MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Division by Zero (1991)
Ted Chiang
(click on names to see more mathematical fiction by the same author)
Highly Rated!
Note: This work of mathematical fiction is recommended by Alex for math majors, math grad students (and maybe even math professors) and literati.

Answers the question: what would happen if we found out that mathematics is inconsistent? This is a great piece of mathematical fiction. (Thanks to Frank Chess who pointed it out to me.)

Renee is a brilliant mathematician. At the age of seven, she found beauty and comfort in the mathematical patterns associated with perfect squares, and felt this same sense of "rightness" throughout her career as she discovered new theorems that got her acclaim (and job offers). However, this is precisely why she is so devastated when her own research leads to a contradiction that demonstrates that mathematics itself is inconsistent. (In particular, she is able to correctly prove that any two numbers are, in fact, equal to each other.) Her biologist husband feels that he should understand her situation as he picks her up from the hospital after her suicide attempt, since he also attempted to kill himself once many years earlier, but he is not able to grasp her dispair over this mathematical result. There is literary irony in the comparison of Renee's feelings about mathematics and her husband's discovery that marriage is not exactly what he thought it was either.

Gödel's research is often misquoted or misused in popular press and fiction. Here, however, it is not only described accurately but used correctly in a very fascinating piece of speculative fiction. One major consequence of Gödel's work is the fact that we cannot prove the consistency of our axiomatic systems (such as arithmetic itself)...at least not from within. Logicians may argue that reality itself as a model demonstrates the consistency of mathematics, but this is clearly a metamathematical statement that relies on the validity of our understanding of reality, which is not completely certain itself. Renee's husband tries such an argument, pointing out that mathematics has been very useful in predicting and understanding reality, but Renee is not comforted by this when she knows now that the numbers 2, pi and 0 are all equal.

The story starts with a nice description of why division by zero is not possible, as well as a famous example of what sorts of contraditions you can get if you forget to exclude it. Russell, Whitehead, Hilbert and Godel are mentioned, as is a 1936 paper of Gerhard Gentzen which uses transfinite induction to prove the consistency of mathematics.

In the author's notes at the end of SOYLAO (see below), Chiang says: "Now consider [Euler's formula]. It's definitely surprising; youcould work with the numbers e, Pi and i for years, each in a dozen different contexts, without realizing they intersected in this particular way. Yet once you've seen the derivation, you feel that this equation really is ineveitable, that this is the only way things could be. It's a feeling of awe, as if you've come into contact with the absolute truth. A proof that mathematics is inconsistent, and that all its wondrous beauty was just an illusion, would, it seemed to me, be one of the worst things you could ever learn."

Originally published in the 1991 anthology Full Spectrum 3, this wonderful story has just been republished in the Ted Chiang collection: Stories of Your Life and Others. (Thanks to Steven H Silver for mentioning SOYLAO to me...)


By keeping track of hits on this Website, I have noted that there is quite a bit more activity on entries labeled as "available free online". Apparently, there are people who are only interested in reading mathematically flavored fiction if they can do so cheaply and without touching any paper. For those people, I am happy to report that Division by Zero, one of my personal favorites, is available free online (see below)!

Contributed by Derin Sherman

Hi - thanks very much for your website. I find it invaluable in my "Science through Film and Fiction" course.

You have listed Ted Chiang's story "Division by Zero" on your site. You might like to provide the following link to the online version of the story

http://www.fantasticmetropolis.com/i/division/full/

Enjoy!

Derin Sherman
Associate Professor of Physics
Cornell College

Contributed by John C. Konrath

This brilliant, moving short story is both emotionally and intellectually satisfying. It challenges the reader to draw his/her own conclusions. A must read!

Contributed by Anonymous

For some (like myself), this story may need to be read twice to understand the complete narrative, since there are 2 storylines to follow with historical sections as well about other mathematicians. Even so, this story is fabulous. The organization contributes to the story as a proof itself. The author splits the text into sections 1, 1a and 1b, then 2, 2a and 2b until 9a = 9b. If this is true, then 1a = 1b, 2a = 2b and so on. The storylines would, then, be one in the same. This is why a second read might benefit the reader's understanding of the entirety of the story.

Buy this work of mathematical fiction and read reviews at amazon.com. Amazon.com logo
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Division by Zero
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Pythagorean Crimes by Tefcros Michaelides
  2. Eye of the Beholder by Alex Kasman
  3. Risqueman by Mike Wood
  4. Not a Chance by Peter Haff
  5. Euclid Alone by William F. Orr
  6. Gödel's Doom by George Zebrowski
  7. Continuums by Robert Carr
  8. Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis
  9. The Oxford Murders by Guillermo Martinez
  10. Luminous by Greg Egan
Ratings for Division by Zero:
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:
4.79/5 (10 votes)
..
Literary Quality:
4.5/5 (10 votes)
..

Categories:
Genre
MotifProving Theorems, Female Mathematicians, Gödel,
TopicAlgebra/Arithmetic/Number Theory, Real Mathematics, Fictional Mathematics, Logic/Set Theory,
MediumShort Stories, Available Free Online,

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Your Help Needed: Some site visitors remember reading works of mathematical fiction that neither they nor I can identify. It is time to crowdsource this problem and ask for your help! You would help a neighbor find a missing pet...can't you also help a fellow site visitor find some missing works of mathematical fiction? Please take a look and let us know if you have seen these missing stories anywhere!.

(Maintained by Alex Kasman, College of Charleston)