a list compiled by Alex Kasman (College of Charleston)
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I did enjoy reading this short story (nominated for a Nebula award in 1985)
in which the famous Greek mathematician Eratosthenes determines the Earth's
circumference and meets a shipwrecked alien, but I am seriously troubled
by it's
historical innacuracies. It is true that Eratosthenes
(also known for his work on prime numbers) came up with a very good
estimate of the circumference of the Earth. His method involved using a
deep well to determine when the sun was directly overhead at one point and
the measurement of a shadow at another point. (If you want to reproduce
his experiment, you can follow the steps at this friendly
website aimed at middleschoolers.) However, Harness has a very
strange idea of what the world was like and especially what was
known at the time.
For instance, Harness has Eratosthenes recognizing that the "other planets" go around the Sun just as the Earth does. Since he is told by the alien that the Earth goes around the sun, I am willing to believe that Eratosthenes could handle this idea. However, he would never have thought this was consequently true of the "other planets". The ancient Greeks did not think of Earth as one of the planets. In fact, the word "planet" itself derives from the fact that they thought of planets as wandering stars and had no way to think of them being in any way like the thing we live on. Similarly, there is no reason to expect that he would be able to conclude from this that the sun is just a star which we are close to...this is not really a logical consequence of a heliocentric solar system. Moreover, the mathematics he consults does not sound believable to me. This story takes place long before the decimal numbering system that we are familiar with, and before trigonometry as we know it. I could be wrong about this (please correct me if you know!) but I seriously doubt that you could have looked up a table of values of the tangent function in 160 BC. I'm sure there are other historical innacuracies. (He has a "rabbi" there among the nonmathematical figures that Eratosthenes encounters. My understanding is that there was no rabbinic Judaism at this point in history. Again, correct me if I'm wrong.) If none of the anachronisms or innaccuracies bother you, what about the idea that on the day after he has determined the Earth's circumference, Eratosthenes just happens to meet an alien who needs this exact piece of information to be able to return home? 
(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.) 

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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 nonfictional 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)