Re: fundamental theorem of algebra

[Vaughan Pratt <pratt@cs.stanford.edu>]

Fred E.J. Linton wrote:
> First, in Birkhoff & Mac Lane (my own undergraduate algebra text),
> Section 3 of Chapter V of the 1953 ("revised") edition offers a
> proof along winding number lines on pp. 107-109.

Thanks, Fred, I wish I'd noticed that before.  I have the sixth printing
(1948) of the 1941 edition, which says, "Many proofs...are known; ...we
have selected one whose non-algebraic part is *especially plausible
intuitively*."  (My emphasis.)  Then they give the proof "I like".

To administer one more lash to this dead horse, the wording in the
Britannica article implies that the absence of an elementary algebraic
argument was the reason for omission of a proof of FTAlg.  Whence the
change of heart about arguments that are "especially plausible
intuitively?"  If they're good enough for an algebra text they should be
even more acceptable for an encyclopaedia article.

Vaughan Pratt