a list compiled by Alex Kasman (College of Charleston)

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Border Guards (1999)
Greg Egan
(click on names to see more mathematical fiction by the same author)

In a virtual universe shaped like a 3-torus, free from disease and death, Jamil is easily depressed but enjoys playing a game of quantum soccer with his old friends, and one new friend. The new friend turns out to be one of the two mathematicians who created this universe, about whom little is known by the other inhabitants who nearly worship them.

Since a big deal is made about the fact that Jamil's hobby is the study of the representation theory of Lie groups, I was both surprised and disappointed that he and his hero did not discuss any mathematics. But then, that's not the focus of the story. It is about life...and death.

It is noted that Jamil lives in the (virtual) city of Noether, named after Emmy Noether, and that the planet is Laplace. As for the toroidal structure of their universe, it is stated that "The topology of this universe lets you see the back of your head, but never your reflection."

By the way, the idea of "quantum soccer", is that team members on a playing field must manipulate the harmonics of a quantum wave function in order to get most of the wave (a certain amount of its probability, if you want to think in terms of the Copenhagen interpretation of QM) into the opponents net. Egan even let's you play the game through a Java applet on his website!

Publication history

  • Interzone #148, October 1999.
  • The Year's Best Science Fiction: Seventeenth Annual Collection, edited by Gardner Dozois; St. Martin's Press, New York, 2000.
  • Year's Best SF 5, edited by David G. Hartwell; HarperPrism/Avon Eos, New York, 2000.
  • Hayakawa's SF Magazine, March 2001. (Japanese translation)
  • Supermen: Tales of the Posthuman Future, edited by Gardner Dozois; St. Martin's Press, New York, 2002.
  • “Guardie di confine” in Cinquant'anni di Futuro, Mondadori/Urania, Milan, 2002. Translated by Roberto Marini. ISSN 1120-5288 / Number 1450 (The Urania SF line is published as a paperback periodical.) (Italian translation)
  • Reasons to be Cheerful and Other Stories (collection, Hayakawa) Translated by Makoto Yamagishi. (Japanese translation)
  • The Locus Awards, edited by Charles N. Brown and Jonathan Strahan; Harper/Eos, New York, 2004.
  • Available Online for Free at Egan's website.
A visitor to this Website, Pierre, gave this story the same rating of 2 out of 5 for "Mathematical Content" that I gave it earlier, but adds:

Contributed by Pierre

I'd say the physics content is about a 3 though. By and large Greg Egan is a very good writer and this story is, I thought, an exceptionally good one. The central theme of the story is how people emotionally handle long life.

Contributed by John C. Konrath

This short story starts in Mr. Egan usual methodical manner and I was wondering were it was headed. Ultimately though this story takes a clear direction and asks the reader some important philosophical questions, not the least of which are 1) how will humankind deal with its ever growing overpopulation problem? & 2) How would people handle immortality? Most of the math is inferred through technological developments.

Contributed by Steve Stuart

I really enjoyed the description of quantum soccer. I plan to assign it as reading in an undergraduate course. I had even resolved to code up a version myself, before finding that Egan already has a version on his web site.

More information about this work can be found at
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Works Similar to Border Guards
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. 3-adica by Greg Egan
  2. Altogether Elsewhere, Vast Herds of Reindeer by Ken Liu
  3. Singleton by Greg Egan
  4. Diaspora by Greg Egan
  5. Schild's Ladder by Greg Egan
  6. The Planck Dive by Greg Egan
  7. The Arrows of Time [Orthogonal Book Three] by Greg Egan
  8. Luminous by Greg Egan
  9. Distress by Greg Egan
  10. Into Darkness by Greg Egan
Ratings for Border Guards:
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:
3.8/5 (5 votes)

GenreScience Fiction,
MotifFemale Mathematicians,
TopicGeometry/Topology/Trigonometry, Algebra/Arithmetic/Number Theory, Mathematical Physics,
MediumShort Stories, Available Free Online,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)