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Many of the smartest mathematicians who have ever lived have spent collective man-decades thinking about this problem. Any idea any of us can come up with in an hour of thought will have been considered and rejected a thousand times already by others.

This is partly why it's such a trap. It's like trisecting an angle or squaring a circle -- easy to state the problem, easy to start playing around with it. In my amateur opinion, any proof related to Collatz would be similar in complexity and non-obviousness as the proof of Fermat by Wiles, if such a proof is even possible.



For most, it's far more fruitful to jump on https://math.stackexchange.com/ and work on questions there. Low impact, but high probability it is within anyone's realm of capabilities. Answering 100 questions people want to know is bigger impact than making 0% progress towards a problem you have no realistic chance of solving.


I know, I know. But I kind of want to figure out why what I'm thinking doesn't work. I want to run up against these problems myself.




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