Symbolism, Imagery, Allegory
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.