A couple of small glosses on these: 1. The Cantor proof goes beautifully if you use `neg' continued fractions (I thought I saw this in D"orrie, but I must have been mistaken). 2. P'olya's theorem is due to Redfield. R. On Fri, 28 Apr 2006, Henry Baker wrote:

Some suggestions:

Hamilton: ii=jj=kk=ijk=-1 (I guess he was left-handed...)

Cantor: |R|>|Z| (diagonalization, which was later used by Godel)

Polya's theory of counting

Newton: solution of 2-body problem is a conic section

Risch: integration in closed form

Newton: "Newton's Method" sqrt, etc., widely applicable to lots of things.

Church's Lambda Calculus (also "combinators") -- theory of substitution in trees.

Tarski: decision procedure for real closed fields.

At 09:08 AM 4/28/2006, Cordwell, William R wrote:

...

One of my students asked me what my favorite theorem was, a question that I found interesting and surprisingly difficult to answer.

So...what's your favorite theorem or proof (and why)?

--Bill C.

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