[FOM] Historical queries

William Tait williamtait at mac.com
Mon Nov 12 13:27:55 EST 2007

X1, the fundamental theorem of ARITHMETIC, is in Euclid, Book vii. X2  
is proved in Euclid, too---Book X, I think. The result is attributed  
by Plato to Theaetetus in the dialogue of that name. (Plato says that  
Theodorus had proved it for numbers up to 17.) I don't know about X3.


On Nov 11, 2007, at 8:54 PM, joeshipman at aol.com wrote:

> For each of the following theorems Xi, I need to know:
> 1) who first assumed Xi (that is, wrote something which makes no sense
> unless they believed Xi to be true even if they did not state it)
> 2) who first explicitly stated Xi as a known result or conjecture
> 3) who first wrote a proof of Xi
> X1: Fundamental Theorem of Algebra (both existence and uniqueness of
> prime factorizations; but since existence is so easy, I will accept a
> statement of uniqueness; the important question is who first  
> recognized
> that there is something that needs proving here)
> X2: Irrationality of all square roots of integers that are not perfect
> squares (also, if anyone stated this for some infinite set of
> non-squares, such as "square roots of primes are irrational", I want  
> to
> know this, because the theorem is easier to prove for primes than in
> general)
> X3: Irrationality of all kth roots of integers that are not perfect  
> kth
> powers, for all integers k>1 (or, again, if this was ever stated for
> some infinite subset, such as "the kth root of 2 is irrational for all
> k").
> --JS
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