Subject: Re: [HM] ... and the unique factorization theorem
From: Don Cook (tdctdc@surfsouth.com)
Date: Fri Feb 11 2000 - 19:50:56 EST
Dear List Members,
Let me suggest another reason for Euclid not to state the fundamental
Theorem of Arithmetic - it's an existence statement as opposed to the
construction method such as finding the greatest common divisor of two
integers.
I was surprised to hear that Gauss is credited with proving three of the
four fundamental theorems - arithmetic, algebra and Abelian groups (is this
true?). The Fundamental Theorem of Arithmetic is used before Gauss. Why the
long wait for a proof? Are there existence theorems proven before Gauss?
Is my suggestion just pop-history? I would like to keep repeating it.
The proof of the Hilbert Basis Theorem is also an existence proof.
Camille Jordan's remark:
The proof of the Hilbert Basis Theorem is not mathematics; it is theology.
Quoted in D MacHale, Comic Sections (Dublin 1993)
Peace,
Don Cook
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