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Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.

*Equations are classified by the highest power (value of the exponent) of their unknowns. If this is one, the equation is of the first degree. If this is two, the equation is of the second degree, and so on. Equations of higher degree than one yield multiple possible values for their unknown quantities. These values are known as roots.**An equation commonly contains one or more so called unknowns, often represented by*x*,*y*,*z*, etc. Values given to the unknowns which yield equality between both sides are said to satisfy the equation and constitute a solution.**Those pointless equations, to which no solution exists, are called absurdities.**A root of an equation is a number which substituted into the equation instead of an unknown converts the equation into an identity. The root is said to satisfy the equation. Solving an equation implies finding all of its roots. An equation that is always satisfied, not matter the choice of values for its unknowns, is called an identity.*

- Larsson is toying with us. He wants to place us in a state of alert confusion so we'll be in the mind to solve some mysteries!
- Larsson is using math to help build Salander's character. We already know that Salander likes puzzles and is good at math. But, what's a little surprising is that she's only now realizing that she loves it, the way some people love reading fiction. Math helps us understand some of how her mysterious mind works. Salander's math knowledge also provides a vivid contrast to the media's portrait of her as a brainless psychopath. Not that math geniuses can't be psychopaths (as Sherlock Holmes will tell you) – but they can't be brainless. The difference between what the reader knows about Salander and what the media says builds suspense. We want to see if the truth will ever come out.
- Larsson is using math and mystery as metaphors for each other. After all, aren't math and mystery both obsessed with eliminating suspects to come up with solutions to problems? Don't they both involve using logic, reason, and the interpretation of symbols and signs? Don't they both also require imagination? In fact, aren't math and mystery
*both*mathematical and mysterious, on some level? (Feel free to disagree; that why we put the question marks.) - The descriptions of mathematical principles can be translated, in a sense, to comment on the novel itself. Maybe this is a stretch, but aren't the epigraphs a fancy way of saying that to solve an equation (or mystery) we need to discover what, or who, is "unknown" from the available possibilities? Ronald Niedermann, Salander's half brother, ends up being the "solution" to the mystery. He is both the killer of Dag, Mia, and Bjurman, and the link to Zala that helps Salander learn the "roots" of her "identity."

Until the end of novel, Niedermann is completely "unknown" to Blomkvist, Salander, and the police. At the end of the novel, although the readers know Niedermann is the killer, his "identity" as such is still "unknown" to the authorities, and to most of the characters. Hopefully, this will be rectified in the final book of the trilogy.

This could mean asking the question, What is the root cause of these problems? Since it's impossible (arguably) to prove precisely what causes humans to mistreat one another in these ways, the question is absurd. The equation (the question, the mystery) becomes an absurdity, something that will give us a big fat headache if we think about it too long. This is not to say that there aren't things to be done to stop those problems from happening, but we might never completely understand why they occur to begin with.

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