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The Girl Who Played with Fire (2009)
Stieg Larsson

In this sequel to the stunningly popular The Girl with the Dragon Tattoo, the self-taught, nearly autistic, young genius, Lisbeth Salander, once again becomes involved in a thrilling mystery allied with journalist Mikael Blomkvist. As a sort of side story, we see that she is also trying to find a proof of Fermat's Last Theorem. She is shown as reading the famous math textbook "Dimensions in Mathematics" by Parnault. However, as this blog from Harvard University Press explains, there is no such book or author. They, like Lisbeth herself, are fictional.

Note that Fermat's Last Theorem (the statement that there are no positive, whole number solutions to the equation xn+yn=zn when n>2) is famous for being a mathematical statement that is very simple to make but notoriously difficult to prove or disprove. In fact, it was an open problem for hundreds of years until Andrew Wiles finally completed a proof in 1994. It is a common popular belief that there must be some elementary proofs of the theorem out there (either waiting to be discovered or known in secret as the story suggests). However, Wiles' proof is quite complicated (depending on advanced mathematical knowledge of elliptic curves and modular functions which are not available to a casual puzzle solver) and it seems likely that the statement cannot be proved in a much more elementary way at all.

The author makes a few disappointing mistakes in his description of FLT. He does not seem to realize, for instance, that the theorem states that there is no solution to the famous equation. Also, he claims that Wiles used "the world's most advanced computer program" in his famous resolution of the problem in the 1990's. (So far as I know, there was no computer assistance involved in Wiles' proof at all.)

In the end, Salander seems to realize that Fermat's solution was a sort of joke rather than anything mathematical at all, even suggesting that it would have been better solved by a philosopher than a mathematician. Although it is not described in detail, it seems that she comes up with some solution to the equation x3+y3=z3 that was more of a pun than an actual solution and so was not something that mathematicians (who are apparently too humorless) would ever think of. Since Fermat originally claimed (and Wiles proved) that there are no integer solutions, this doesn't make any sense to me at all. I mean, I think Larsson was trying to make a joke, but that he didn't understand the math enough and so his joke falls flat for anyone who even understands what FLT says.

This book seems to please readers as a thriller, gaining enormous popularity around the world after the author's untimely death, but as mathematical fiction I'm afraid I cannot recommend it.

Contributed by Sarah Kate Magee

Not math in fiction per say, but an excellent read that references math at a few places.

Contributed by Paul Green

In addition to the confusion already noted regarding the Fermat conjecture, Larsson does not seem to distinguish clearly between the general case and the special case n=3, with which Salander appears to be obsessed, and which was settled by Euler in the eighteenth century. Salander supposedly skips the proof of the conjecture in a general mathematics text she is reading in order to discover it for herself. Wiles' proof of the general case could not possibly appear in such a text, whereas Euler's proof for n=3 (or Fermat's own proof for n=4) certainly could.

Incidentally, there is a passing reference to Salander's involvement with the Fermat conjecture in the final novel of the sequence, "The Girl who Kicked the Hornets' Nest".

Jessica writes with an interpretation based on the use of "Zzzzz..." to represent snoring:

Contributed by Jessica

Instead of looking at it from a maths point of view, the author directs the reader to approach it as a riddle or puzzle, and specifically says it is similar to a rebus which is a puzzle in which words are represented by combinations of pictures and individual letters, or a type of pun.

x3+y3 = z3

x3+y3 = zzz

x3+y3 = will send you to sleep (haha that's funny)

and the higher the exponent the more the damn puzzle puts you to sleep and the more z’s you have. (which I also find funny)

x100+y100= zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz (didn't count them but you get the picture - hehe I bet the mathematician in you wants to count them)

But.... the funniest part of the joke is that there is also a very subversive humour in the fictional "fact" that all these self-important, balding, grey-haired, crusty, walk-short, knee-high socks 'n' sandals, cardigan and pocket-protector wearing (insert stereotype here) mathematical geniuses have spent years and years trying to solve/prove a theorem when all along, Fermat has been (fictionally) what we in NZ call "taking the piss", and that his theorem is in fact a joke or riddle or rebus, but instead of being able to see it, he's had all these mathematicians busting a gut over something which they are (by their mathematical nature) too blind to see. ( I don't know if Americans use the term "taking the piss" but it is basically having a subversive or mocking joke at someone else's expense ).

This joke does not quite work for me, in part because it seems that Fermat did somehow recognize that there were no positive integer solutions to xn+yn=zn when n>2 and that he apparently thought this was interesting (not sleep inducing), and also because (as Jessica herself questions) it is not certain that the "Zzzzz..."/sleep correspondence would have been recognized in 17th Century France. Furthermore, I don't think Fermat actually had any z's in his formulation of it. (As far as I know, all he wrote on the subject was "To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.") However, none of these objection particularly matter in this case because it could well be that this is what Larsson intended...or that other readers get a kick out of Jessica's interpretation even if Larsson had no particular idea in mind.

Contributed by Anonymous

This is a excellent novel and Salander may be one of my favorite fictional heroines, so I was thrilled to read that we share a common interest in number theory. Unfortunately, I too thought the presentation of the history of FLT was a bit off.

And Lisbeth, read whatever you like; there are no spoilers to FLT.

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Works Similar to The Girl Who Played with Fire
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Last Theorem by Arthur C. Clarke / Frederik Pohl
  2. Thursday Next: First Among Sequels by Jasper Fforde
  3. The Boy Who Escaped Paradise by J.M. Lee (author) / Chi-Young Kim (translator)
  4. Fermat's Room (La Habitacion de Fermat) by Luis Piedrahita / Rodrigo Sopeña
  5. The Lure by Bill Napier
  6. Oh, Brother by Stanley Hart
  7. The Cipher by John C. Ford
  8. Gauntlet by Richard Aaron
  9. Simple Genius by David Baldacci
  10. Turing's Delirium by Edmundo Paz Soldan
Ratings for The Girl Who Played with Fire:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
2.4/5 (5 votes)
Literary Quality:
4.2/5 (5 votes)

MotifProdigies, Anti-social Mathematicians, Proving Theorems, Female Mathematicians, Autism,
TopicAlgebra/Arithmetic/Number Theory,

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(Maintained by Alex Kasman, College of Charleston)