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Or has it remained a terminal node at the frontier of mathematics?

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I assume you mean Morley's Angle Trisector Theorem. For that there is a wikipedia article, en.wikipedia.org/wiki/Morley%27s_trisector_theorem, which includes links to recent work by (Fields Medalist) Alain Connes. So your question seems a little vague to me: further than what? –  Pete L. Clark Oct 24 '10 at 0:46
    
@Pete. Amazing! A paper about plane, classical geometry in Pub. IHES! :-DD Thanks for your link. –  a.r. Oct 24 '10 at 7:59
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I think Morley's trisector theorem is amazing and difficult but I wouldn't say that it is a "terminal node at the frontier of mathematics". Rather, despite Connes' paper at the IHES, I would say "terminal" meaning "dead". To the best of my knowledge -i.e., my ignorance- there is little, if any, research in plane, classical geometry. (But maybe I'm being a little pretentious.) –  a.r. Oct 24 '10 at 17:56
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up vote 12 down vote accepted

Oakley and Baker's 1978 paper The Morley Trisector Theorem describes very nicely how Morley came on this result "from above", meaning that he had a much more complicated result of which this theorem was a particularly nice special case. (Such a trivial case, in fact, that Morley didn't consider it worth publishing.) So even from the beginning, this theorem was not an investigational endpoint, but more of a beautiful side comment.

Oakley and Baker's paper also mentions that "Morley's theorem has connections with many notable point-line-plane-circle-polygon configurations bearing such names as Apollonius, Brianchon, Ceva, Desargues, Feuerbach, Hesse, Lemoine, Menelaus, Pascal, Ptolomy, Simson, Spieker, Steiner, etc.".

Morley's theorem is from 1899(†), and 110 years later, in 2009, we see a very nice and very short paper by Brian Stonebridge,  A Simple Geometric Proof of Morley's Trisector Theorem. It was not 110 years of silence, either — the Oakley and Baker paper alone gives 120 references! As Stonebridge appears to be unaware of Alain Connes's proof mentioned above, apparently there is currently no single complete list of proofs — no terminus, as it were.

(†) according to Stonebridge, Wikipedia, Cut The Knot, and others who categorically date it with no discussion. However, both Coxeter and Oakley and Baker appear very knowledgable about the history, and they are more vague about the date, hinting at something maybe around 1904. Since Morley didn't publish it, but merely slowly started mentioning it to friends, it is difficult to date.

I think any of us would be happy to have people still working on our theorems over one hundred years later — Morley's theorem is not and never has been a terminal node!

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Very good. I've up-voted and accepted your answer. I apologize for not having done so sooner. –  Mike Jones Sep 28 '11 at 8:51
    
@Mike: No apology needed, in fact, your response to my answer was even faster than my response to your question!! –  Matt Oct 2 '11 at 12:06
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