would I know that? I don't speak Chinese. If found it at a flea market" (9.46).
If we had to guess, we'd say the characters say something about friendship, but even if they don't, that's what the cigarette case symbolizes. When Salander is buried alive by Niedermann and Zala, what does she use to dig her way out of the hole? Why the cigarette case, of course!
This must feel particularly ironic for Salander, who is nursing heavy doses of guilt over the fact that Mimmi was kidnapped and beaten by Niedermann. Now she's using Mimmi's gift to save her own life. This simple, inexpensive gift becomes, at the end of the novel, Salander's most prized possession. It not only reminds her that someone out there really does care about her, but also literally saves her life. It's another example of how Salander isn't alone, despite her Salander-against-the-world mentality.
The 1991 Police Report
The police report, authored by Gunnar Björck under the pseudonym Sven Jansson, is a symbol of everything that's wrong in Salander's life, and she's never even seen a copy of it until she finds the one Bjurman got his hands on. The report details Salander's attack on Zala when she was twelve. This resulted in her being placed in the psychiatric hospital for children and her life becoming a total horror show. It's been buried by the Secret Police, who want to keep Zala from becoming known to the public, so it also symbolizes the secrecy and corruption which also contribute greatly to Salander's wretched situation.
From the police report, Bjurman finds out that Zala and Salander are connected, and he contacts Zala, sparking the novel's major plot lines. It's also the key piece of evidence Salander uses to figure out that Zala's crimes are being actively covered up by the Secret Police, and that her confinement to St. Stefan Hospital's was no random accident. So, it also becomes a symbol of the idea that secrets always come to light sooner or later, especially if they are written down on paper.
In his review of the final novel in the trilogy, critic David Camp comments on the constant coffee drinking featured in Stieg Larsson's novels. Irreverently (but hilariously) he says,
Many of the Larsson faithful subscribe to a belief that [Stieg Larsson] was made dead by the very sorts of heavies who crop up in his novels. But such talk has been emphatically dismissed by Larsson's intimates. So let me advance my own theory: Coffee killed him. If we accept that Blomkvist is, in many respects, a romanticized version of Larsson, and that Blomkvist's habits reflected the author's own, Larsson overcaffeinated himself to death. (source)
Well, we might point out that you could view coffee is a symbol of alertness, a necessary quality for solving mysteries. Of course, it also symbolizes artificially keeping the body awake when it should be sleeping. The characters in Larsson's novels have to drink lots of coffee. How else could we explain their ability to continue to function after days of missed sleep?
Some readers respond to Camp's review with the argument that people in Scandinavian countries simply drink more coffee than people in the US; that this is a cultural thing. Hmm…Now that's rather hard to fathom considering the Starbucks on every corner, isn't it. Plus, the US has its very own mystery writer who relies just as much on coffee as Larsson. That would be Walter Mosley, author of the acclaimed Easy Rawlin's mysteries. In those novels, you'll find just as many coffee cups, coffee thermoses, and coffee addicts as in Larsson's.
Do The Math
What do Lisbeth Salander and starship captain Jean Luc Picard have in common? Sure the Captain is the picture of diplomacy, while Salander spits in the face of diplomacy – but aren't they both super brainy, extremely moral, and ready to face any challenge? What's more, they're both become obsessed with a mathematical mystery known as Fermat's Last Theorem (source). The theorem also shows up in any number of popular ventures, including, of course, The Simpsons, like everything else. (See "Treehouse of Horror VI" and "The Wizard of Evergreen Terrace.")
As discussed in The Girl Who Played With Fire, Pierre de Fermat was a seventeenth century Frenchman who came up with a theorem that continues to boggle the minds of the mathematically inclined. If you've ever been to math class, you've probably heard of Pythagoras' Theorem (x2 + y2 = z2 ), which is used to measure the hypotenuse (the side opposite the right, or ninety degree, angle) of any right triangle. Fermat claimed that if you modify the equation using powers of three or higher (x3 + y3 = z3 , x4 + y4 = z4 , etc.) that there are no numbers that can possible satisfy the equation. Then, he died without leaving behind the proof he claimed to have devised.
In the meantime, you might be asking yourself, why were mathematicians so obsessed with this? Why are they obsessed with it still? It's kind of like why we are so obsessed with Stieg Larsson's trilogy of novels – we all love mysteries and puzzles and we want to solve them, or at least to see them solved. Even though Fermat's Theorem has now been solved, Salander wants to understand it herself. She wants to understand logically why the equation can never be satisfied, why there are no numbers in the infinite set of all numbers.
Salander's love of math, and her obsession with one of the world's most mysterious math problems is a character builder. Readers and people who know Salander can see that she's a true genius and would fit right in at NASA. This presents an ironic contrast to the media's portrayal of her as person without enough brain power to tie a shoelace, much less work out complicated math problems. But, we can take this even further if we think about the theorem as a symbol of a formula that is never true, and as a symbol of something very difficult to prove.
This ties in nicely with the novels themes of "Identity," and "Justice and Judgment." The media, the police, the social welfare system are all trying to find out what formula they can apply to Salander, how they can measure her, how they can classify her, how they can make the events of her life equal the real person they see before them. But, no equation they devise, no theory of Salander is true. As we see, once those Salander theories are out there, it's very difficult to prove that they don't in fact apply to her. Of all Salander's friends and enemies, Blomkvist is the one person who doesn't try to fit her into a neat formula, but accepts her as a unique individual who defies classification.