FOM: Is chess as interesting as mathematics?
charles silver
silver_1 at mindspring.com
Wed Feb 20 06:39:26 EST 2002
The discussion of intuition vs. rigor seems to have taken some strange
turns. Isn't it the case that Godel simply "saw" the incompleteness
results while working on something else? I believe he realized way before
he worked out all the gory details that proofs had to be a proper subset of
truths. I'd call having something like this pop into one's mind
"intuition." On the other hand, there are accounts of mathematicians who
have an over-abundance of ideas (read: intuitions) that turn out to be
false. In favor of rigor, obviously it's needed to back up intuitions,
though it has been mentioned that intuitive accounts by people like
Thurston are sometimes acceptable even when no technical details
at all have been provided. I have heard one mathematician in
Thurston's area complain about this, saying that it's frustrating to
listen to him just alluding to ideas and waving his hands while not
presenting anything resembling a traditional proof. However,
rigor completely uncoordinated with intuitions or insight can be
mechanical and not very interesting. Is chess as "interesting"
as mathematics?
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