Subject: Re: [HM] Emmy Noether
From: Colin McLarty (cxm7@po.cwru.edu)
Date: Sat Feb 05 2000 - 08:05:49 EST
William Waterhouse wrote:
On the fact that Emmy Noether is cited more for her conservation
theorems than for commutative algebra, and often by physicists:
> I think this is just a difference in custom. Consider for instance
> the paper "Idealtheorie in Ringbereichen," Math. Ann. 83 (1921), 24-66
> (= Collected Papers 354-396). This is a famous and extremely important
> paper in which Noether developed the theory of primary decomposition
> of ideals in (as we now say) noetherian rings. But no mathematician
> really using noetherian rings or primary decompositions is likely
> to refer all the way back to this paper. Either the whole topic would
> be assumed familiar or the reference would be to a recent textbook
> presentation. The basic purpose of a mathematical reference, after all,
> is to tell the intended readers where they can (if necessary) look up
> proofs of things the author is assuming known.
I think there is a lot to that. Noether's commutative algebra is
presumed much more familiar than her conservation theorems, and rightly
so, and thus it need not be cited.
So Eisenbud citing her extensively in his COMMUTATIVE ALGEBRA can
be seen as a shift in the mathematical culture. That book clearly urges more
history, more motivation, and more explicit link of the highest theory to
the most computational methods, than textbooks have usually had. I think it
a great success but the obvious downside is that it is 785 pages long --
compare Atiyah and Mac Donald at 126 pages.
But there was also a historical problem, as Noether's theorems were
presumed familiar but her authorship of them was not. When I was an
undergrad in the 1970s several profs told me they were not sure which
Noether was meant in the name "Noetherian rings" and one algebraist (not a
specialist in Noetherian rings or primary decomposition) said it almost had
to be Max since such a fundamental idea must be at least that old.
Colin McLarty
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