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> I'm fairly sure that people are only getting hung up on the size of this finite set, for no good reason. I think that is exactly correct, except for the "no
by roenxi 2y ago
> I'm fairly sure that people are only getting hung up on the size of this finite set, for no good reason.
I think that is exactly correct, except for the "no good reason" part. There aren't many (any?) practical situations where the 4-colour theory's provability matters. So the major reason for studying it is coming up with a pattern that can be used in future work.
Having a pattern with a small set (single digit numbers) means that it can be stored in the human brain. 633 objects can't be. That limits the proof.
- myst 2y agoThe nature does not care whether it fits in our brains.
- dartos 2y agoThat’s why we use math to describe nature in a way that fits in our brains. That’s the whole point of math.
- username332211 2y ago> So the major reason for studying it is coming up with a pattern that can be used in future work. Surely, reducing the infinite way in which polygons can be placed on a plane to a finite set, no matter how large, must involve some pattern useful for future work?
- dartos 2y agoBut why stop at “some” pattern when you can find the most general pattern.
- lacker 2y agoTo me, the four-color theorem is a very interesting proof of concept, perhaps the most interesting mathematical proof of the past 50 years. Perhaps the "pattern that can be used in future work" is the idea of having computers enumerate a large number of cases, which they then solve in individually straightforward ways. But, I can understand if pure mathematicians don't feel this way. This might be only really an intriguing and beautiful concept to someone who is interested in scaling up algorithms and AI.