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>David Fowler
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>PS Do we have any evidence that Book X and Theatetus is "a story which has
>served for a couple of millennia or so as a teaching aid"? I wouldn't like
>to try to teach Book X to a school class, or even to a university one, for
>that matter! The Arabs wrote many commenraries on it, but they look these
>the notes of mathematicians who are trying to understand it for themselves.
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I didn't mean that the story about Theaetetus was used as an aid in
teaching Euclid's Book X. I just meant that in the days when Euclid's
*Elements* were a central part of mathematics education, teachers may have
liked to refer to the young Theaetetus as a whiz and inspiration, and to
give a somewhat romantic story about a mathematician. Similarly Galois
seems to be often used for the same purpose at levels where teaching about
symmetric functions and roots of algebraic equations (or lack of them)
would be out of place. Teachers like to try to show that mathematicians
aren't always nerds who would be reluctant to go to war or would back out
of duels.
I have the book by Szabo (in German), and read it years ago, but I don't
remember what he says about Theaetetus. I'll have a look when I get around
to it. My memory of the central point of that book was to demonstrate
relationships between music theory and geometry, especially with regard to
incommensurability.
Why do you think Theodorus doesn't fit? Also, you say "But, to counter this
opinion, it is worth observing that our chronologically first unambiguous
reference to incommensurability is in the dialogue, and, if it isn't about
mathematics, then what is it about?" Do you mean what is the dialogue
*Theaetetus* about? In my view, the dialogue is about epistemological
problems, and the notorious square root of 17 stuff is used to make
concrete an inquiry about what we now call induction.
Gordon Fisher gfisher@shentel.net