[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.
Bill
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
> ________________________________________________________________________
> Email and AIM finally together. You've gotta check out free AOL
> Mail! -
> http://mail.aol.com
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
More information about the FOM
mailing list