Posted by: Dave Richeson | May 24, 2010

## Mathematics in novels and Martin Gardner RIP

I always enjoy encountering mathematics in non-mathematical works of fiction. (I posted excerpts from Candide and The Brothers Karamazov last fall.) Here are a few more that I came across recently.

The first is in Dashiell Hammett’s 1934 murder mystery The Thin Man. Here is a conversation between private eye Nick Charles and his wife Nora at the end of the novel.

“But this is just a theory, isn’t it?”

“Call it any name you like. It’s good enough for me.”

“But I thought everybody was supposed to be considered innocent until they were proved guilty and if there was any reasonable doubt, they—”

“That’s for juries, not detectives. You find the guy you think did the murder and you slam him in the can and let everybody know you think he’s guilty and put his picture all over newspapers, and the District Attorney builds up the best theory he can on what information you’ve got and meanwhile you pick up additional details here and there, and people who recognize his picture in the paper—as well as people who’d think he was innocent if you hadn’t arrested him—come in and tell you things about him and presently you’ve got him sitting on the electric chair.”…

“But that seems so loose.”

When murders are committed by mathematicians,” I said, “you can solve them by mathematics. Most of them aren’t and this one wasn’t. I don’t want to go against your idea of what’s right and wrong, but when I say he probably dissected the body so he could carry it into town in bags I’m only saying what seems most probable.”

“I haven’t fascinated her; perhaps I was fascinated myself in my folly. But she won’t care a straw whether it’s you or I, so long as somebody sits beside her, sighing…. I can’t explain the position, brother… look here, you are good at mathematics, and working at it now… begin teaching her the integral calculus; upon my soul, I’m not joking, I’m in earnest, it’ll be just the same to her. She will gaze at you and sigh for a whole year together. I talked to her once for two days at a time about the Prussian House of Lords (for one must talk of something)—she just sighed and perspired! And you mustn’t talk of love—she’s bashful to hysterics—but just let her see you can’t tear yourself away—that’s enough. It’s fearfully comfortable; you’re quite at home, you can read, sit, lie about, write. You may even venture on a kiss, if you’re careful.”

Like the rest of the world I was sucked into Steig Larsson’s Millennium trilogy. In his second book The Girl Who Played with Fire we find out that the protagonist Lisbeth Salander is fascinated by mathematics. Her interest began after reading L. C. Parnault’s 1200-page book Dimensions in Mathematics (Harvard University Press, 1999). This lead to an obsession with Fermat’s last theorem. (You can read about this in the the first chapter, which was reprinted in its entirety in the NY Times.)

The first I heard about Dimensions in Mathematics was in an email message I received from a senior administrator at my college who was reading Larsson’s novel. Does this book really exist, he wanted to know? I had never heard of it, so I was doubtful. After a little checking I found that this book does not exist. In fact, probably inundated with questions, Harvard University Press issued a press release saying so.

Here’s a sample excerpt of the mathematics in the book. In the passage below Larsson asserts that Wiles used a computer to prove Fermat’s last theorem (oops!). Then he goes on to say that Salander unravelled a hidden meaning behind Fermat’s famous margin-note. Although the passage is a little vague, he makes it sound as though Fermat didn’t have a proof of the theorem, but rather was making a joke or giving a rebus or a riddle; it turns out that mathematicians were misinterpreting Fermat all this time! Perhaps this lost something in translation from the original Swedish.

Salander began her advance towards the house, moving in a circle through the woods. She had gone about a hundred and fifty yards when suddenly she stopped in mid-stride.

In the margin of his copy of Arithmetica, Pierre de Fermat had jotted the words I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.

The square had been converted to a cube ($x^3+y^3=z^3$), and mathematicians had spent centuries looking for the answer to Fermat’s riddle. By the time Andrew Wiles solved the puzzle in the 1990s, he had been at it for ten years using the world’s most advanced computer programme.

And all of a sudden she understood. The answer was so disarmingly simple. A game with numbers that lined up and then fell into place in a simple formula that was most similar to a rebus.

Fermat had no computer, of course, and Wiles’s solution was based on mathematics that had not been invented when Fermat formulated his theorem. Fermat would never have been able to produce the proof that Wiles had presented. Fermat’s solution was quite different.

She was so stunned that she had to sit down on a tree stump. She gazed straight ahead as she checked the equation.

So that’s what he meant. No wonder mathematicians were tearing out their hair.

Then she giggled.

A philosopher would have had a better chance of solving this riddle.

She wished she could have known Fermat.

He was a cocky devil.

After a while she stood up and continued her approach through the trees. She kept the barn between her and the house.

In the first chapter of the book Larsson mentions Martin Gardner. As you may know, Martin Gardner passed away yesterday at 95.

He was a huge influence on me, and I strive to be half the writer that he was. I remember loving and being fascinated by Gardner’s 1982 aha! Gotcha as a pre-teen. That was my first exposure to Hilbert’s Hotel. I loved reading his Scientific American columns as a boy. Several years ago I purchased the MAA CD Martin Gardner’s Mathematical Games, which contains pdf’s of 15 of his books. I loved browsing them as I was looking for interesting topological tidbits to include in my book. I even had my students read some of his writings when I taught a first-year seminar on science and pseudoscience.

We’ll miss you Martin Gardner.

## Responses

1. Still not sure of the point of “The Flight of Peter Fromm” unless Gardner was just a new atheist ahead of his time. As long as he stuck to math without injecting loads of his philosophical baggage then the reading was quite informative and served as primers to further study.

2. […] – Division by Zero: Mathematics in novels and Martin Gardner RIP […]

3. Peter Fromm was an autobiographical account of the steps Gardner went through in is loss of religious faith. he was never an atheist.

4. Dostoevsky has some good passages about non-Euclidean geometry in The Brothers Karamazov, too.

5. I Think that something was lost in the translation but if you think a little, it’s kind of ovbious that Larson try to said that a “square” (shape) is converted into a “cube” (shape) so that’s why he said the thing about the philosopher. A cube, due to his tridimentional proportion can be drawn in paper, also he said “most similar to a rebus” that means that is more similar to a Symbol than a equation.

• but remember we are also told to line it up

But the thing is you don’t need an in depth knowledge of this to understand Salander’s solution, and as she says, a philosopher would have more chance – it is a riddle, a rebus, you “line it up” and it is simple and the answer is funny: a rebus is a play or pun (roughly) and if you line up the z’s
x3+y3=z3
in other words
x3+y3=zzz and zzz=sleep
an unsolvable maths problem puts you to sleep, and the higher the exponent the more the damn puzzle puts you to sleep ie the higher the exponent the more z’s you have. That is why Salander giggles and why she calls him a cocky devil
…..and the more Zs you have the less likely it is to fit in the margin…..

6. It was something lost in the translation in Stieg Larsson’s book when Lisbeth Salander was figuring out Fermat’s Last Theorem. If you were as intrigued as I was, and being a math novice on the side who once pursued a math degree but decided psychological assessment (which uses calculus and advanced statistics) as a major was better suited for who I was, my opinion (and I can be proven wrong) was that it was not a discrete solution of finite solutions such as a^2 + b^2=c^2. No finite solution exists, except that spatial ability would have to be implemented to get it. Any number(s) in the cubed equation would prove false, and the equation would never equal out, being therefore always calculated into infinite non possiblities, therefore taking on a three dimensional “shape” to figure itself out. The solution is not linear but at least three dimensional or more, giving it no solutions in a 2-dimensional linear plane…hence all variables being cubed. And I am not a man, but a woman, just my mathematical sense seems more “manly” (Just wanted to give props to the women). Just went to a rigorous superb top rated university and at a good Mid-Western Graduate School.

• While I do like the cube theory, and it is a clever interpretation, it doesn’t fit all the other clues we are given. The only reason we are tied to z3 is because that prevents us from trying all the other integers out there. It serves to keep the riddle simple, we are told it is a rebus and to line it up.
z3 lined up is zzz and zzz is sleep.
The higher the “n’ or to the power of, the more Zs you get and the less likely you can fit all the Zs on the page.
Remember that this has to be true for x^n + y^n = z^n and not JUST 3.
An unsolvable maths problem puts you to sleep, and the higher the exponent the more the damn puzzle puts you to sleep ie the higher the exponent the more z’s you have.